texts: How does IS-LM model reduced investor confidence?

texts:
I am doing an essay on how a sovereign debt rating downgrade to junk status affects the economy. I wanted to use a theoretical framework to think about it, and seeing as an increase in the interest rate is involved, I decided to use the IS-LM model. Please tell me if the following is correct or not. I think it's a bit unconventional to shift the LM curve when money demands shifts, but the reason why I do that is because output was not the driving force of the shift in money demand. As I understand it, if output increases, that increases money demand, which is a movement along the LM curve. However, in this case, investor confidence affects the interest rate directly, without an initial effect on output. That is why I have shifted the LM curve upwards.

I presented the model as follows. Investor confidence drops with the news of a rating downgrade, so financial investors sell their bonds, which increases the demand for money, and decreases the prices of bonds. Because the prices of bonds decrease, interest rates on those bonds increase. Also, new bonds will have higher interest rates because they are seen as more risky. This is shown graphically in the money market model below as the first increase in money demand from $D_{M_1}$ to $D_{M_2}$. (I find it a bit confusing to think about foreign investors demanding more money (like M1), because I think they would want to sell the rand in exchange for their own currency, but I think this is true for the domestic economy.)

Because the money market is the basis of the LM relation, this shifts the LM curve upwards as the interest rate increases (shown as the increase from $LM_1$ to $LM_2$). Higher interest rates lead to lower real investment (i.e. investment in capital, land, labour and enterprise), government spending and consumption. This is equivalent to a movement upwards along the IS curve. The IS relation shows equilibrium in the goods market, which is given by $Y=C+I+G$. $I(i)$ is a (decreasing) function of the interest rate, and the interest rate increasing is what causes real investment to drop. It is a negative relationship because higher interest rates make it harder to borrow money to finance investments. In our situation, government spending decreases because the cost of credit for them increases, but rising Treasury bond interest rates also raises other interest rates throughout the economy due to competition, which then reduces private investment. The result is a decrease in the growth rate of output. The drop in output actually dampens the increase in the demand for money, because income decreases. So, the hike in interest rates is attenuated as output growth slows down. This can be reflected in the money market as a downwards shift in the demand for money curve from $D_{M_2}$ to $D_{M_3}$.

Another thing I want to check is if it is fine to think of there being only one interest rate in the graph on the left, due to the way central bank interest rate and other financial instrument interest rates rise due to arbitrage. The interest rate on Treasury bills is obviously what is affected, so is it fine to think of the demand for 'money' (is that demand for all the money in the entire economy?) as interacting with that interest rate?

I presume that reduced investor confidence is a fairly standard problem to model, yet I'm not so sure about how I've done it.


texts: Set of consumption over all period is convex in $\mathbb{R}^T_+$?

texts:
Today in class, the professor said that the set of all consumption $c(S)$ is non-empty, compact and convex subset of $\mathbb{R}^T_+$. i.e. we know $\sum \limits_{t=1} ^T c_t = S$ where $c_t$ is consumption in period t and $S$ is total wealth. The set  $c(S)$ is the set of all T-period consumption plan.
I could understand why $c(S)$ is compact, but I have no clue why it has to be convex and non-empty.
Following the same question, the professor also mentioned that $W(c)$ the summation of all the T-period utility functions denoted by $W(c)=\sum \limits_{t=1} ^T U(c_t)$ is continuous on $c(S)$. I do not understand why $W(c)$ has to be  continuous on $c(S)$
I think this has something to with Berge's Maximum theorem, but I am unable to link it properly. Any help will be very appreciated.


texts: Extraction and royalty time path for a non-renewable resource under a monopolist assumption

texts:
I am trying to understand the time path of extraction and royalty (price) for a non-renewable resource under a monopolist framework.
The problem is that in the main books on environmental/resource economics and in the resources that I could find on internet the "results", either quantitative or qualitative, are given without proof, and the assumptions are not given ("most cases" :-( ).

Using optimal control, I have no problem to find that the Hotelling rule is here applied to the marginal profit over the extraction quantity, or that its discounted value remains constant and it is below the market price.
But what are the specific assumptions required to claim that (a) the initial price is higher than under perfect market competition/benevolent social planner; (b) that the depletion time is longer and finally (c) that the growth rate of price is lower than the (constant) growth rate of marginal profit ?


texts: Decreasing and increasing returns to scale question

texts:
Hi, I have deduced that this function exhibit increasing returns to scale but I am not sure how to verify part d. My answer doesn't show that there is decreasing returns to scale but I can't be sure d is wrong. I am unsure between choosing c and d.

Thanks


texts: Kimball (1995) Specification of Final Good Production

texts:
Kimball (1995) defines production of the final good ($Y$) with intermediate goods $y_l$ in his equation (1) as

$$ 1 = \int_0^1 G\left(\frac{y_l}{Y}\right) dl $$

with $G(1) = 1$, $G'(x) > 0$ and $G''(x) < 0$.

I have never seen such a construct before. What does the $1$ on the left-hand-side mean, is that a normalization or some cost construct? An introduction into this type of production function would be greatly appreciated.


texts: Private Investment Impact on Bond Yields

texts:
From Japan to the US to Germany, we are currently seeing longer term bond yields falling at an alarming rate.

I tune into a fair bit of economic commentary, and can often come to some sort of understanding of the factors that commentators say are at play in the current situation. But one I struggle with is the idea that weak private investment is a factor in declining yields.

Can somebody please explain why this is the case? Is the idea that weak private investment leads to weaker GDP growth, which leads to weaker inflation, which leads to higher bond prices? Or is there something else at play here?


texts:
I pay the doctor before he conducts the surgery.

Can anyone explain to me whether this statement shows moral hazard or adverse selection?


texts:
I am reading a paper with an extended CES final good setting:

The representative household consists of a continuum of members, indexed by $k$
$C_{t}=\int C_{k, t} d k$
$C_{k, t}=\left(\int_{j \in \Omega_{t}} \theta_{k, j}^{\frac{1}{\eta}} c_{k, j, t}^{\frac{\eta-1}{\eta}} d j\right)^{\frac{\eta}{\eta-1}}$, where $\theta_{k, j}$ is a utility weight summarized by a CDF $F_{j}\left(\theta_{k, j}\right)$
Define utility weight for good $j$ at the household level $\kappa_{j}\left(s_{j, t}\right)=\int \theta_{k, j} d F_{j}\left(\theta_{k, j}\right)$
Then $C_{t}=\left(\int_{j \in \Omega_{t}}\left[\kappa_{j}\left(s_{j, t}\right)\right]^{\frac{1}{n}} c_{j, t}^{\frac{\eta-1}{\eta}} d j\right)^{\frac{\eta}{\eta-1}}$

I don't understand how to derive the last equation? Why can I simply change the order of integration when the inner integral is to a power?
Thanks.


texts: How are payoff values in game theories calculated / estimated?

texts: In game theories such as Nash Equilibrium, exactly how are each of the players' payoff values for each of their potential strategies created?  In the common 2x2 matrices I've seen in academic papers, the various payoff values seem to just "appear" in the matrices without an explanation of how they were derived / calculated / estimated, whether or not those values have (or need) a confidence level associated with them, etc.  Is it possible, for example to have a range of payoff values rather than a single number for a given player/strategy choice?


texts: How does this demand function satisfy the Weak axiom if it doesnt satisfy the necessary and sufficient conditions?

texts:
Let $x_k = \frac{w}{\sum{p_l}}$ for $k = 1...L$ be the demand function.

This demand function does satisfy the weak axiom and this can be shown simply.

The slutsky matrix is an $L \times L$  matrix of $0$'s for any (p,w).
In Mas-Colell Microeconomic Theory page 35 and also in this publication - https://www.jstor.org/stable/1911539 , necessary and sufficient condition for the weak axiom to hold are that (i) S(p,w) is Negative semi-definite and (ii) $v^TS(p,w)v < 0 $ whenever $v \neq \alpha p$ for any scalar $\alpha$, $v \neq 0$.

Clearly (i) is satisfied for this demand function and slutsky matrix. However, consider the price vector $[1,1,1,...1]$. The slutsky matrix is still the matrix of zeros. Consider $v=[2,1,1...1]$. $v^TS(p,w)v = 0$ which is not less than 0. Note that $v$ is not proportional to $p$. This appears to violate (ii). Where have I gone wrong?

This is exercise 2.F.17 from Mas-Colell Microeconomic theory.


texts: Is there any mechanism to prevent tariff 'exile'?

texts:
I am expecting a decline in trade between the US and its key trading partners (China, Europe, Canada, Mexico).

Is there any mechanism / force that prevents US trading partners from cooperating amongst themselves to ramp-up trade amongst themselves to compensate for not trading with the US?  Does the US offer goods, which have no substitute?


texts: Explaining the size of the canadian banking sector

texts:
Canadian banks are among the largest in the world and I think that only the UK compares in terms of having your economy dominated by banking. Of course some of the US banks are much larger but so is the country's population.

Searching on the subject doesn't lead me anywhere, I suspect that the big 5 of Canada do a good job of exporting financial services (of which none shows up in the trade balance, if I'm correct) and that Canada somehow provides advantages to its big 5 that other countries cannot compete with. Having said that, I would like to know what those predisposition that lead to the growth of a banking industry.


texts: CES production function profit and supply function

texts:
I need to derive the profit function for the following CES function: $$ f(z) = (\sqrt{z_{1}^{\rho} + z_{2}^{\rho}})^{1/ \rho}$$ where $\rho \leq 1$. This is the answer that I am supposed to be getting:

If $ \rho <1$ then
$$ \pi(w) = \begin{cases}
      \infty \;\;\;\;\; \text{if} & w_{1}^{\rho/(\rho -1)} + w_{2}^{\rho/(\rho -1)} <1 \\
      0 \;\;\;\;\; \text{if} & w_{1}^{\rho/(\rho -1)} + w_{2}^{\rho/(\rho -1)}
 \geq 1\
   \end{cases}
$$

If $\rho = 1$, then:

$$ \pi(w) = \begin{cases}
      0 & \text{if} \;\ Min\{w_{1},w_{2}\} \geq 1 \\
      \infty & \text{if} \;\; Min\{w_{1},w_{2}\} < 1 \\
   \end{cases}
$$

Normally I simply use profit maximization or cost minimization FOCs to obtain the profit function, as well as the supply one. But I have been trying to get around this problem and I really cannot get around these results or (of particular importance) how to derive them. That being said any tips, intuition, or just help with the derivation if you're feeling particularly selfless would be greatly appreciated.

Thanks in advance!


texts: Why will inflation raise sellers' purchasing power?

texts:
According to my textbook, in the chapter on inflation,

"When a price rises, buyers of that good must pay more, but sellers get more revenue when they sell it. The loss in buyers' purchasing power is matched by the rise in sellers' purchasing power."

I understand the part of falling purchasing power for buyers (since each dollar can now buy less compared to previously), but why so for the seller? For instance, suppose each orange was sold for 1 dollar in the past. The price then rose to 2 dollars (reflecting the rise in general price level in the economy) - but if 2 dollars post-inflation is worth the same as 1 dollar before the price rise, then there really is no change in the sellers' purchasing power right? When the seller uses the 2 dollars to buy other things, it will still fetch him the same as 1 dollar did previously!

I'm not sure if I'm missing something here, and would really appreciate some clarification, thank you!


texts:
Your utility from having $x$ dolars is $u(x)$.

There is a gamble in which the winnings in dollars are a random variable, $Y$. It is known that $E[u(Y)]>E[u(1)]$, so you prefer to bet than to get one dollar for sure.

But now you are offered the following options. You select a large number $T$ (which may depend on the distribution of $Y$), and then you can choose between two options:

A. Receive $T+1$ dollars.

B. Bet $T$ times, where all bets are statistically independent and distributed like $Y$.

For what utility functions $u$ would you prefer option B (for a sufficiently large $T$)?

The expected utility of option B is:

$$E\left[u\left(\sum_{t=1}^T Y_t\right)\right]$$

where $Y_t$ are i.i.d. variables distributed like $Y$. So the question is actually: for what functions is it true that, for a sufficiently large $T$:

$$E\left[u\left(\sum_{t=1}^T Y_t\right)\right] > u(1 + T)\; ?$$

One obvious answer is when $u(x)=x$, since in that case:

$$E\left[u\left(\sum_{t=1}^T Y_t\right)\right] = \sum_{t=1}^T E[Y_t] = T E[Y_t]$$

since $E[Y_t]>E[u(1)]=1$, it is clear that for a sufficiently large $T$:

$$T \cdot E[Y_t] > T + 1$$

What other utility functions have this property?


texts: Principal component analysis interpretation

texts:
Suppose a wealth index is computed using information on a set of 14 assets that a household possesses.
 The index is generated using principal components, as the 14 individual asset variables are highly
collinear. A OLS regression of education expenditures (in Rupees per household) on the wealth
 index yields a coefficient of 0.4.

It is harder to interpret coefficients principal components in terms of original regressors. But can I interpret wealth index as its own ie can I say - increase in wealth index by a score of 1 will increase education expenditure by 0.4?

Is there any alternative
 formulation of doing this exercise that may be preferred?


texts: References about leading, lagging, and coincident economic indicators

texts:
Reading about macroeconomics, I've come across a great deal of information regarding leading, lagging, and coincident indicators. I'd like to learn more, specifically information related to measurements.

For the most part, in the books that I've read, indicators are graphed along side changes in the economy. I imagine that economists do not just graph items and visually inspect whether they are (1) indicators and (2) if they are leading, lagging, or coincident, etc.

What articles/texts are available that discuss the statistical methods behind identifying and measuring economic indicators?


texts: Does risk aversion of utility function cause the existence of positive interest rate?

texts: In standard macro model, it is usually time preference that causes positive interest rate. But is there anything to do with risk aversion of utility function that causes existence of positive interest rate?


texts: Leontief input output model with column sum greater than 1

texts:
In a linear algebra textbook I came across the following question (not included in the answer key):

Consider an open economy with a consumption matrix
\begin{equation}
     C =
     \begin{pmatrix}
           0.5 &  0.25  & 0.25 \\
           0.5 &  0.125 & 0.25 \\
           0.5 &  0.25  & 0.125 \\
     \end{pmatrix}
   \end{equation}
If the open sector demands the same dollar value from each product-producing sector, which such sector
must produce the greatest dollar value to meet the demand? Is the
economy productive?

This textbook defines productive as:
"Economies for which $(I − C)^{−1}$ has nonnegative entries are said to be productive.".
Below is a theorem from the textbook.

If $C$ is the consumption matrix for an open economy, and if all of the column sums are less than $1$, then the matrix $I − C$ is invertible, the entries of $(I − C)^{−1}$ are nonnegative, and the economy is productive.

Immediately I notice that the column sum of $C$'s first column is greater than $1$, and from what the textbook says that means the given sector requires more inputs than its output, thus it's not profitable. However, it turns out that this given matrix is invertible and its inverse has nonnegative entries.
I understand mathematically in the cited theorem that the column sums being less than $1$ is not an if and only if condition and thus exceptional circumstances are possible.
However, in economic terms the question seems odd, in other words, asking whether an economy with an unprofitable sector is productive.
If the question is not faulty: how would you explain this in economic terms? Or if it is, what is wrong with the question?


texts: Solving a HJB with additional constraints on control and state variables

texts:
I am trying to solve a Hamiltonian-Jacobi-Bellman equation with additional constraints on the state and control variables, but I am a bit confused on how to do that.
In Intrilligator 2002, it is written that

"Dynamic programming can also be used to treat the constrained
calculus of variations (...). For example, for the isoperimetric
problem, where the constraint is $$\int_{t_{0}}^{t_{1}} G(\mathbf{x},
 \dot{\mathbf{x}}, t)=c$$, Bellman's equation takes the form
$$-\frac{\partial J^{*}}{\partial t}=\max_{\{\dot{x}\}}\left[I(\mathbf{x}, \dot{\mathbf{x}}, t)+\frac{\partial J^{*}}{\partial \mathbf{x}} \dot{\mathbf{x}}+\frac{\partial
J^{*}}{\partial c} G(\mathbf{x}, \dot{\mathbf{x}}, t)\right]$$ which
yields the same conditions as the calculus of variations formulation
since the Lagrange multiplier is $$y=\frac{\partial J^{*}}{\partial
 c}$$ i.e., the variation in the optimal value of the functional with
respect to the constant c of the constraint."

However, I am not sure how to apply this formulation to the following maximization problem:

A firm maximizes its discounted profits $\max_{i_t} \int_0^{\infty} e^{-rt}\pi_t dt$ where $\pi_t=f(q_t)-i_t-\tau q_t$. Assume $f(q_t)$ is increasing and concave in $q_t$. The two control variables are $i_t$, the investment decision, and $q_t$, the level of installed capital used
This maximization program is subject to the following constraints

A law of motion of capital $\dot{k} = i_t - \delta k_t$ where $\delta$
is a parameter defining the rate of depreciation of capital.
Investment is irreversible $i_t\geq 0$
A physical constraint on $q_t$: $q_t\leq k_t$, which simply states that the firm cannot use more capital that it has installed.

I know how to solve this problem using a Hamiltonian, but I would like to find how to do it using dynamic programming, and thus a HJB.
With a current-value Hamiltonian, I would write
\begin{align*}
H = f(q_t)-i_t-\tau q_t + \lambda_t(i_t-\delta k_t)+ \psi_t i_t +\beta_t (k_t-q_t)
\end{align*}
Which would yield the following FOC:
\begin{align*}
-1+\lambda_t + \psi_t = 0 \\
f'(q_t)-\tau - \beta_t = 0 \\
-\delta \lambda_t + \beta_t = r\lambda_t - \dot{\lambda}_t
\end{align*}
However, I wonder how I could solve this problem using dynamic programming and a Hamilton-Jacobi-Equation. Using the formulation of Intrilligator, I would include the additional constraints into the HJB
$$ rV = \max_{q,i} \left\{f(q_t)-i_t-\tau q_t + V_{k}(i_t-\delta k_t) + V_{i}i_t+V_{q}(k_t-q_t) \right\} $$
But I am not sure if this is right (I write $V_k$ for the derivative of the value function with respect to $k$).
Following Walde 2012, I take the FOCs
\begin{align*}
-1+V_k+V_i = 0 \\
f'(q_t)-\tau - V_q=0
\end{align*}
However, I have more difficulty with the envelope conditions. Is it ok to write
\begin{align*}
rV_{k} =V_{k,k}(i_t-\delta k_t) - \delta V_k +V_{i,k} i_t + V_{q,k}(k_t-q_t)+V_{q}?
\end{align*}
Then, I would write
$$ \dot{V_k}=V_{k,k}(i_t-\delta k_t)$$
and substituting using the envelope condition to find
$$ \dot{V_k}=V_k(r+\delta)- V_{i,k} i_t - V_{q,k}(k_t-q_t)-V_q$$
But I am not sure that this is the desired result because of those extra cross-derivatives $V_{i,k}$ and $V_{q,k}$...
My questions are:

Do you need to include the additional constraints in the HJB, and how do you do it?
How do you take into account those additional constraints in the envelope condition?
Is it ok not to include the constraints into the HJB but to solve the maximization problem with a Lagrangian? That is, to write only $rV=\max_{q,i} \left\{f(q)-i_t-\tau q_t + V_k (i_t-\delta k_t)\right\}$ but to solve this maximization with the following $$ L =f(q)-i_t-\tau q_t + V_k (i_t-\delta k_t)+\psi_t i_t+\beta_t(k_t-q_t) $$
Thank you for your help!

Note: I posted this question originally on mathSE, but it didn't receive a lot of attention and I thought it might be more appropriated here.


texts:
I've noticed that certificates of deposit have dropped their interest rates in my country. This seems to be due to lack of trust in economic opportunities and has caused an increase of liquidity in banks that has not been able to be released via loans.

This leads me to think that loans will be favored, although interests rates for them are actually high due (I suppose) to an inherent risk in the local economy and therefore the typical loan is small ($\sim 3000 $ $). So, what are the typical purposes --other than immediate consumption-- that these type of loans have for households (i.e. not for starting a new business) as a whole?

Let me rephrase my question: what incentive would there be for families to borrow during a recession?


texts: Specifying a Diff-In-Diff with multiple treated groups over multiple years

texts:
Suppose I have a group of 100 counties. Further suppose that the state decides to allocate a lump sum amount of money to some counties each year to boost spending on education in that county (until, say, 50 of the 100 counties have received money). Suppose my goal is to use a dif-in-dif approach to analyze the effect of the spending increase.

How would I specify this DID regression? The basic idea is that, for each year, I want to compare educational outcomes in counties that receive increased funding with those that do not. I want to do this so that I eventually get to evaluate the effect for all 50 counties that receive this educational funding boost.

My guess is something like this: I need to specify a typical DID regression with year and county FE s.t. for any given year, a county that receives funding is in the treated group and any county without the funding boost is in the control group. However, the effect of that funding boost means that a county treated in year $t$ ought not be included in the control group in year $t+1$, despite not receiving a funding boost in $t+1$.

Am I over complicating this? It doesn't seem to me like specifying a normal DID with year and county FE will quite work.


texts: Econometrics: Weights in regression that contains averages

texts:
Let's say I have a regression of the form:

$$y_j=a_0+a_1*T_j+a_2*X_j+u_j$$

where $j$ stands for county, and $y$ and $X$ are averages over worker outcomes/characteristics for each county, and $T$ is a continuous treatment variable that varies at county level.

When estimating in Stata I was suggested to use "aweight" option, where analytical weights are derived from county population.

Question:

Now I want to include county population as a control variable. Wouldn't this cause a problem as I am already using county population for weights?

Thanks!


texts: Which are some proven methods to compare alternative economic theories?

texts:
Based on this question about alternative schools of thought, this question about untested economic theories, and the rather unsatisfactory answer (imo) to this question about which is the "most correct" growth theory at the moment, it would be great to learn more about how to compare economic models or theories. Anyone familiar with this literature, which I think belongs to philosophy and methodology of economics?

I have rudimentary ideas here, like Occam's razor and Friedman's defense of unrealistic assumptions, but this is deeply unsatisfactory for such an important question (imo).


texts: Are there any economic reasons that could justify a higher tax rate on housing repairs than on construction of new houses?

texts:
In the UK, a builder constructing a new home need not add tax to the price charged, but a builder undertaking repairs or renovations to an existing home must add value added tax (VAT, currently 20%).  (There are some exceptions but that's the general rule - details can be found in HMRC Notice 708).

Question: Are there any economic reasons that could justify a higher tax rate on repairs and renovations than on new construction?  I am interested in general economic arguments, whether applicable to the UK or not.

A possible argument for not taxing construction of new homes (even if most goods and services are subject to VAT) is that VAT should be regarded as a tax on consumption, and should instead be charged on the consumption of housing services (Barker K (2014) Housing: Where's the Plan? p 64). That presumably means that, for owner-occupiers, the tax authorities should determine the value of the housing services they consume each year and charge VAT on that.  However, even this argument does not seem to justify the differential taxation of new construction, since the same argument could be applied to renovations and repairs, implying that what is taxed should be any resulting increase in the value of housing services.

Addendum 14/9/2017: I've slightly changed the wording so that it invites answers on either side, either yes there are reasons or no there are not.


texts: What would happen if stock markets were open 24 hours?

texts:
Suppose you are a broker or a trader, and the stock markets will be open 24 hours a day.

What would be the implication for you as a broker in this scenario?
I mean:

How will your strategies change?
Will it be more difficult or easier to trade?
What algorithms that you know that would have to be adjusted in this scenario?


texts: When the Central Bank sells a bond, where does the money go ultimately?

texts:
As the accepted answer points out, the premise of my question was flawed. Thank you for the dispelling of my wrong assumptions. The original question follows.

There are two related questions (and feel free to assume the Central Bank in the questions is USA's Fed):

When the Central Bank sells bonds, where does the money go ultimately?
How separate is the Central Bank budget from the government's budget?

To clarify: If the Central Bank sells \$1000M worth of bonds in order to repay \$800M old maturing debt and to raise an extra \$200M, does this \$200M simply become available for use to the government? Or is there some extra process in order to transfer money between the government and the central bank? Who decides (central bank, executive branch, legislative branch) how much new debt the central bank will be selling?


texts: What are the alternative uses of unlimited wants and scarce resource?

texts: Actually I want to know what does it mean by alternative uses of this two terms of economy.


texts: Was factory beef farming (in the USA) the result of government-subsidized corn?

texts:
In The Omnivore's Dilemma, Michael Pollan writes that industrial beef farming, in the form of concentrated animal feeding operations (CAFOs), is dependent on low corn prices for its cost-effectiveness. He also implies that corn prices low enough to justify CAFOs were only possible because the US agriculture policy artificially depressed the price of corn.

Pollan attests that the first CAFOs began in the 1950s. But he also spends a good deal of time in the previous chapter discussing how Earl Butz, under President Nixon (that is, in the 1970s), was instrumental in ending the New Deal corn price stabilization policies (a buffer-stock scheme) and replacing them with corn supply subsidies (direct payments to farmers).

If that's the case, then how did the first CAFOs manage to be profitable, or even seem like a good idea, if corn was not to become artificially cheap for at least another decade? Or were CAFOs always profitable, but received a tremendous boon when corn prices were later driven down by policy?

This is as much a question about the timeline as it is about the underlying economics, so I'd prefer to see an answer based in some kind of scholarly source.

Also I'd appreciate it if someone with more than 150 rep could create an "agriculture" tag for this question. I had wanted to add "prices" and "subsidies" tags as well.


texts: Have there been instances where economists have advocated a trade embargo?

texts:
Due to Comparative Advantage, it is generally accepted among economists that free-trade is the best policy for a country and increases the standard of living for the citizens of that country and the country with which it trades.

I have heard, however, that there are certain instances where it would be more beneficial (on the whole for that particular country) for the country to restrict trade with other nations.  Have there been instances like this where economists have advocated a trade embargo with another nation?


texts:
I am analyzing pricing for a new streaming service for a school project. My thought is to calculate the demand function of a player in the same industry and then calculate the optimal price. I am a little confused about calculating the demand function for Netflix. I have their subscription fees (converted to annual) since 2007 - x axis and subscribers - y axis. I am getting an upward slope.

Below is the output of regression.

Subscribers = 76.5 + 0.5 Fee_per_year

I would appreciate it if someone can point out what mistake I am making.


texts: Is the income derived from owning a live animal profit or rent?

texts:
Natural resources are considered non-produced and yield rents, including land and the fruits of the land, e.g. trees. Does this extend to live animals? Or are live animals considered “produced” goods (capital) that yield profits?

Does it make a difference whether the tree or animal is wild or has been planted on a plantation or bred in captivity respectively?


texts: Are overlapping generation (OLG) models extensions of a DSGE model?

texts: Are overlapping generation models (OLG) extensions of a dynamic stochastic general equilibrium (DSGE) model? Or aren't these DSGE per se?


texts:
I'm doing an optimisation problem but don't understand what the terms mean.

Suppose someone wants to invest $110,000.

They have 4 choices as to what they invest their money into:

municipal bond yielding 6%,
an industrial bond yielding 13%,
Treasury bills at 10%,
certificates of deposit (CDs) at 9%.

I want to maximise their annual interest (in dollars)

There are some constraints (which I haven't typed) but I just want to know what these terms mean. Say, they invest $27,500 on each one, what would their annual interest be (in dollars)?


texts: Why would the economy return to equilibrium at full employment after a supply side shock?

texts: As far as I'm aware, in the absence of any changes in the long run aggregate supply LRAS, any changes in the level of aggregate demand AD or short run aggreagete supply SRAS should eventually in the long run see the economy return to full employment, as per monetarist theory. How does the economy return to full employment when there is a change in the SRAS, when, for example, SRAS decreases?


texts: Are there any estimates for what percentage of the jobs lost this spring are "permanent" at least for the rest of the year?

texts:
In a "view from the helicopter" video by The Economist on the aftereffects of Covid-19, one of the editors says that it's very unlikely we'll see a return to normal this year e.g. in the restaurant business, even if lockdowns are officially ended. (I suspect air travel business is in a similar situation. Also of some interest, WSJ video on job losses in the US healthcare sector said to normally be "recession proof"; that video also says some of these [US healthcare] jobs are unlikely to return.)

So are there any attempts to estimate how many of the jobs lost this spring are "permanent" at least for the rest of the year, despite the prognosis of a V-shaped recovery that some/many predict?

I'm not asking about a particular country, but I suspect the US, Europe or China are the places most likely to have such studies/estimates. I'm mainly interested in models for how such an issue could even be estimated, this is why I'm not very particular about the country.


texts: Why is overlapping generation model not a main model in macroeconomics?

texts: It seems that overlapping generation model has far more realistic assumptions than ordinary Ramsey-Prescott RBC model for use in macroeconomics. Why is Ramsey-Prescott ones, even New Keynesian variants, are more popular than overlapping generation ones? Is this just due to simplicity, or is there any fundamental problem with the consequences of overlapping generation model?


texts: What branch of Economics does 'e-governance' fall under?

texts:
I need to work on a project regarding e-governance in a region of India, and, I need to consult professors in education institutes who would have knowledge in this subject. So, for that I need to know what part of Economics does e-governance come under?

Does it come under Development Economics, Public Economics or any other field?


texts: What are the criteria which have been proposed to deal with the problem of interpersonal comparison of utility?


texts:
Please look at only part ii.

I wrote budget constraint $x_1+x_2=10-f$

When I don’t pay fee, my optimal value values${}=(1,1).$

In the case of free disposal, $b_1=b_2=5$ but I consume only $x_1=0$ and $x_2=5.$

However I couldn’t find the value of $f.$ How can I find?


texts: If we add up all the income while finding GDP of a country, is income counted multiple times?

texts: Suppose 9 others and I are government employees. We get salary which will be counted while calculating GDP. Let's assume that we 10 are the only customers of a shop (for simplicity). The shopkeeper's income is derived from the 10 of us. Now if we calculate the shopkeeper's income while calculating GDP, then the the income will be counted twice since it was counted as our income at first place. So how are situations like this handled?


texts: Logistic regression: Equation for marginal effect at the mean

texts:
I am estimating the following logistic regression (binomial family) by maximum likelihood:

$$ \ln\left(\frac{Y}{1-Y}\right) = \beta_{0} + \beta_{1}D + \beta_{2}X + \epsilon$$

where D is a dummy. I am interested in the marginal effect at the mean of $D$, i.e. $\beta_{1}$ is of interest. What does the marginal effect at the mean look like in equation form? Would it be:

$$ \frac{1}{\bar{Y}} \left(\frac{e^{\beta_{0}+\beta_{1}+\beta_{2}\bar{X}}}{1+e^{\beta_{0}+\beta_{1}+\beta_{2}\bar{X}}} - \frac{e^{\beta_{0}+\beta_{2}\bar{X}}}{1+e^{\beta_{0}+\beta_{2}\bar{X}}}\right) $$

or

$$\left(\frac{e^{\beta_{0}+\beta_{1}+\beta_{2}\bar{X}}}{1+e^{\beta_{0}+\beta_{1}+\beta_{2}\bar{X}}} - \frac{e^{\beta_{0}+\beta_{2}\bar{X}}}{1+e^{\beta_{0}+\beta_{2}\bar{X}}}\right) $$

My intuition is that Y corresponds to the probability of the event occurring, and the e/(1+e) terms also correspond to the probability of the event occurring, but at specific values of Y. What would the rationale for dividing by $\bar{Y}$ be? Thank you.


texts:
I'm new to economics. I want to ask that what remedies that the government can actually employ to address the deficit/surplus in the fish trade balances over time?

My attempt,

Trade deficit

(i) The government can strengthen the diplomatic relationship with foreign countries by signing five to ten years contract with the purpose of buying more Malaysia’s fish commodities but at a lower price. This action can increase the export of our country’s fish commodities and earn a long term profit.
(ii) Provide the export incentive to local fish industries in order to help them remain competitive in the global market by exporting more fish commodities. Export incentive will reduce the cost of export and therefore increase the competitive force of local industry in global market.

Trade surplus

(i) the government can eliminate the trade tariff in order to induce foreign countries to import more fish commodities in our country. This will make the import and export of Malaysia equivalence.
(ii) The government can buy the fish commodities surplus of local fish industries and store them to reduce the export.

Is my answers correct? Is there better solution? Thanks in advance.


texts: How can the VNM completeness axiom be derived from the transitivity and continuity axioms?

texts: My teacher mentioned off-hand that the first Von Neumann Morgenstern axiom of completeness is not actually necessary to prove the Expected Utility Property, and that the axiom of completeness is in fact implied by the axioms of continuity and transitivity. I don't see why this is.


texts: Why did foreigners keep buying Swiss francs at -41% (not a typo) interest rate in the 1970s?

texts:
A Bloomberg (opinion) piece notes

  In January 1975, the Swiss government held an emergency meeting and then took the extraordinary step of slapping a 41% annual penalty on foreign deposits. But even this failed to stem the tide. The franc continued to appreciate against the dollar — a total of 70% in nominal terms between 1971 and 1975 alone.

I feel that something is missing in this story... What sane investor would put their money into an account earning -41%, even in the mid-70s?! So what explain this story, if it is actually accurate?


texts: Monopoly: Demand Curve and Marginal Revenue Curve Intercepts

texts:
I'm doing an introductory economics course, having never done economics before. In our topics, we covered monopoly and the principle that the marginal revenue slope is twice that of the demand slope. I have also seen it stated elsewhere that the y-intercept of the two is also the same. However, if I calculate the marginal revenue equation and if I graph it, I get a different y-intercept to that of the demand slope (see below). As a result, I am always 0.5 units away from the given solution.
If the demand equation is as follows: $P = k + aQ$, then $MR = Q\times(k+aQ) - (Q-1)(k+a(Q-1))$. This simplifies to $MR = (k-a) + 2aQ$. (Note, a is normally negative, so $-a$ would essentially be adding to $k$).
Can anyone explain to me what I'm doing wrong?
The demand curve of one example was given as: $P = 120 - 2Q$
Here are my calculations:
$MR = Q \times (120 - 2Q) - (Q - 1) \times (120 - 2(Q - 1))$
$MR = 120 Q - 2Q^2 - (Q - 1) \times (122 - 2Q)$
$MR = 120Q - 2Q^2 - (122Q - 2Q^2 - 122 + 2Q)$
$MR = 120Q - 2Q^2 - 124Q + 2Q^2 + 122$
$MR = 122 - 4Q$


texts: How can intermediate goods and final goods be differentiated?

texts:
The calculation of GDP(using expenditures) is: $C+I+G+Xn$,

where we calculate the spending on final goods and services within a country. However, how exactly are final and intermediate goods differentiated when calculating spending?

For instance, if one firm sells a product to another firm that adds to that same product and sells it again, how exactly do governments account for this when calculating GDP?


texts: A possible typo in Herbst and Schorfheide book of DSGE estimation

texts:
In a state-space representation, the measurement equation is something of this form $O_t=H_t s_t + u_t$, where $O_t$ are the observational data at time $t$, $H_t$ is a possibly time-dependent matrix relating the state $s_t$ and the observational data. We can see $u_t$ as the measurement errors at time $t$.

However, in Herbst and Schorfheide book (Bayesian estimation of DSGE models),

we have $s_t$ dependent on $y_{t}$, but not $y_{t-1}$, while the measurement equations are of the form:

Is this a typo? Should I add the $y_{t-1}$ term to $s_t$?


texts: How to calculate the risk-free rate of cryptocurrencies?

texts: For a conference I need to show the Sharpe ratio's of bitcoin portfolios using different trading strategies. To calculate the Sharpe ratio, I need the Bitcoin's risk-free rate. Risk-free rate for normal stock markets is usually taken from Treasury documents. But cryptocurrencies have no central government and are not affiliated to any country. So how to determine the risk-free rate for, for example, Bitcoin? Is it simply 0?


texts:
Consider a profit maximising monopolist with linear demand Q(P*) and total production cost C(Q(P*)) who faces a per unit tax t. Suppose the slope of marginal cost is decreasing in some parameter, μ. Let P* denote the monopolist’ profit maximising choice of price. Being careful to explain your method and interpret your result, determine the comparative static:
∂²P*/∂μ∂t
I got to P*= price Q = Q(P*) t=t(Q(P*)) C=C(Q(P*))
πmax = P*(Q(P*))-C(Q(P*))-t(Q(P*))
dπ/dP* = Q'(P*)[-C'(Q(P*))-t'(Q(P*))+P*]+Q(P*)=0 dπ/dP* = μ + Q'(P*)[-t'(Q(P*))+P*]+Q(P*)
Equilibrum: PQ'(P)=t'(Q(P*))Q(P))-μ-Q(P*)
P* = t'(Q(P*))- μ/(Q'(P*)) - Q(P*)/Q'(P*)
This is where I got to, when I solved the comparative static partial differentiation I got an answer of 0, I don't believe this is correct, can anyone help me solve this? Thanks!
If 0 is somehow the correct answer, what does it mean?


texts:
As education moves to the internet, so are research seminars. Some of these seminars are regular and others appear to be temporary due to the covid-19 and the lockdown.

Here are some examples from the American Economic Association

Regular seminar(s)

The Chamberlain Seminar - A regular open online international
inter-institutional econometrics seminar in honor of Gary Chamberlain
(1948–2020)

Temporary Seminars

Virtual Macro Seminar Series
Online Seminar in Gender Economics
Virtual IO seminar
...

And also,

Princeton Webinar Series on COVID Economics

Beyond the AEA list and the Princeton webseminar, I am looking for links to find conferences, workshops, and talks hosted by economic research institutions from all over the world. One requirement is that registration be open to all, as some of the online seminars are reserved for faculty only.

Update

Virtual Economics stores various online seminars with a super useful calendar.


texts:
From what I understand after reading mainstream media, quantitative easing increases the supply of money in the economy without direct government spending (fiscal policy).

It seems to have all the benefits of monetary policy (decreasing interest rates), but can still be done with rock-bottom interest rates.

Is my understanding correct? What's the downside I'm missing?


texts:
In econometrics, ( this material is in a lot of the literature but, IMHO, can most clearly be found in Harvey's text, "econometric analysis of time series"), there are generally two versions of a specific lagged dependent variable which is usually  termed the koyck distributed lag. ( It's a very special case of a distributed lag ).

I write down version 1 and version 2 below.

Version 1 is shown below.

1):   $y_t = \rho \times y_{t-1} + \beta \times x_t + \epsilon_t$

where $\epsilon_t = (v_t - \rho v_{t-1}) \sim N(0, \sigma^2) $.

There is also version 2 which is

2):     $y_t = \rho \times y_{t-1} + \beta \times x_t + \epsilon_t$

where $\epsilon_t \sim N(0, \sigma^2) $.

So, in version 1, the error term is such that $v_t$ is AR(1) and in version 2), the error term is pure noise.

My question is the following: Is there a way to write to a version where the error term is MA(1) ? I initially figured there must be some kind of symmetry because  we have the pure noise case and the AR(1) case so I figured there must be a version with an MA(1) error term. But now I'm not so sure and actually don't think do.  Thanks for any insights.

EDIT BASED ON GOOD QUESTION IN COMMENT:

Hi: $\frac{\epsilon_t}{(1 - \rho L)} = v_t$ where $L$ is the lag operator.

Therefore, $v_{t}$ can be thought of as an exponentially smoothed average of the past white noise error terms $\epsilon_{i}$.

Now, version 1) of the model can be re-written in the following way:

$y_t = \rho \times y_{t-1} + \beta \times x_t + (1-\rho L) v_{t} $

which can be re-written as

$y_{t}(1 - \rho L) = \beta \times x_t + (1 - \rho L) v_{t} $

Then, dividing the whole the equation by $(1 - \rho L)$ results in what I call the long form of version 1 of the model:

$y_{t} =  \beta \times \sum_{i=0}^{\infty} \rho^{i} x_{t-i} +  v_{t}$

So, the model implies that response is $\beta$ times an exponentially smoothed average of the past $x_{i}$  plus v_{t}. But, we can re-write the last term which results in

$y_{t} =  \beta \times \sum_{i=0}^{\infty} \rho^{i} \times x_{t-i} + \sum_{i=0}^\infty \rho^{i} \epsilon_{t-i}$

So, in version 1), the response can be thought of as an exponentially smoothed version of the past $x_{t}$ plus the exponentially smoothed version of the past error terms, namely the $\epsilon_{i}$.

I won't write it out, but, in  the long form of version 2, the error term is not an exponentially smoothed average of the past $\epsilon_{i}$. The past error terms  are not involved and the error term is just $\epsilon_{t}$.

Thanks for good question.

SECOND EDIT BASED ON GOOD QUESTION IN COMMENT:

When your question made me write it out in the long form, it hit me that
an MA(1) structure could just be:

$y_{t} =  \beta \times \sum_{i=0}^{\infty} \rho^{i} \times x_{t-i} + \epsilon_t + \rho \epsilon_{t-1} $

This would be an MA(1) error term for the koyck distributed lag. I don't think it simplifies in any way by writing it in the short form but it's still a nice way of thinking of a third possibility. In one case, the error term lasts on period. in another case, the error term is  is an exp smoothed average of past errors and in the last case, the error is linear combination of the last two errors. Clearly your question totally led to this and I think what you're saying in your comment is the same as here, so thanks much for insight.


texts:
While reading Mazzucato's "The value of everything", I come across this

  The rise in private debt in the US and UK has resulted in household
  savings falling as a percentage of disposable income - income minus
  taxes - especially in periods of sustained economic growth (during the
  1980s, the late 1990s and the beginning of the 2000s.

I wonder if this is based on observation or if there is a cause and effect (as suggested by "resulted"), in which case I'd be grateful if anyone could provide some intuition of why such a relationship would exist.


texts: What would an investment bank have to gain by warning of an impending financial crisis?

texts:
After reading a recent article and a discussion with a friend, I was left wondering what an investment bank would have to gain by claiming that a financial crisis is coming.

I can see an obvious answer which is that by instilling fear in the market you can lower stock prices of shares that you would be interested in buying. However I find that this is a very dangerous game to play, because if the panic spreads, overall their portfolio would lose a lot.

Whether their prediction is accurate or realistic doesn't concern me. I just want to know what they'd gain if they did lie about it.


texts: Does Efficient Market Hypothesis make anticipated monetary policies useless?

texts: Since the market perfectly captures all the information, is it true that any anticipated monetary policy has no impact on equity prices? Or the “information” has an immediate impact but the “event” itself has no impact.


texts: How to calculate fiscal space for a country?

texts: I would greatly appreciate if you could explain me how to calculate fiscal space for an specific country. Or, could you please introduce me some references which explain it's calculation step by step or via a numerical example. I found this document but the numbers are not exactly reproducible. Therefore, I am not sure about it.


texts: Calvo Price setting in a Multi-sector NK Model

texts:
In Calstrom-Fuerst-Ghironi (2004) "Does It Matter (for Equilibrium Determinacy) What Price Index the Central Bank Targets?", they used a standard two-sector NK model, and the optimal price setting condition reads (equation 14):
$\frac{P_{t}^{j}}{P_{t}}=\frac{1}{Z_{t}^{j}}\frac{W_{t}^{j}}{P_{t}}$,
where $P_{t}^{j}$ is the price index for sector j, $P_{t}$ is aggregate price level, $W_{t}^{j}$  is wage for sector j, $Z_{t}^{j}$  is the marginal cost in sector j, so that $1/{Z_{t}^{j}}$ is the markup of price over marginal cost.
I do not understand how this equation is derived. My understanding is that in multi-sector models we still have pricing equation to be in the form of $P_{t}^{j}=\frac{\epsilon}{\epsilon-1}\frac{E_{t}[\cdots]}{E_{t}[\cdots]}$.
The equation in Calstrom-Fuerst-Ghironi (2004) also showed up in another paper of theirs using multi-sector NK model. In both papers, they say refer to Yun (1996), but I do not see a form like this in Yun (1996).
Any help is greatly appreciated!


texts:
I am looking for economics papers which use concepts, techniques and theorems from geometry. I am mainly interested in Euclidean geometry, the kind of material that is taught on high-schools (e.g. proving theorems about triangles, squares, circles, etc.). But, other kinds of geometry are also interesting.

I looked at some papers about land economics, thinking that it geometry can be useful there (after all, the word "geometry" means "measurement of land"). But, the papers I found used mostly advanced measure theory and topology. I am looking for more basic geometric methods.


texts:
Question:Assume no non-labor income, Alice's labor supply function is $h(w) =\frac{w}{16}$. Her preferences are given by $u(c, l) =\sqrt{c}+3l$.
When the wage rate increases, Alice's labor supply increases because of? (Substitution effect or income effect only, or both? If both, are they moving along the same direction?)

This is our homework question and when I solve this, I apply lagrange to the utility function and get $h(w) =\frac{w}{36}$,which contradicts with the equation given by $h(w) =\frac{w}{16}$. Does this mean that it is not appropriate to apply lagrange's method in this question? I found the utility function to be quasilinear so I selected that there's no income effect, but I got it wrong. What am I supposed to do to analyse this equation? Any help will be appreciated.


texts: How do We Determine the Start or End of Investment Phase for the Oil Industry

texts:
I am trying to do an analysis of the oil industry, and while doing research I came across the following chart that has one of the factors I want to include: Investment Phase vs Exploitation Phase

The creators cite the US Energy Information Agency, so at least I know where to find the data. However, what I'm not sure is how do the creators of the graph 'know' where the investment phase begins and ends.

My question is: How do we know when the industry is in an investment phase? Are we to simply eyeball the graph? Or is there some kind of criterion or statistical heuristic? Perhaps another variable's data is needed?


texts: Calibration of labor market frictions parameters

texts:
I want to refer to the following paper A Three State Model of Worker Flows.
My questions are regarding the calibration of parameters. First, I would appreciate any help when on p. 11 it says that $\alpha$ (disutility of work) is set so that the steady state value of employment is equal to 0.632.
Second, loosely speaking, let $\sigma$ be the exogenous job separation rate and $\lambda_w$ the exogenous arrival rate. This model is a variation of the standard growth model. In the calibration section, they mention the following: "We choose $\lambda_w$ so that the steady state unemployment rate in our model is equal to 0.083" (p. 11) and also that "for our benchmark case we target the flow rate from employment to unemployment of 0.021 [to pin down the value of $\sigma$]" (p. 12). My question is, how is this procedure done? Since the model kind of combines some features of the Pissarides model, I tried following the same logic, that in the steady state the number of people that go from employment to unemployment is equal to the number of people that go from employment to unemployment, but I don't think this is the correct approach.
I would appreciate any help/guide you can provide me.
Update: Now I understand that when it says that they target the flow rate from employment to unemployment of 0.021, it means the following:
$\begin{gather}
EU_t=\sigma(1-\lambda_w)E_t \\
\frac{EU_t}{E_t} = \sigma(1-\lambda_w) \\
\sigma(1-\lambda_w)=0.021 \quad \quad \text{(1)}
\end{gather}$
So this is one equation that must hold. In regard to a second equation, given that the paper uses a steady state value of employment of 0.632 and the unemployment rate $U/(E+U)$ of 0.083, one can derive that $U=0.057$. Given that $N_t=1-E_t-U_t$, I though that in steady state we could also get the value of $N=0.311$. Thus, the law of motion of unemployed people would be as follows:
$\begin{equation}
U_{t+1} = \sigma(1-\lambda_w)E_t + (1-\lambda_w)U_t + (1-\lambda_w)N_t \quad \quad \text{(2)}
\end{equation}$
Intuitively, this means that the stock of unemployed people would be equal to those workers who lost their job and did not find one in $t+1$ + those who were unemployed and continued to being so in $t+1$ with probability $1-\lambda_w$ + those who were out of the labor forcein $t$, decided to enter in $t+1$, but did not find a job with the same probability $1-\lambda_w$.
So with these two equations I tried estimating the parameters, but I failed. I pressume Equation (2) is somehow wrong, so I would appreciate any comments on that. Also, I still don't know how to calibrate $\alpha$. Thank you in advance.


texts:
I read an article in BusinessWeek that talked about income inequality in the US.

The article attributed the difference to the Intel chip that came in 1971. Since that time big hi-tech companies have grown in US, which caused income growth among wealthy people and also didn't lead to a relatively large growth in jobs because a lot of work was outsourced to places like China.

To what extent is this explanation valid in the US... or is it insignificant in accounting for the income differences between the rich and the poor?


texts: Does higher tax on luxury goods does more harm than benefit?

texts:
I was studying Fiscal policy and I came across measures to reduce income inequality by using fiscal tools. One of the tool mentioned in that was - Higher taxes on luxury goods

This makes sense that luxury good are enjoyed by rich so imposing higher taxes is a sound and prudent measure to take for welfare of poor but here is my thought -
Let's say if we don't impose high tax on luxury goods then it would drive more consumption which in turn will cause firms to hire labor for production and poor will benefit with employment and better income opportunities. Government will also benefit from the taxes - both production and consumption taxes! so Wouldn't it be more feasible? Raising incomes of poor through employment is far better.

Also, I believe the reason why it is not done because government doesn't want to be seen as favouring business or corporates over poor which profoundly mars the chance of political party.

Please share your thoughts, critique and if possible help me find fault in my line of thinking.

Note - In India when government imposed highest tax bracket on luxury cars, cars sales did see a slump so the argument that rich will continue to consume regardless of taxes might not hold true broadly also.


texts: Externalities, Pigouvian Taxes and Wikipedia

texts:
It states on Wikipedia:

  A Pigovian tax (also called Pigouvian tax, after economist Arthur C.
  Pigou) is a tax imposed that is equal in value to the negative
  externality. The result is that the market outcome would be reduced to
  the efficient amount. A side effect is that revenue is raised for the
  government, reducing the amount of distortionary taxes that the
  government must impose elsewhere. Governments justify the use of
  Pigovian taxes saying that these taxes help the market reach an
  efficient outcome because this tax bridges the gap between marginal
  social costs and marginal private costs.

Q: When it says, "A side effect is that revenue is raised for the government, reducing the amount of distortionary taxes that the government must impose elsewhere", what does that even mean?


texts: Does the break even analysis contradict the law of supply?

texts:
The law of supply shows a positive relationship between price and quantity
However, a firm producing at break even level of output would have to increase the quantity supplied if the price of the commodity goes down in order to break even.
Does that mean that a firm producing at break even level is an exception to the law or that the analysis contradicts the law of supply ? ( please correct me if there are any inconsistencies in the logic)


texts: What happens when a reserve bank runs out of foreign currency reserve?

texts: What happens to a country when a reserve bank runs out of foreign currency reserve?


texts: Why don't most of the highly educated people in poorer part of Europe migrate to the Western part?

texts:
There are a lot of people working in universities in countries like Ukraine, Belarus, Romania, Bulgaria, Poland, and so on with low salaries. Those people have high skills and education.

I saw some students pursuing PhDs in those countries with low salaries when they can just cross the border to earn much more.

Why don't most of them migrate to Western Europe?

What factors bind them in their countries?


texts: What would the indifference curve of min{√x,y} looks like?

texts: The locus of kinks would follow x=y^2 but what would the arms look like?


texts: Do discontinuous preferences imply no continuous utility function?

texts:
I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function.

I know that you can represent continuous preferences with a discontinuous utility function, but I am not sure if the opposite is true. I am struggling to show that NO such continuous utility function exists.

My thoughts are that if you can define something with discontinuous preferences then maybe you can use this to imply that there do not exist any continuous utility functions. Note that Lexiographic preferences will not work because I am interested in a preference that can be represented by a utility function (albeit discontinuous).


texts: Intuition on cumulative prospect theory, based on equi-probable outcomes?

texts:
I am trying to build my intuition on the weighting/decision function in cumulative prospect theory. I have a hard time getting a clear picture for even the simple case of equi-probabilities.
Assume ten possible outcomes, 5  positive, 5 negative (hence using 0 as reference point), all with equi-probability 1/10. If I were to use just prospect theory, I would apply a single weighting function on these probabilities, so here the 1/10 would be either over- or under-weighted depending on the choice of the function. Now prospect theory adds a rank-dependent utility function based on the cumulative probability.
In this simple-case of equi-probability, what does this imply? That higher positive and lower negative outcomes are going to be over-weighted, or under-weighted? How can we illustrate that? The standard plot of weights vs probabilities would look quite sad (as we have only one prob), how would the plot of weights versus rank of the outcome look like?
Thanks!


texts: Converting current to constant USD values for trade data (UN Comtrade)

texts:
I am using WB (country GDP) data in combination with UN Comtrade (bilateral trade) data. I need to divide bilateral trade by GDP so as to find out which % of a country's GDP comes from bilateral trade.
The problem is WB has values in constant 2010 USD while UN Comtrade in current USD.

How can I transform the current USD values in constant 2010 USD values?


texts: Marginal product of capital net of depreciation

texts:
I am trying to understand how marginal product of capital net of depreciation is the following:

Given that the production function is quite standard

I understand the first term of the marginal product, but I am asking about the depreciation part.


texts: What were the specific conditions that the Federal Reserve attached to the capital injections forced upon the major Wall St. banks during the Great Recession? How and why do they differ from normally legal and binding regulations?


texts: Why does the Laffer curve for consumption have no peak?

texts:
According to Trabant and Uhlig (2009), the Laffer curve for consumption has no peak.

As far as I can make out, the argument is based on the fact that money extracted by taxing consumption ends up back with consumers and then gets taxed again. However I don't understand why the standard idea that taxes deter activity doesn't create a peak.


texts: Can someone help me prove that the CES function is also a Cobb-Douglass function

texts:
I would like some assistance with a problem that I have showing a CES function is also a Cobb-Douglass utility function.
Question: we have a CES function: $Y=A[\alpha K^{((1-\sigma)/\sigma))}+(1-\alpha) L^{(\sigma-1)/(\sigma)}]^{\sigma/(\sigma-1)}$ $\sigma \geq 0$ $\alpha\in [0,1]$ show it is equivalent to Cobb- Douglass when sigma equals 1
Attempted solution:
$Y=$ $A[\alpha K^{((1-\sigma)/\sigma))}+(1-\alpha) L^{(\sigma-1)/(\sigma)}]^{\sigma/(\sigma-1)}$
$\ln Y=$ $ \ln[A[\alpha K^{((1-\sigma)/\sigma))}+(1-\alpha) L^{(\sigma-1)/(\sigma)}]^{\sigma/(\sigma-1)}]$
$\ln Y=$ $ \frac{\sigma \ln [A[\alpha K^{((1-\sigma)/\sigma))}+(1-\alpha) L^{(\sigma-1)/(\sigma)}]}{\sigma-1}$
Then I take the limit of both sides as $\sigma$ approaches 1
$\lim_{\sigma \rightarrow 1} \ln Y= \\
\lim_{\sigma \rightarrow 1}\frac{\sigma \ln [A[\alpha K^{((1-\sigma)/\sigma))}+(1-\alpha) L^{(\sigma-1)/(\sigma)}]}{\sigma-1}$
I am stuck here. I keep getting $\frac{\ln[1]}{0}=\frac{0}{0}$.
My guess is tht I should use L’hops rule, but I am not sure if my function is differentiable. Even then I doubt I could solve such a complex derivative. Any thoughts, advice, etc.? Also, if I can take the derivative how do I do so? (It’s been a while, LOL)


texts: Lexicographic preference relation cannot be represented by a utility function

texts:
I am stuck on the following exercise, related to preference relations and von-Neumann-Morgenstern utility function.

A farmer wants to dig a well in a square field $[0,1000]\times[0,1000]$. The preferences of the farmer on the possible locations are lexicographic, i.e:

If $x_1<x_2$ then $(x_1,y_1)\prec(x_2,y_2)$ for all $y_1,y_2$.
If $x_1=x_2=x$, then $(x,y_1)\prec(x,y_2)$ iff $y_1 < y_2$.

Initially, assume that the well location must have integer coordinates.
Is there a preference relation on lotteries, that satisfies the von-Neumann-Morgenstern axioms, and extends the lexicographic preference relation? If so, what is a linear utility function that represents this relation?

I think the answer is yes, and a possible linear utility function is: $u(x,y)=100000x + y$.

Now, assume that the well location can have real coordinates. Prove that there is no linear utility function that represents the preference relation on lotteries.
Which one of von-Neumann-Morgenstern axioms is violated by the preference relation on lotteries?

Here I am stuck. I don't understand why the utility function I suggested above doesn't work? And what axiom is violated here?


texts: Departure point for research in economics

texts:
I hope this is the place to ask this question.
I am in the first year of PhD in economics. As most of PhD students in economics, I try to show some economic mechanisms by modelling.

Most of time, I have a tendency to base largely on other models in the literature. I try to incorporate my idea in existing models but it does not work really well.
For those who are in economics, how do you start to model your idea ? Do you start from a really basic model and complexify after ?


texts: I am searching for some exntensive details about HARA preferences.  Where could I find some extensive details for HARA preferences? Something like a textbook or notes


texts: How to adjust salaries of more than two countries to a common year given that the data was collected in different years?

texts:
I want to compare salaries of more than two countries. The data I am using is based on the Occupational Wages around the World (OWW) database. Let's say I want to look at the salaries of the nurse. The salaries are specified in US Dollars and not all of them are collected in the same year, so we have sort of an incomplete data. As an example:

Year: 2008, Country: Azerbaijan, Annual Salary (USD): 1678.15
Year: 2007, Country: Singapore, Annual Salary (USD):  19523.57 (no 2008 data)
Year: 2006, Country: China, Annual Salary (USD): 3338.208 (no 2008 or 2007 data)

According to the author of the database (Freeman and Oostendorp), to compare living standards, we have to deflate wages using Purchasing Power Parity (PPP) instead of exchange rates for the US dollars (It seems to me that their data is in local currency, rather than in USD as the example above). However, it is not clear to me how we adjust these salaries to a common year, say 2009.

Is it correct to do the following to my data above? Or is there a better way to compare salaries over countries and time to a common year? I use World Bank Indicator (http://data.worldbank.org/indicator) to compute things.

First, we multiply the USD salary with their corresponding LCU/USD exchange rate [Indicator: "Official exchange rate (LCU per US$, period average)"]
Then, we divide by the PPP-correction [Indicator: "PPP conversion factor, GDP (LCU per international $)"]
To adjust across time, then we multiply the result by ratio of GDP per capita, PPP between the common year (2009) and the year the data is collected (2008) [Indicator: "GDP per capita, PPP (current international $)"]

I would greatly appreciate any help.


texts: What are key economic mechanisms explaining long term damage during Great Recession

texts: can you tell me what could be key economic mechanisms that explain long-term damage of the Great Recession?


texts: Do corporations outside of the Eurozone issue bonds in Euro?

texts:
Do corporate issuers outside of the Eurozone (as in the wider EU area, or non-EU countries) issue bonds in Euros (EUR)? How relatively common is this, compared to issuing bonds in USD, if you are a non-US and non-Eurozone debtor?

Would that qualify for what's referred to as "Euro denominated" bonds, or does that simply mean that the price of the bond is listed/represented in EUR?

Note that I'm not referring to so called "Eurobonds" which is something different:

  A Eurobond is an international bond that is denominated in a currency
  not native to the country where it is issued. Also called external
  bond; "external bonds which, strictly, are neither Eurobonds nor
  foreign bonds […]


texts: Keynesian Cross and Balanced Budget Multiplier

texts:
Hi! I am trying to understand the problem above, and was wondering if someone could help me with the last question. I think I am fine with all other questions.

Here is my attempt:

(i)
The fiscal multiplier is $\frac{1}{1-c} \Delta G$, as it is the infinite sum $ \Delta G + c\Delta G + c^2\Delta G + ... $.

Depends on c because the increase in government spending first leads to an increase in Y, which leads to an increase in C, which then leads to another increase in Y, but this time the increase in only $cY$, as part of the income is saved.

(ii) Balanced budget multiplier is 1, as $\Delta Y = \frac{1}{1-c} \Delta G + \frac{-c}{1-c} \Delta T$ with $ \Delta T = \Delta G$

This means that an increase in government spending that is matched by an identical increase in lump sum taxed increases output by the same amount as the increase in G (and T).

(iii) $$\Delta Y = \frac{\Delta X}{0.01} = 100$$

This means that giving me an additional unit of currency will increase total income by 100, as it feeds back into income and consumption infinitely.

(iv) This is the question where I would like some guidance. Here is my work so far:

We have:
$$ C= a + c(Y-T) - d\alpha Y$$

The multiplier associated with an increase in G should now be:
$$\frac{1}{1-c} + \frac{1}{1-d\alpha}$$
The first part is the "old multiplier, the second is the effect of the new part of the consumption function? I am not sure that this is correct, happy to receive comments!

This would mean that $c=d\alpha$.

And then, the multiplier associated with an increase in T:

1st round: Y increases by $c\Delta T$
2nd round: C increases by $c^2\Delta T + d\alpha \Delta T = 2 c^2\Delta T$
Then Y increases by $2 c^2\Delta T$
3rd round: C increases by $4 c^3\Delta T$

Does this mean that the multiplier is this sum: $$2^0C^1\Delta T + 2^1C^2\Delta T + 2^2C^2\Delta T + ... $$

And then the balanced budget multiplier would be this last result + 1 (the other multiplier, from the increase in G)?

I'd be super grateful to anyone who could help me with question (iv)!


texts:
Mueller (2015, working paper) says that an HP filter with smoothing parameter 900,000 (for monthly data) corresponds to a smoothing parameter of 100,000 for quarterly data.

How does one do this exact calculation? If I were to calculate the corresponding annual parameter, how would I proceed?


texts: Are there any studies, academic papers or articles that defy "common" knowledge", i.e that patents give an incentive for R&D to private business?

texts:
In Economic Growth and particularly dynamic optimization. My professor taught us that an intertemporal allocation is a dynamic optimum(Pareto Optimum) only if(necessary condition) at any given instance it is a stationary(instant, contemporary) optimum.

I questioned about patents. We are sacrificing the present for R&D. We are creating a monopoly to give incentives for R&D. So obviously it cannot be at present, instantly pareto optimal. Nonetheless couldn't patents help? Since probably they give incentives for R&D?

The professor replied saying that this is exactly why some researchers in Industrial Organization defy, question patents and their benefits.

Could pharmaceuticals work just as well or even better with no patents? In work just as well I mean the intensity of the incentives for R&D.


texts: How to prove that the walrasian demand function $x(p,w)$ is continuous in $p$ and $w$?

texts: If the utility function $u$ is continuous and satisfies local nonsatiation, and walrasian demand function $x(p, w)$ is a function (i.e. always map to only single values), how to prove that $x(p,w)$ is continuous in $p$ (price vector) and $w$ (wealth)?


texts: Interpretation of the growth rate of consumption in a simple one-good model

texts:
In Perman et al. "The efficient and optimal use of natural resources" it is presented a simple single-good model of welfare dynamic optimisation with non-renewable natural resource where:

Obj:
$$
max \int_{t=0}^{t=inf}{U(C) e^{-\rho t} dt}
$$
s.t.
$$
\dot S_t = -R_t
$$
$$
\dot K_t = Q(K_t,R_t)-C_t
$$

That is, the economy is comprised of a single output Q that can be either consumed or added to the capital stock K (that doesn't depreciate).

Solving the model and rearranging the first order conditions, the book found that among the optimal path the growth rate of consumption is:

$$
\frac{\dot C} {C} = \frac {Q_k - \rho}{\eta}
$$

where $Q_k$ is the marginal product of the capital, $\rho$ is the social discount rate and $\eta$ being the elasticity of the marginal utility with respect to consumption is, under bland assumptions, guaranteed to be positive.

Now, my problem is the interpretation of the sign implications of this equation.

If $Q_K$ is greater than $\rho$, the consumption rate increases (and the opposite). What does it mean?

The books explains it considering that $\rho$ (the social discount rate) reflects impatience for future consumption, and $Q_K$ (the marginal product of capital) is the pay-off to delayed consumption.

Under this interpretation the relation implies that along an optimal path
when ‘pay-off’ is greater than ‘impatience’ "consumption is increasing", or that "the economy will be accumulating K and hence growing".

But in my experience if $Q_K$ is higher than the discount rate, I have an higher incentive to stock K rather than consume, so how the consumption could increase ?
Also, it is said that "when ‘pay-off’ is less than ‘impatience’, the economy will be running down K.", but how can the K reduce in this simple model where there is no capital depreciation?


texts: How can 1 BTC gain value in USD if inflation is happening?

texts:
So, right now, 1 BTC (bitcoin) is worth ≈ 578.25 USD. But, with the inflation of the USD, how can 1 BTC still hold its value at 578.25? Why doesn't it decrease?

Let's set this example:

1 BTC = 1 USD.

Then, the USD loses half of its value; 1 USD is now actually worth 0.50.

Why won't the BTC lose half of its value?

I guess this principle applies to any currency and I can't seem to grasp the idea.

So, any help will be appreciate.

I also hope that you can understand my question and if you need clarification, please ask!


texts: Is optimal labour zero when (i) capital fixed and (ii) elasticity of substitution less than 1?

texts:
I am getting some "weird results". I find that in a CES, with short term fixed capital and elasticity of substitution smaller than one, it is optimal for firms to hire zero labour, which seems at odd with the idea that the marginal product of labour is always positive (except in the extreme case of Leontief, where $\rho = -\infty$).

Assume a simple CES production function:

$$Y = A\left( \alpha L^{\rho} + (1-\alpha)K^{\rho} \right)^{\frac{1}{\rho}}$$

Assume that capital is fixed in the short term, so the firm only optimises over  $L$. Importantly, the firm must pay the cost of capital anyway. Therefore, as long as $p>0$, the firm is always better off by producing something. Thus, the key question is how much labour to hire.

Under competitive markets, optimal labour comes from:

\begin{equation}
\frac{\partial Y}{\partial L} \equiv \alpha A^{\rho} \left(\frac{Y^*}{L^*}\right)^{1-\rho}  = \left(\frac{w}{p}\right)
\end{equation}

Importantly, notice that MPL is (i) always positive, (ii) for $\rho<1$ (including negative values) and $L^*=0$, it is infinity!. In other words, whenever there is imperfect substitution of factors, and the wage rate is non-infinity, you want to produce with some labour.

Replacing output into the above yields a single equation with only one unknown ($L_i^*$), which solution is:

$$ L^* = K \Omega^{\frac{1}{\rho}}  $$

where

$$ \Omega = \left(\dfrac{(1-\alpha)}{\left(\frac{w}{A p \alpha}\right)^{\frac{\rho}{1-\rho}}-\alpha}\right) $$

Now, discard the parameterisations where $\Omega<0$. These are corner solutions where $L^*=0$.

So far so good. Except for some strange result when $\rho<0$. To see this, let us replace optimal labour into the production function. After some rearranging, you get:

$$ Y^* = AK\left(\alpha\Omega + (1-\alpha)\right)^{\frac{1}{\rho}} $$

Now, compare this with the case of zero labour. Let us call this $Y_0$. Here, output is:

$$ Y_0 = AK(1-\alpha)^{\frac{1}{\rho}} $$

Now, we want to know under which parameterisation the firm is better off producing with zero labour. Profits with optimal labour and with zero labour are respectively:

$$ \pi = pY^* - rK - wL^* $$

$$ \pi_0 = pY_0 - rK $$

Thus, the firm will produce with no labour iff $\pi_0> \pi$, which is:

$$ wL^* > p(Y-Y_0) $$

So, if the labour costs do not compensate for extra profits, the firm will choose $L^*=0$. Here is where the problem arises: for $\rho<0$, $Y-Y_0$ is always negative! Which means firm will produce with zero labour.

To see this, let us find the conditions under which $\Delta Y=Y-Y_0<0$. This is,

$$ AK\left[\left( \alpha \Omega + (1-\alpha)\right)^{\frac{1}{\rho}} - (1-\alpha)^{\frac{1}{\rho}}  \right] <0 $$

$$ \left( \alpha \Omega + (1-\alpha)\right)^{\frac{1}{\rho}} < (1-\alpha)^{\frac{1}{\rho}} $$

Noting that $\rho<0$ will invert the components, you get:

$$ \frac{1}{\left( \alpha \Omega + (1-\alpha)\right)} < \frac{1}{1-\alpha} $$

Which is clearly true for:

$$ 0< \alpha\Omega $$

So, for "normal" parameterisations where $\Omega>0$, we can see that $Y-Y_0<0$ is always true.

I have confirmed this in R. The following code produces delta in output = -15:

rm(list=ls())

rho       <- -0.5
alpha     <- .6
A <- 1
p <- 1
w <- 0.7

K <- 2.756729
omega = (1-alpha)/((w/(alpha*A*p))^(rho/(1-rho))-alpha)
L = K*omega^(1/rho)

ll = alpha*L^rho
kk = (1-alpha)*K^rho
tr = (1/rho)
Y = A*(ll+kk)^tr
Y0 = A*(kk)^tr

delta_output = Y-Y0

delta_profits = p*(Y-Y0)-w*L

if I change $\rho$ to 0.5, you get the desired result (that using labour does increases output).

You can also see the plot of delta output here. It is clear that the delta output is always negative, and asymptotically zero for $x=\infty$, which is when $L^*=0$.


texts: In March 2020, why did stock indices of Asian countries that curbed COVID19 still plummet?

texts: By March 1 2020, both HK and Japan restrained and quelled COVID19, compared to  France, USA, UK. Don't hesitate to discuss other countries unscathed by COVID-19.


texts: Why is the current WDI missing CPI data for some countries (including the UK and China)?

texts:
I'm downloading data on inflation in different countries, and using the World Bank's World Development Indicators (WDI). Specifically, the Consumer Price Index series (CPI). (http://data.worldbank.org/indicator/FP.CPI.TOTL)

Current edition of WDI (annual CPI data) has some weird missing data series. There is no data provided for CPI in the UK from 1960-1987. The series for China starts in 2010. For Argentina, no data until 2014.

I could certainly believe there is insufficient data for some countries in some years (say, France during World War II). But it's hard to believe that data in the UK were insufficient to calculate a CPI prior to 1988. Similarly for the other examples.

Anyone have any ideas?


texts: What is the difference between risk, uncertainty and ambiguity

texts:
I am trying to pin down the difference between risk, uncertainty and ambiguity.

As I understand, when behavioral economists talk about choice under uncertainty, they mean choice when agents face risk (known probability distribution over a range of outcomes) versus ambiguity (unknown probability distribution). So uncertainty is a blanket concept that can be broken down into risk and ambiguity. See for example Dannenberg et al (2014).

I also understand there is a debate on the meaning of these terms going back to Knight (1921) and Ellsberg (1961). Are there any competing definitions to the one above?


texts: So what exactly happens to the real interest rate in the long run?

texts:
I have two books both written by MIT professors, Macroeconomics by Blanchard and Economics by Acemoglu.

Regarding to what happens to real interest rate in the medium/long run after the central bank lowers the interest rate, the two books has two very different explanations.

Blanchard explains through the IS-LM and AS-AD model that increase in real money stock leads to decrease in real and nominal interest rate in the short run, but in the medium run, because output returns to natural level of output, the real interest rate returns to the natural interest rate. Therefore money growth has no effect on real interest rate in the medium run.

But in Acemoglu's book it says and I quote

  The long-term real interest rate is the long-term nominal interest
  rate minus the long-term expected inflation rate. When the Fed
  influences short-term interest rates, such as the federal funds rate,
  this affects the long-term nominal interest rate. A long-term loan is
  like a combination of short-term loans. You can think of a 10-year
  loan as ten 1-year loans lined up one after the other. When the
  federal funds rate goes down, the interest rate for the first 1-year
  loan goes down. In addition, a change in the federal funds rate is
  usually not reversed for several years, so several of the 1-year loans
  in the 10-year loan package are affected. In most cases, when the Fed
  lowers the federal funds rate this has little impact on long-term
  inflationary expectations. Summing this up, the long-term real
  interest rate tends to fall when the federal funds rate falls because
  the long-term nominal interest rate falls and inflation expectations
  tend to stay roughly the same.

Did I misinterpret the two authors or what?

Can I assume Blanchard's medium run and Acemoglu's long-term are the same thing in this context?


texts:
Walras's law is stated for an exchange market: each agent comes to the market with a certain endowment of each commodity, a price-vector is determined, and the demand of each agent is the best bundle that the agent can afford by selling his endowment in the given prices. Walras's law says that, in any price-vector, the total value of the excess demand (i.e., the price-vector times the excess-demand vector) is zero.

There is a different model called a Fisher market, in which each agent comes with a certain budget of fiat money, the market-manager comes with a fixed quantity of each commodity, a price is determined, and the demand of each agent is the best bundle that the agent can afford with his given budget.
In such a market, it does not seem true that the total value of the excess demand is zero. For example, if the prices are very low, then all agents will want to buy all commodities, so the excess demand will be positive.
Is there a variant of Walras's law that holds in a Fisher market?


texts: For what demand function is a monopoly most harmful?

texts:
Consider a firm with zero marginal cost. If it gives the product for free, then all the demand is satisfied and the social welfare increases by the maximum possible amount; call this increase $W$.

But because the firm is a monopoly, it reduces the demand and increases the price in order to optimize its revenue. Now the social welfare increases by a smaller amount, say, $V$.

Define the relative loss of welfare (deadweight loss) as: $W/V$. This ratio depends on the shape of the demand function. So my question is: is this ratio bounded, or can it be arbitrarily large? In particular:

If $W/V$ is bounded, then for what demand function is it maximized?
If $W/V$ is unbounded, then for what family of demand functions can it become arbitrarily large?

Here is what I tried so far. Let $u(x)$ be the consumers' marginal utility function (which is also the inverse demand function). Assume that it is finite, smooth, monotonically decreasing, and scaled to the domain $x\in[0,1]$. Let $U(x)$ be its anti-derivative. Then:

$W = U(1)-U(0)$, the total area under $u$.
$V = U(x_m)-U(0)$, where $x_m$ is the amount produced by the monopoly. This is the area under $u$ except the "deadweight loss" part.
$x_m = \arg \max (x \cdot u(x))$ = the quantity which maximizes the producer's revenue (the marked rectangle).
$x_m$ can usually be calculated using the first-order condition: $u(x_m) = -x_m u'(x_m)$.

To get some feeling of how $W/V$ behaves, I tried some function families.

  Let $u(x)=(1-x)^{t-1}$, where $t>1$ is a parameter. Then:

  $U(x)=-(1-x)^{t}/t$.
  The first-order condition gives: $x_m=1/t$.
  $W=U(1)-U(0) = 1/t$
  $V=U(x_m)-U(0)=(1-(\frac{t-1}{t})^{t})/t$
  $W/V=1/[1-(\frac{t-1}{t})^{t}]$

  When $t\to\infty$,  $W/V \to 1/(1-1/e)\approx 1.58$, so for this family, $W/V$ is bounded.

But what happens with other families? Here is another example:

  Let $u(x)=e^{-t x}$, where $t>0$ is a parameter. Then:

  $U(x)=-e^{-t x}/t$.
  The first-order condition gives: $x_m=1/t$.
  $W=U(1)-U(0) = (1-e^{-t})/t$
  $V=U(x_m)-U(0)=(1-e^{-1})/t$
  $W/V=(1-e^{-t})/(1-e^{-1})$

  When $t\to\infty$, again $W/V \to 1/(1-1/e)\approx 1.58$, so here again $W/V$ is bounded.

And a third example, which I had to solve numerically:

  Let $u(x)=\ln(a-x)$, where $a>2$ is a parameter. Then:

  $U(x)=-(a-x)log(a-x)-x$.
  The first-order condition gives: $x_m=(a-x_m)\ln(a-x_m)$. Using this desmos graph, I found out that $x_m \approx 0.55(a-1)$. Of course this solution is only valid when $0.55(a-1)\leq 1$; otherwise we get $x_m=1$ and there is no deadweight loss.
  Using the same graph, I found out that $W/V$ is decreasing with $a$, so its supremum value is when $a=2$, and it is approximately 1.3.

Is there another family of finite functions for which $W/V$ can grow infinitely?


texts: Assume  a random sample X1, ..., Xn with a normal distribution with mean μ and variance σ2.  How do we know the following estimator is unbiased, but inconsistent?


texts: CES production function application problem

texts:
I'm currently trying to do some estimations using the micEconCES package in R by Henningsen/Henningsen (2011). My issue is that I am not very familiar with R and I'm trying to implement my own dataset to get the estimations with the package. They authors of the paper created this data set for the estimations.

R> set.seed( 123 )
R> cesData <- data.frame(x1 = rchisq(200, 10), x2 = rchisq(200, 10), x3 = rchisq(200, 10), x4 = rchisq(200, 10) )
R> cesData$y2 <- cesCalc( xNames = c( "x1", "x2" ), data = cesData, + coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) )
R> cesData$y2 <- cesData$y2 + 2.5 * rnorm( 200 )
R> cesData$y3 <- cesCalc(xNames = c("x1", "x2", "x3"), data = cesData, coef = c( gamma = 1, delta_1 = 0.7, delta = 0.6, rho_1 = 0.3, rho = 0.5, + nu = 1.1), nested = TRUE )
R> cesData$y3 <- cesData$y3 + 1.5 * rnorm(200)
R> cesData$y4 <- cesCalc(xNames = c("x1", "x2", "x3", "x4"), data = cesData, coef = c(gamma = 1, delta_1 = 0.7, delta_2 = 0.6, delta = 0.5, rho_1 = 0.3, rho_2 = 0.4, rho = 0.5, nu = 1.1), nested = TRUE )
R> cesData$y4 <- cesData$y4 + 1.5 * rnorm(200)

The ﬁrst line sets the“seed”for the random number generator so that these examples can be replicated with exactly the same data set. The second line creates a data set with four input variables (called x1, x2, x3, and x4) that each have 200 observations and are generated from random χ2 distributions with 10 degrees of freedom. The third, ﬁfth, and seventh commands use the function cesCalc, which is included in the micEconCES package, to calculate the deterministic output variables for the CES functions with two, three, and four inputs (called y2, y3, and y4, respectively) given a CES production function. Now in my paper I'm trying to estimate the CES function for the U.S. at the Aggregate Level for the two input case with capital and labor. So what I did is I gathered data from the World Bank Data Base from 1990-2015, where I used Gross Fixed Capital Formation for capital and total Labor Force for Labor.

The authors did f.e. a non linear estimation the following way

R> cesNls <- nls( y2 ~ gamma * ( delta * x1^(-rho) + (1 - delta) * x2^(-rho) )^(-phi / rho), + data = cesData, start = c( gamma = 0.5, delta = 0.5, rho = 0.25, phi = 1 ) )
R> print( cesNls )

Now I want the exact same thing for my own data Set which is called Data_Extract_From_World_Development_Indicators. So what I did is firstly

R> ceslan <- cesCalc( xNames = c( "GrossFixedCapitalFormation", "LaborForce" ), data = Data_Extract_From_World_Development_Indicators, coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) )

So i replicated

R> cesData$y2 <- cesCalc( xNames = c( "x1", "x2" ), data = cesData, coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) )

All I did was changing the name of the Dataset and replaced x1 and x2 with my two variables for capital and Labor.

Afterwards I tried to do the non linear estimation

R> cesulan <- nls(y2 ~ gamma * (delta * GrossFixedCapitalFormation^(-rho) + (1-delta)*LaborForce^(-rho))^(-phi / rho), data = Data_Extract_From_World_Development_Indicators, start = c(gamma = 0.5, delta = 0.5, rho = 0.25, phi = 1) )

Now this is where my Problem is: I dont know what variable is meant to be y2 in my dataset. I can see in the formula that y2 ~ gamma *... so ist plotted against the rest of the term, but I dont know what Kind of value I need to plug in there. Does anyone have any advice?


texts: Data of Inflation and unemployment for a Panel Data

texts:
I am looking for data of Inflation and unemployment to run a Panel Data of a Philips Curve.

Can anybody help me with some website/source that I can find data like these?

In my mind I would need too many countries (60 is enough) with this information through, for example, 2010 until 2019. Is it possible to obtain these data?

Many thanks


texts: Money in utility function - Value function

texts:
I am reading Walsh's (2003) book on monetary economics. Specifically the chapter on money in utility function. I understand the basics of a value functions but I can't seem to get the same results as the author.

Where

I.e the per capita budget constraint. He then finds an expression for $w_{t+1}$:

This is the first source of my confusion. Previously he defines output per worker as a function of capital per worker, i.e $y_{t}=f(\frac{k_{t-1}}{1+n})$ where $n$ is the population growth rate. But all of a sudden he changes it to $\frac{f(k_{t-1})}{1+n}$. I am aware that there are many typos in this book, is this just one of them or am I missing something trivial?

Either way, he uses the budget constraint to express $k_{t}$ as $w_{t}-c_{t}-m_{t}-b_{t}$ and the definition of $w_{t+1}$ to express the value function as:

Now, I don't know if it is because I am sleep deprived or because there is a typo, but I just can't seem to get the same results as Walsh. E.g, differentiating w.r.t $c_{t}$ I get:

$u_{c}(c_{t},m_{t}) + \beta*V_{w}(w_{t+1})[\frac{-f'(w_{t}-c_{t}-m_{t}-b_{t})}{1+n}(-1)+\frac{1+\delta}{1+n}(-1)]$

While Walsh gets

Am I missing something obvious or is there a typo?

Thanks in advance!


texts: What Creates the Price in the First Place

texts:
I just wanted to know if price changes how much quantity is supplied or demanded then what creates the price in the first place?

If you say that price affects supply and demand and supply and demand affect price then this just sounds like circular logic to me.

Thanks


texts: Has anyone ever done an analysis of the flexibility of the demand curve for summer camps?

texts: I'm trying to support an argument being made with respect to camp fee changes, and I would need to know if anyone has ever come up with a "rule of thumb" for demand drop due to price increases for a standard 1-week sleep-away summer camp?  No fancy expert training, or limited-access development, just standard summer camp  activities.


texts: What makes a shareholder a "shareholder of record"?

texts:
In public companies filling some reports with the SEC (10K for example), there is a mention of the number of shareholders of record.
Example:
"As of April 20, 2021, we had approximately 40 shareholders of record of our common stock."
Source: DTST 10K filling
A. What makes me legally titled the shareholder of record?
B. Is there a minimum equity to be owned to be recognized as a shareholder of record?
For example, if I bought 1 stock, am I included?
C. Can I view the list of shareholders, or get any information about them, or is it censored?


texts: Is non-monotonic local non-satiation supported by consumer theory in economics?

texts: In general (Walrasian) equilibrium, local non-satiation is one of the assumptions that guarantee existence of equilibrium. Question is, is non-monotonic local non-satiation preference supported by rational consumer theory in economics?


texts:
I'm asking just one question (it's in bold). If you treat any sentence with a question mark as another question and thus violating the policy on "focusedness", please steer clear of the text below the sentence in bold.
What impact does the paid vacation leave have on labor productivity? Do employees get re-energized and work better, or is there no such effect (or is it outweighed by 160 or whatever lost working hours)? Are there any studies on that, what are their conclusions? Are American employers stupid or, on the contrary, prudent when they show reluctance to grant such leaves to their employees in the absence of employee-oriented labor laws in the US? Note, I'm not asking whether there is any positive effect of paid vacation leaves generally (on mental health, reported happiness, etc.).


texts: What methods - inspired by Haavelmo’s Structural Econometrics - can show that a partial equilibrium model is unreliable?

texts:
According to Spanos 2014 Revisiting Haavelmo's Structural econometrics: Bridging the gap between theory and data Dynamic Stochastic General Equilibrium models are statistically inadequate, in such an order of magnitude as to render them useless.

  The most serious problem with DSGE models is that they are often statistically inadequate. Advocates of DSGE modeling, however, have
  put forward a number of arguments to explain away the unreliability of
  their evidence, such as ‘the price one has to pay for rigorous and
  policy-relevant theoretical models’ (Lucas, 1980, p. 696), or simply
  inevitable: “The models constructed within this theoretical framework
  are necessarily highly abstract. Consequently, they are necessarily
  false, and statistical hypothesis testing will reject them. This does
  not imply, however, that nothing can be learned from such quantitative
  theoretical exercises.” (Prescott, 1986, p. 10)

Part of my research involves using a partial equilibrium models to simulate a particular segment of an economy.

Considering the above, what methods would you start with to show that a given equilibrium model is statistically unreliable?


texts: Did the Bank Of England say QE doesn't work?

texts:
https://www.bankofengland.co.uk/working-paper/2020/does-quantitative-easing-boost-bank-lending-to-the-real-economy
Staff Working Paper No. 883 Published on 14 August 2020
From the conclusion:

If the policy objective is to provide an additional boost to the economy through supporting bank lending in a time of stress and uncertainty, it might be valuable consider using alternative credit easing tools. This may include programs such as Funding for Lending Scheme (FLS), Term Funding Scheme (TFS) and Term Funding Scheme with additional incentives for SMEs (TFSME). Other alternatives include guaranteed lending to small businesses, with no access to capital markets, or allow access to central bank balance sheet, maybe through a central bank digital currency. Our findings also encourage policy makers to pay attention to the type of asset purchased via the QE programs in relation with banks’ exposures (Rodnyansky and Darmouni, 2015). This is key to achieve an effective transmission of QE impact to the real economy via bank lending.

Am I understanding this correctly as saying that QE doesn't meet the stated goals? Or is it (in some way I don't follow) saying that it doesn't meet some subset of goals? If the latter, what does it achieve?
If it is saying that it achieves nothing much, why still do it?
(Edit, picking up @brian-romanchuk comment)
The abstract says

Overall, our findings suggest that, if banks are not adequately capitalised, risk-based capital constraints can limit the transmission of expansionary unconventional monetary policies via the bank lending channel, and provide incentives for carry trade activities.

What I'm asking is, what work is "via the bank lending channel" doing in this sentence? Is QE achieving things in some other channel?


texts: Limits to Growth: Is environmental collapse by 2030 a likely scenerio?

texts:
According to a simulation from 1972, the results of which were published in 'The Limits to Growth' environmental collapse is due mid 21st century. The Guardian reports that Dr. Graham Turner reran the simulations using recent data and the collapse is actually due sooner. Here is the referred paper by Dr. Graham Turner:
Quoting from his profile by the Guardian:

Dr. Graham Turner is principal research fellow at the University of Melbourne's Melbourne Sustainable Society Institute. He has a background in applied physics and his current work involves whole-of-system analysis on the long-term physical sustainability of the environment and economy.

As economists do you think Dr. Turner is right?


texts: If I don't pay a debt, then the creditor takes my goods. Why, then, do Greek creditors not take Greece?

texts:
Normally, when you don't pay a debt, your creditors take your goods (house, car, etc).

If Greece cannot pay its debt, can its creditors take Greek goods (structures, cities, industries, lands, etc)? Can Germany, or other organizations, become owners of Greece?

Maybe that's a silly question, but for a non-expert it sounds logical.


texts: Is there proof that today more than 50% of the lowest income society lives worse than 50 years ago

texts:
The Economist on 12.11.2016 number (first number after getting US election results) wrote: "In real terms median male earnings are still lower than they were in the 1970s. In the past 50 years, barring the expansion of the 1990s, middle-ranking households have taken longer to claw back lost income with each recessions. Social mobility is too low to hold out the promise of something better. The resulting loss of self-respect is not neutralised by a few quarters or rising wages".

Are there economic data that supports the thesis "more than 50% of the lowest income society today lives worse than 50 years ago"? Of course - I have temptation to ask the following as well: and if yes - then what are the reasons of such failure of economic development and what economists suggest to do about this? But I will leave those two questions for other posts if the thesis will be true.

My intuition is that this thesis can be true. It is true, that computers, smart phones and other electronics are more available today but if we factor all the costs of living - starting from the bloated housing and real estate prices, increased cost of medicine and tuition fee then the result can be true - lowest income part of the society is living worse than 50 years ago when lasers, semiconductor technologies and lot of other technologies were nascent only.


texts:
Why is the method of moments estimator $g(\bar{Y})$ of $\theta$ only unbiased if $g(\mu)$ is a linear function of $\mu$?  (Note: It is assumed that $\theta=g(\mu)$ for some function $g$ and $\bar{Y}$ is a consistent and unbiased estimator of $\mu$)

I'm working in Appendix C (p.685) in the 6th edition of Wooldridge's Introductory Econometrics.  Many thanks in advance for helping me develop an intuition.