texts: Basic question on trade based on comparative advantage

texts:
The following question is taken from Economics: Principles and Applications 6th Edition, by Hall and Lieberman.

This question about applying the theory of comparative advantage between a hypothetical trade situation between US and China. Trade between these two countries involve only two goods - soybeans and T-Shirts. It has been established that the US has CA in soybean production whilst China has CA in T-Shirts. It is further known that, for the US, the opportunity cost of producing 100 bushels of soybeans is 200 T-Shirts. Now consider Qtn 9b in the top image.

My working is in bottom image and my final answer is that the US consumers will gain 70 more T-Shirts for consumption, compared to the situation before trade. However, in  an answer I found online, the US has 270 more T-Shirts available for consumption, compared to the situation before trade.

My answer was 70 more T-Shirts. Consumption experiences a net gain of 70. The raw gain in consumption due to importing from China is 270 but that is AFTER the US incurs the opportunity cost of producing 100 bushels of soybeans (due to specialisation) - which is decreasing production of T-Shirts by 200.

Where did I go wrong?


texts: Consumer preferences and government spending

texts:
I am studying for an exam and I am focusing on different types of preferences and shocks and the respective responses. This problem has been causing me trouble.

The representative consumer in an economy has the lifetime utility function:

$U = \sum \beta^t U(c_t, l_t)$, where $c_t$ is consumption in period t and $l_t$ is labor supply and $U(c_t, l_t)= c_t^\frac{1}{2} - l_t$. The production technology is given by $y_t= A_t \times l_t$ where $y_t$ is output in period t. Consumers can lend and borrow freely at the interest rate $r_t$ and the government spending in period t, $g_t$ is exogeneously given and is financed by lump-sum taxes and government debt.

1) What is the intertemporal elasticity of substitution in consumption?

I know the IES is is the measure of responsiveness to the growth rate of consumption to the real interest rate.

2) Derive equilibrium levels of consumption, output, employment and interest rate in each period in terms of exogenous variables and given parameters in the model.

3) Discuss the effects of changes in government spending on consumption, output, employment and interest rate. Is there a crowding out effect of government spending in this economy?

4) Is it true that the level of government spending is irrelevant in this economy?

I think the answer to this is no intuitively.

5) Is it true that the distribution of government debt across time is irrelevant in this economy?

I think the answer to this is yes, it is true due to Ricardian equivalence.


texts: How can trailing and forward P/E ratio of main stock markets show such huge difference

texts:
I've recently found this web page, listing the average P/E Ratios of main stock markets:

http://www.zutosmoney.com/

Here I reproduce just a small extract:

INDEX - Country - Trailing PER - Forward PER
CAC40 - France - 24.3 - 13.2
IBEX35 - Spain - 21.4 - 12.7
NASDAQ - US - 34.5 - 18

I've noticed two things:

Most trailing P/E ratios are quite high: I understand that 'normal' values should be in the range of 16 - 20.
There is a very big difference between trailing P/R and forward P/R. I understand that trailing is calculated using the actual earnings of past year, and forward is calculated with the companies' annual forecasts.

Am I right concluding that:

Stock markets are probably over-evaluated, considering the earnings in 2016?
Stock markets are possibly over-optimistic regarding the earnings in 2017?

[Edit: I've corrected my conclusions after answer from Klas Lindbäck, to avoid expressing too strongly my personal concerns about the earnings of companies in 2017]


texts: Can the internet be characterized as a public utility?

texts:
The idea of what a public utility is, economically, rather than just legally is not a new point of discussion. Philosophers like John Stuart Mill argued for the public provision of water and gas, based on them being natural monopolies (see here, V.11.36).

Public utilities are a type of public good provision related to services that may have a tendency to form a natural monopoly. Natural monopolies are cases where it may be more efficient to have one provider rather than competing providers for a service, due to large economies of scale, large barriers to entry, inelastic demand of consumers, the need for over-engineering (being able to provide for peak demands), among other factors. Providing tap water, gas, or electricity, usually requires a lot of infrastructure that is expensive to put into place, so this is one example of why these goods do not have a lot of competition in their provision, as these goods tend to exhibit naturally monopolistic tendencies.

Although the internet requires a large infrastructure and may have large economies of scale, it does not seem to neatly fit the idea of a public good. A public good is usually non-rivalrous and non-excludable, but the internet however seems to definitely be excludable, and in some places, rivalrous, at least partially (sharing bandwidth with your extended family and/or your neighbor who downloads a lot of mysterious content). There is also a laymen argument to be made that the internet could be a luxury good instead of a necessity, making it inappropriate to regulate as a public utility.

There is some evidence that monopolies or oligopolistic competition in related industries, such as cable television, decrease the quality of its provision in the absence of regulation, but my concern is not to debate regulation with this question.

  My question is, what economic literature is there for characterizing the economic properties of the internet, either as a public utility as opposed to a luxury or something else?

In discussing the answer to this question, papers regarding whether the internet should be regulated as a public utility may pop up, and that is okay. But the primary question I have is not what the nature of regulation should be, if any.


texts: Specification form for household utility function

texts:
What determines the choice of the functional form to be adopted for the household CRRA utility function, when utility depends on consumption and leisure?

For examples, we have these three functional specifications:

$U(c,l)=\left[\dfrac{c^φ l^{1-φ}}{1-θ}\right]^{1-θ}$
$U(c,l)=\dfrac{c^{1-φ}}{1-φ}+\alpha \dfrac{(1-N)^{1-γ}}{1-γ}$
$U(c,l)=\dfrac{c^{1-θ}}{1-θ}-\alpha \dfrac{N^{1-γ}}{1-γ}$

c: consumption, l: leisure, N: labor supplied. Total time endowment: unity


texts: Should I include country dummies when I combine datasets of 3 countries?

texts:
I am currently doing the analysis using firm-level data of three countries combining together.
Also, it is a cross-sectional analysis. Therefore, in the regression, I control for industry dummies to account for differential effects in industry level.

I think I don't need to control for country dummies due to some reasons:
(1) The countries that I use in my analysis share similar characteristics including development level, political, and socio-economic conditions.
(2) There are only three countries in my analysis.

In this case, I expect that the results will not be affected even though I don't control for country specifics.

However, I am not sure if my idea is appropriate since I cannot find any reference to support it yet.
Therefore, I would like to ask everybody here if you have any idea whether or not country dummies is necessary in my case.

Thank you!


texts: General equilibrium papers on universal basic income

texts:
Are there any microeconomics or general equilibrium articles on universal basic income?

Papers dealing with general wealth transfer mechanisms where a basic universal income would be a subset of the general transfer mechanism discussed are also fine.


texts:
Why are the way banks are established and spread out in Canada and US so different?

Canada:
There are only six major banks and most products offered are very competitive. Its almost unusual to hear or see any other minor or regional bank.

US:
Literally, there are thousands of banks. Although there are few big ones, like BoA, Wells Fargo, Chase, there are thousands of regional banks, even down to county levels.

What are the advantages of having multiple individual banks?

Why did US encourage this type of proliferation of banks while it did not happen in Canada?


texts: Goldfeld - Quandt test statistic equal to 1

texts:
I wonder what it means if the statistic (ratio) of this test is one?
The statistic is built from sample splitting. Then you have to calculate the ratio RSS2 / RSS1, which are the Residual Sum Squares of the new subsamples.
I think it means that both subsamples have the same variance but I am not sure at all.
Thank you in advance.


texts: If the relative share of inputs is constant in a production process, does that mean that the inputs are used in fixed proportion?

texts:
One of the assumptions in Euler's adding up theorem is:

  Fourth, the relative shares of the factors are constant and independent of the level of the product.

Does this mean that the factors are used in fixed proportions? Does this further mean that the elasticity of substitution is 0?

If not, what is the difference between having relative shares of factors constant and fixed proportions?


texts:
To my understanding, all systems have a function.  For instance, the function of the respiratory system is to supply oxygen to the body.  The function of the digestive system is to break down and disseminate nutrients.  The function of a mass transit system is to facilitate large scale public transport.

Capitalism is defined in Merriam-Webster as,

  an economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market

So clearly, capitalism is a system, but I can't glean from that definition its purpose.

What would most economists consider the function of capitalism?

Please be clear to separate, if you will, this system's function from the functions of other economic systems in your answer.


texts: Can the cyclicality of the real wage be used as a measure for the degree of competiveness in the labour market?

texts:
When reading the answers to this question of mine, I'm left wondering if cyclicality of real wages can be seen as an indicator for the nature and degree of competition in the labour market.

In perfect competition, we would have high procyclical wages, under monopsony acyclicality.

What would be the cyclicality, if the labour market could resemble a oligopoly(a highly unionized market could resemble an oligopoly, right?), or if the labour market worked as if in monopolistic competition?


texts: What are concrete values of public goods?

texts: Are there any good studies on what are estimated values of public goods? For example, suppose a public library, bridge, school, or lighthouse is a public good, what is the value per person for these goods? I am just looking for typical cases, like a public park in a typical American city.


texts:
I'm trying to solve followed first-price auction problem.

Bidder's pdf is
$$
f(v_i)= \begin{cases}
\dfrac{1}{8}v_i, & \text{if} & 0\leq v_i\leq4\\
0, & \text{if} &  \text{otherwise}\\
\end{cases}
$$

Bidders only know their own values. One gets 0 if lose the auction and ($v_i-b_i$) if win the auction game.

The question asks the symmetric bidders' bid under Bayesian Nash equilibrium and expected payoff of bidders and seller.

So, one bidder will maximize as follows:

$$\max_{b_1}\,\,(v_1-b_1)\Pr(b_1>b_2)$$

If we take the derivative with respect to $b_1$ we get

$$b(v_1)=\dfrac{\int v_1f(v_1)\,dv_1}{F(v_1)}$$

We know from question $f(v_1)=\dfrac{1}{8}v_i$ and we can find $F(v_1)=\dfrac{1}{16}v_i^2$. If we replace them, we get

$$b(v_1)=\dfrac{\int v_1\dfrac{1}{8}v_1\,dv_1}{\dfrac{1}{16}v_1^2} = \dfrac{2}{3}v_1$$

So this is the bidding of bidder 1. However, I couldn't find the expected payoff bidder 1 and bidder 2. My question is how can I use PDF or CDF to find the expected payoffs of the bidders.


texts:
Cross-ownership is a phenomenon where companies own parts of other companies they do business with. An example:

  Two companies are now involved in the diamond operation, the mining group Anglo-American, and De Beers. The two are umbilically linked, making them impregnable to corporate raids. Some reshuffling has gone on of late but not much has changed: De Beers owns 42 per cent of Anglo- American and a similar share of its capital is owned by the mining group.

Source

Assume that asset prices are the net present value of all future dividends, i.e. they contain no bubbles. (Incredible assumption, I know.)
Suppose Anglo-American changes a minor operating procedure and as a result will save a small amount of money each year, hence the net present value of its profits increase by \$1. This should increase the company value (and hence stock price) of Anglo-American, but since De Beers owns parts of the company it will share the increased cashflow and its company value (and hence stock price) should increase as well, increasing the company value of Anglo-American again, etc.

If I wanted to calculate the exact change in company value would I be correct in assuming I would have to create some sort of ownership matrix:
$$
M =
\begin{bmatrix}
58\% & 42\% \\
42\% & 58\%
\end{bmatrix}
$$
and take the Leontief inverse of this?
$$
\begin{bmatrix}
\Delta p_{AA} \\
\Delta p_{DB}
\end{bmatrix}
= (E-M)^{-1} \begin{bmatrix}
1 \\
0
\end{bmatrix}
$$

What if the Leontief inverse of the ownership matrix does not exist? E.g. both companies own half of the other. Is there any way to proceed in this case? (Note: I am not sure if it was possible to price companies with such an ownership structure to begin with.)


texts: Showing that production technology exhibits decreasing returns to Scale

texts:
The Question
Suppose a firm has a production function given by
$$y=F(L,K)=L^{1/4}K^{1/4}$$
where L and K denote inputs used in the production of y units of output.
(a) Determine whether marginal products are diminishing
(b) Show that production technology exhibits decreasing returns to scale
My attempt
(a) So the marginal products, $MP_L$ , $MP_K$ are:
$$MP_L={\partial{F}\over\partial{L}}={1\over{4}}L^{-3\over{4}}K^{1\over{4}}$$
$$MP_k={\partial{F}\over\partial{K}}={1\over{4}}L^{1\over{4}}K^{-3\over{4}}$$
To determine if the marginal products are diminishing one needs to simply derive the equations again. Which would be:
$${\partial{MP_L}\over{\partial{L}}}={-3\over{16}}L^{-7\over{4}}K^{1/4}$$
and
$${\partial{MP_k}\over{\partial{K}}}={-3\over{16}}L^{1\over{4}}K^{-7\over{4}}$$
When both Marginal products are derived, their results are both are $<0$ which would imply that they are diminishing.
(b) This is where I get a little confused, is it not because we know that the Marginal products are diminishing, we know that the production technology exhibits decreasing returns to scale?


texts: Why slope is constant in demand/supply curve?

texts: I was reading Mankiw and it showed variation of demand/supply curve with external factors. However, in all the cases the curves only shifted but didn't change in shape. What I am wondering is why the slope of these curves don't change?


texts: Non-negative deviations from Nash Equilibrium

texts: I know that in a Nash Equilibrium, no player can profitably deviate from the equilibrium strategy assuming that the strategies of the other players remain the same. My question is, what if a player can deviate to a different strategy that generates an equivalent payoff? Would this no longer be a Nash Equilibrium?


texts: Effect of risk premium on the money demand (LM curve)

texts: In short, I'm having problems understanding the LM curve, as the explanation given by the picture is for me, the 4th row is counter intuitive. When risk premium increases it causes the interest rates to go higher, but I don't understand how is it related to the lower demand of money? When there's more demand of money, the interest rates get higher and the curve should shift to the left. Please help.


texts: Can a game with a unique pure strategy Nash equilibrium also have a mixed strategy equilibria?

texts:
Consider an arbitrary 2x2 simultaneous game with complete information. Say that the model has only one pure-strategy Nash equilibrium. For example (first pay-off refers to Player 1):

                    Player 2
           +---+-------+-------+
           |   |   A   |   B   |
           +---+-------+-------+
Player 1   | A | (1,2) | (2,1) |
           | B | (3,3) | (1,1) |
           +---+-------+-------+

Here, (3,3) is the only pure-strategy Nash equilibrium. The reason there is just one is, apparently, because one of the players have a dominant strategy (Player 2 always prefers A). If we change this, we would get two pure-strategy equilibria.

Abstracting from the fact that the pure-strategy equilibrium is also a mixed strategy one with probability 0/100%, does any simple game with just one pure-strategy equilibrium have no mixed strategy equilibrium? Is there a formal proof of this?

I educated guess is that there is no mixed strategy equilibrium. The "proof" I can think of is a best response plot. Basically, one player has a dominant strategy which means that for any probability, her response is a vertical/horizontal line at 0 or 1 (depending how probability is defined). Thus, regardless of how the other player's best response line looks like (i.e. where the indifference probability is), it will only cross the other player's line in one point. That point is the pure-strategy equilibrium.

PS: the adjective "simple" is to avoid more complex game scenarios like repetition, cooperation, incomplete information, etc.


texts: Should unemployment caused by the government closing non-essential businesses during quarantine be counted as structrural unemployment?

texts:
I have following definition of structural unemployment (taken from "Modern principles of economics" by Tyler Cowen and Alex Tabarrok):

  Long-term unemployment caused by shocks or permanent features of economy making it harder for certain workers to find a job

So the answer to the question in the title would seem to be "No, because quarantine won't last so long that prices of wages and other factors of production would fully adjust to inflation. So unemployment wouldn't be long-term, thus it wouldn't be structrual unemployment".

But on the other hand, other three types of unemployment (seasonal, frictional, cyclical) don't seem to fit the bill. An example: Suppose prostituion is legal and I'm a prostitute. Due to pandemic the government decides that prostitution isn't an essential business and because it's not something that can be done online brothels are forced to be closed, including my brothel. My brothel is also a small business with very thin profit margins (consequence of very competitive market caused by low price of entering the market). In short, without its workers working it's unable to pay its rent and is kicked out by its landlord, spelling end to it. I try to find another job, but due to many other businesses closing down competition for very few vacant jobs is crazy and they disappear with speed of light. Is my unemployment seasonal? No, we don't have seasonal nationwide quarantines. Is it cyclical? No, because even if economy was booming nationwide quarantine and ban on non-essential businesses would still leave me and many other people without job. Is it frictional? No, I'm fairly certain that there is no a vacant job that is waiting for me to find it. Structrual unemployment seems to be closest to that I experience by its sprit. So, maybe the definition is too narrow and it's possible for unemployment be both short-run and structrual?


texts:
My professor stated four axioms in class

Scarcity
Rationality (aka purposive behavior)
Stable Preferences
Equilibrium

I don't understand what these axioms are for. I am used to axioms with distinct mathematical properties (eg definition of a vector space) and these axioms don't have that.
I had an exam question that said

  True/False/Uncertain. The Law of Demand is a direct result of diminishing marginal utility.

and I was supposed to use the scarcity axiom. But what does it mean to show this claim is false? The principle of scarcity is just that "resources are scarce". That's not mathematical. How can I prove the above statement is false using it?

My Question:

How can I tell when a question requires a proof versus merely conceptual reasoning / explaining? What is the difference between the two?


texts: Confusion about the EMP approach to perfect complements. Solved UMP but struggling with EMP

texts:
I have successfully done the UMP for perfect complements. I got

$$x^* = y^* = \frac{m}{p_x +p_y}$$
This makes intuitive sense  because for whichever good I have the least of, I don't want to buy more units of the other. So the total amount I should spend should be the optimum quantity times $p_x + p_y$.

However, I am completely lost about how to do the EMP version of this. I keep going in circles.

I have done the Lagrangian and gotten for $x > y$,  $e = p_y \bar{U}$ and for $x <y$ that $e = p_x \bar{U}$.

Here is my work:

https://math.stackexchange.com/questions/1252173/can-one-optimize-a-function-with-minx-y-as-a-constraint/1252341#1252341

But this doesn't make sense to me.  don't see how this relates to the solution I got for the UMP which did make sense.

What I am misunderstanding about the EMP that is leading to these nonsensical results that don't match what I did for the UMP?


texts: Supply and Demand: Why should lower costs lead to a rise in supply?

texts:
I know that the conventional explanation linking fall in cost of production and rise in supply is that a fall in cost of production of A means that it is more profitable to produce A. Thus, suppliers will be incentivised to produce more of A, hence rise in supply of A.

My question is - why should suppliers even want to produce more? Can't they just enjoy the higher profits attained automatically through the fall in COP? What exactly is the explanation for them wanting to produce more?

This is the missing link in many explanations I see and I hope to clarify this, thanks!


texts: Measuring macroeconomic variables more frequently

texts: What would be the costs and benefits of collecting and releasing macroeconomic data, say, monthly instead of quarterly, or weekly instead of monthly? And what are the barriers to doing so?


texts: What is Stated Capital? I have found some definitions on the Google, but I have not been able to comprehend it from this definitions. Could somebody explain it to me?


texts: Why the total value of the whole economy is constantly appreciating?

texts:
Take S&P for example. In the long run it just keeps climbing. Same for the market as a whole. Why would this happen? Why the market keeps going up (in the long term) all the time?

(source)


texts: Why is it that poverty incidence is high in the agricultural sector?

texts:
I read this article earlier, and the "experts" there say:

  "The incidence of poverty is very high in agriculture because of its low productivity."

  "The incidence of poverty is very high in agriculture because of its relatively slow growth."

But why do they say that? How about you? What do you think is the cause? To me, they keep saying that:

  "[T]he share of agriculture in GDP, and not the demand for agriculture per se, which declines as income per capita increases"

But why would you want to be more productive/produce more goods when people in general are going to have a pretty much similar demand for the product ('cause it says there that demand for agri products don't necessarily decline)?


texts: Why are future expenses considered less costly than expenses in the present?

texts:
I understand that future income is less valuable than income in the present because of the concept of present value, where money available today can be invested to earn interest or can be spent to avoid paying interest, whereas money that is not collected until the future cannot generate interest income or pay interest expenses.

However, if I want to explain why future expenses are considered less costly than expenses in the present, can I use the concept of present value to explain? I know it is linked somehow, but I don't know how to put it into words.

I would appreciate any help or hints. Thank you.


texts: Who really pays transaction taxes like VAT or sales tax?

texts:
In Europe, shop prices are typically displayed including VAT. This gives the impression that the seller is paying the VAT. They have to offer a competitive price, then a percentage of that is taken out as tax. But, if VAT didn't exist, sellers could offer a lower price. So in another sense, buyers pay the tax.

In the US, sales tax is typically added at the till. This makes it feel like the buyer is paying the tax. But ultimately, VAT and sales tax are the same (at the point of final sale) - does it really make a difference how the prices are displayed?

The same issue exists with income tax, stamp duty, and presumably many other taxes. It's quite integral to Western life that income tax is paid by the employee - you hear people say "I pay my taxes, I'm part of this society". But the need to pay income tax means that employers need to pay higher wages, so the employer is bearing the cost as well.

Does it make a difference what happens when the rate changes? For example, if income tax rises, typically salaries do not rise to match. But if sales tax rises, the the amount added at the till immediately rises too.


texts: Approximate factor model: Weakly correlated and eigenvalue

texts:
To my best knowledge, in Ross's APT, it is assumed that the pricing model is  the exact factor model.

Chamberlain (1983 ECTA) expanded it into the approximate factor model.

In the exact factor model, the covariance matrix of the error term is diagonal matrix with each variance on its diagonals, while in approximate factor model, the errors of the cross section can be "weakly correlated", which makes the covariance matrix non-diagonal matrix.

My questions are,

(1) Can we define "weakly correlated" in a rigorous statistical definition?

This paper(https://arxiv.org/pdf/1612.04990.pdf) defines it as "If we have an approximate factor structure, we expect a vanishing largest eigenvalue (of the covariance matrix)"

(2)Could you explain why the discussion of the strength of the correlation of the cross-section (off-diagonal of the covariance matrix) can be delivered with eigenvalues?


texts: Why does US jobs and inflation have an affect on European equities?

texts:
There are articles such as 'European shares crawl higher as investors eye US inflation data'. Is this just put down to Americans may have more money to spend overseas so investors speculate higher earnings or is there another relationship?

https://www.reuters.com/article/us-europe-stocks/u-s-jobs-report-boosts-european-stocks-idUSKCN1GL0ZU

Edit: Added article link for clarification.


texts: Wealth - Bond Market and Liquidity Preference Framework

texts:
I've been told that an increase in wealth will lead to an increase in both the demand for Bonds determined by the Theory of Asset Demand. This should shift the bond curve to the right, increasing Price and decreasing interest rate.

But for the liquidity preference framework, it says that an increase in income leads to an increase in wealth thus shifting the demand curve for money to the right and increasing interest rate.

How can wealth increase decrease the interest rate in the bonds graph but increase it in the quantity of money supply graph. I'm sure I'm missing out on something obvious.


texts: Under what condition is a cost function strictly concave in prices?

texts:
Define the unit cost function as
$$
c(w) = \min_{z\geq 0} w\cdot z
$$
subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We know from standard results that $c$ is concave and homogenous of degree one, but I would like to establish conditions on $f$ such that $c$ is also strictly concave.


texts: Solution method in Smith (2006) A Closed Form Solution to the Ramsey Model

texts:
I am trying to understand the way Smith demonstrates that the general solution to his equation (12) is (13) (see page 6).

  (12) \begin{eqnarray}
\dot{z} &=& (1- \alpha)\left[1-\left(\delta + \frac{\bar{x}}{1+\bar{x}Ae^{\bar{x}t}}\right)z\right]
\end{eqnarray}

  In the Appendix I demonstrate that the general solution to Equation (12) is:

  (13)\begin{eqnarray}
z &=& \frac{1}{\bar{x}+\delta} 2F1(1-\alpha,1,d;\omega)+B\bar{x}^{\alpha-1}e^{-(1-\alpha)(\bar{x}+\delta)t}(1+\bar{x}Ae^{\bar{x}t})^{1-\alpha}
\end{eqnarray}

  The Appendix:
  A.1
  \begin{eqnarray}
\dot{z} &=& -(1- \alpha)\left(\delta + \frac{\bar{x}}{1+\bar{x}Ae^{\bar{x}t}}\right)z
\end{eqnarray}
  This can be integrated to find the complementary solution:(A.2)
  \begin{eqnarray}
z_c &=& \bar{x}^{\alpha-1}e^{-(1-\alpha)(\bar{x}+\delta)t}(1+\bar{x}Ae^{\bar{x}t})^{1-\alpha}
\end{eqnarray}

  To find the particular solution to equation (12), I will use the method of variation of parameters. Conjecture that the particular solution is $z_p$ $=$ $z_c$$\Psi$, where $\Psi$ is an unknown function of time. Substituting this conjecture into equation (12), it follows that:
  (A.3)
  \begin{eqnarray}
\dot{\Psi} &=& \frac{1-\alpha}{z_c} &=& (1-\alpha)\bar{x}^{1-\alpha}e^{(1-\alpha)(\bar{x}+\delta)t}(1+\bar{x}Ae^{\bar{x}t})^{\alpha-1}
\end{eqnarray}

First, is (A.2) then just an integrated version of (A.1) or are there any other steps involved?

Second, I really do not see how he substituted the conjecture into 12 and how can he obtain (A.3) from this substitution? Especially here I am really lost and am lacking the imagination how he came up with $\dot{\Psi}$. Did he substitute $z_p$ for $\dot{z}$ or $z$ in (12)?

Citation: [Smith, William. (2006). A Closed Form Solution to the Ramsey Model. Contributions to Macroeconomics. 6.]


texts: What are the effects of abolishing the minimum wage?

texts:
There's this one guy out there, Peter Schiff, and he aired on Joe Rogan a while back. One part of the podcast really caught my attention, and it was when Schiff said that the minimum wage should be abolished.
Without making this question subjective, I'll provide an overview of his arguments, however, that's where I need some help since I'm not so sure on how they stack up to the real world.

Here's the arguments he made:
1. Fixes unemployment rate
A company is not going to hire someone for 15 dollars an hour (or whatever the minimum wage is) if their skill level is only worth 5/h. The company will lose 10/h if they hire someone like that! So instead, reduce the minimum wage so that company's can now pay people 3/h, opening the market for everyone.
Think of a wage as a ladder. It starts at zero, making it accessible for everyone to climb. However, a minimum wage raises the ladder, making it unaccessible to people that don't have good skills. By abolishing the minimum wage, the ladder will be at the ground, so everyone can climb up.
2. Provides an alternative to college/university
If you don't go to college for whatever reason, then your skill level is probably not above the minimum wage. This will make it extremely difficult to find a job. However, with the minimum wage, you can start at the bottom, making 2/h, and work your way up. Even if it's a simple job like moving boxes, you still learn discipline.
3. A minimum wage limits the ability to sell labour
If you can only worth 5/h, you'll never get a job with a minimum wage of 15/h. You'll actually lose money for the company. However, with the abolishment of the minimum wage, then people can sell their labour based on whatever skill their at.
4. Brings jobs back to us
Most jobs will soon be automated, or moved overseas where it's cheaper (India or someplace). However, without a minimum wage, these jobs will start migrating back to us, the original country.
This will create thousands of jobs and create new opportunities for people.

There, that should be Schiff's view on things in chronological order if I did everything right.
Now what I'm wondering is if these arguments actually stack up against the real world.
However, I do have some specific questions:

1. Will this fix unemployment?
2. Would competition naturally raise, prices? And by how much?
3. Whould this bring jobs back to the country?

Anything would help. Thanks.


texts:
I'm trying to understand how GPDI / GFCF are used in the real GDP calculations (when compared to net investment). In both the US / Denmark, the real GDP numbers seem to directly GPDI / GFCF without factoring in depreciation. Am I missing something here?

(Example: https://www.bea.gov/sites/default/files/2020-05/gdp1q20_2nd_0.pdf, the GPDI row has values that far exceed the 1-2% net investment estimate for the US).


texts: How does advertising improve the utility of a product?

texts:
In this research paper titled: Advertising Spillovers: Field-Experiment Evidence and Implications for Returns from Advertising, I come across the following assumption:

  Utility of a product at time t($u_t$) = Awareness about the
  product($alpha_t$) + Advertising intensity of the product at time
  t$f(A_it)$

Claim in the paper: (If utility is high, there is more likelihood that the user would buy the product.)

Advertising intensity means the number of times the user has seen the ad of the product in a single session on the website.

And the function $f(.)$ is non-decreasing.

So, my question is: How does the advertising intensity increase the utility of a product?

(Is it due to the $+ve$ information about the product given to the user through advertising, or did I go wrong in understanding the concept of utility somewhere?)


texts: Solving a maximization problem by substitution when the constraint is in implicit form

texts:
I am trying to understand how the first order conditions for an interior solution of a maximization problem were derived using the substitution method.

The problem is:
$$\max\limits_{x\ge0,y\ge0}P(a-x)+(1-P)(b-y)$$
subject to
$$Pf(x)+(1-P)f(y)=c$$
where: $a,b,c>0$, $P\in (0,1)$, $f:[0,+\infty]\to[0,+\infty]$, increasing and strictly concave over its domain.

I can see how this is solved using a lagrangian to find from the first order conditions that $f'(x^*)=f'(y^*)$. Strict concavity of $f$ then implies $x^*=y^*$. But I'm at a loss as to how we can solve it by substituting the constraint in the objective function. Since $f$ is invertible, if $y$ did not appear in the constraint I would find $x$ from the constraint by inverting $f$ and substitute it in the objective function. Doing this here leads to complications that seem unnecessary for this simple problem. There has to be a simpler way that I cannot figure out: what is it? Thanks!


texts: Question about Federal reserve open market operations - reducing money supply

texts:
I'm trying to understand how open market operations work to reduce money supply.

So the Federal Reserve sells bonds... when this happens, the bank balances of the bond-purchasers goes down... the bank balance of the Federal reserve goes up.

So now what does the Federal reserve do with this money... is the money just eliminated from the system completely? Or does the Federal Reserve hold that money? Does it even make a difference... Thanks.


texts: What's the status on uncertainty shocks?

texts:
Bloom (2009) analyzes the impact of uncertainty shocks, and Bloom et al (2014) propose a business cycle model based on these shocks.

It seems to be a young field, but is there any consensus on strength and weaknesses of this new shock? Is it the answer to some puzzles such as the risk premium puzzle?

What is the opinion of the literature about this field, and is there already a handbook chapter on this?


texts:
I'm not sure about this, can I ask you if I'm wrong? Thanks.
Data:
$$Q_{s}=P/2$$
$$Q_{d}=P-42$$
Questions:
a) How many units will be traded at 35 dollars? At $14 dollars?
b) What quantity at what price will be in equilibrium?
c) What is the total revenue from sales?
Answer a
$$Q_{s}=P/2 => P=2Q_{s}$$
$$Q_{d}=P-42 => P=Q_{d}+42$$
$$P/2=P-42$$
$$P_{eq}=84$$
35 dollars is below 84 dollars, therefore, there is a shortage (we should plug the 35 dollars into the supply equation)
=> 17 units will be sold at that price (am I correct to round down?)
$$Q_{s}=35/2 = 17.5$$
14 dollars also is below 84 dollars, therefore, there is a shortage too (we should plug the 14 dollars into the supply equation)
=> 7 units will be sold at that price
$$Q_{s}=14/2 = 7$$
Answer b
$$P_{eq}=84$$
$$Q_{eq}=P_{eq} /2 = P_{eq}-42$$
$$Q_{eq}= 42$$
Answer c
The total revenue would be, respectively:
$$84*42 = 3528$$
$$35*17 = 595$$
$$14*7 = 98$$
I know it's supposed to be simple but not sure if I'm rounding correctly (17.5 to 17) and if those dramatic drops in revenue are to be expected.
Thank you.


texts: Calculating risk interest rate within a two period model

texts:
I am trying to calculate how to determine the interest rate ( = risk free rate + premium) within the following model where a consumer decides to invest in a safe asset or in a risky asset. The utility is a CRRA function: $U(C) = \frac{c^{1-\frac{1}{\sigma}}}{1-\frac{1}{\sigma}}$ where $\sigma$ is the intertemporal elasticity of substitution. Hence, the consumer decides to maximize its utility by the following max problem where $1-p$ is the probability of default (consumer) does not get its savings + return back and $p$ is the probability of no default.
$$max \: U = u(c_1) + \beta E [(1-p)u(c_2(D))] + \beta E [(p) u(c_2(s))]$$
and he faces the following budget constraints:
$$C_1 = Y_1 - T_1 - S^1 - S^2$$
for period 2 consumption in case of default and no default:
$$C_2 (D) = Y_2-T_2+(1+r^1)S^1$$
$$C_2 (S) = Y_2 - T_2 + (1+r^1)S^1 + (1+r^2)S^2$$
So, I substituted these two budget constraints in the maximization problem and differentiated with respect to savings (1) and savings (2) and got the following Euler equations:
$$u^\prime(C_1) = \beta (1+r^1) E [(1-p)u^\prime (C_2(D))] + \beta  (1+r^1) E[p u^\prime(C_2(S))]$$
$$u^\prime(C_1) = \beta E[p (1+r^2) u^\prime(C_2(S))]$$
The risk free rate, $r^1$ is exogenously determined. I am trying to calculate $r^2$ by dividing the first Euler equation by the other, since the marginal utility of period 1 consumption is equal to each other. However, I can not find a solution, am I doing this corrrect?


texts: Price discriminating monopolist question

texts:
A price discriminating monopolist sells in two markets. Inverse demand in market 1 is given by: $$P_1(Q_1) = 80 - (1/2)Q_1$$ and inverse demand in market 2 is given by: $$P_2(Q_2) = 100 - Q_2$$ The monopolist's cost function is $C(Q) = (Q_1 + Q_2)^2$
a. Formulate the monopoly's function as a function of $Q_1$ and $Q_2$.
b. Calculate the monopoly's profit maximizing quantity sold in markets 1 and 2 and the corresponding prices.
Now suppose the government forbids price discrimination, so the monopolist can only set a single price for the two markets.
c. Compute the monopoly price and quantity.
d. How much is sold in market 1 and market 2, respectively?
e. Was the government intervention beneficial for social welfare or not?

a. This one is straightforward. $$= Q_1(80 - Q_1/2) + Q_2(100 - Q_2) - (Q_1 + Q_2)^2$$
b. This one I believed to be straightforward - set MR = MC. Thus, $$MR_1 = 80 - Q_1$$ $$MR_2 = 100 - 2Q_2$$ $$MC_1 = 2Q_1$$ $$MC_2 = 2Q_2$$ which gives $$(Q_1, Q_2, P_1, P_2) = (\frac{80}{3}, 25, \frac{200}{3}, 75)$$
c. This is where I start to get a bit messed up. Setting $P_1 = P_2$ gives a total demand function $$Q_1 + Q_2 = Q = 260 - 3P$$ I then solve for price, and get $$MR = \frac{260}{3} - \frac{2Q}{3}$$ and $$MC = 2Q$$ Thus, I'm left with $$(P,Q) = (75.8333, 32.5)$$

However, I feel as though I must have made a mistake. The profit when the monopolist is able to price discriminate actually ends up being lower than the profit when limited to one price. This surely can't be the case - where is my thinking going wrong here? Is my methodology off?


texts:
I am doing a Engle-Granger test for cointegration and I am unsure about some commands.

"Cointegration and the ECM" (document) from learneconometric.com says I should use:

regress b f
predict ehat, residual
regress D.ehat L.ehat L.D.ehat, noconstant

However, "Time series" (document from Princeton Uni) says I should use:

regress b f
predict ehat, resid
dfuller ehat, lags(10)

So I am unsure about the last commands here. Should I use regress D.ehat L.ehat L.D.ehat, noconstant or dfuller ehat, lags(10) and what is the difference here? Also, how many "lags" should I include for the Dickey Fuller test?


texts:
IMHO, scalping tickets is no different from legitimate arbitrage unless manipulative.

Iirc, arbitrage increases surplus and hindering scalping is setting a price ceiling which leads to deadweight loss or something like that.

So why do some states ban scalping tickets?

I'm assuming that such states think there is some perceived harm to their economy. Strangely enough, why tickets? Why not bags, clothes or phones?


texts: What does the vertical axis of the Kuznets curve depict (mathematically)?

texts: I do not understand what does the word "inequality" means on the vertical axis of the Kuznets curve. Can someone please explain?


texts: Mechanism design when the set of feasible decisions depends on types

texts:
Q : Can the tools of mechanism design be applied when the set of feasible decisions $D$ depends on the types $\theta$?
For example, when $d \in D$ represents the total funding allocated toward some good and $\theta_i$ represents the funds $i$ has available, $D = \{ d | 0 < d < \sum\limits_i\theta_i\}$.
Q : If not, is there some other approach that analyzes this sort of scenario?


texts:
I am facing some problems in deriving the two equations for trade balance (from which we derive that the trade balance is zero within each country) in the article "A SIMPLE FRAMEWORK FOR INTERNATIONAL MONETARY POLICY ANALYSIS" (2002) that you can find here.
My objective is to derive equations 28 and 29 of that paper. In order to do that, I used the following equations:

Firstly, I tried to substitute the value of  given by equation 7a in equation 25, but what I got was not right:

Then I tried to get the value of  from equation 25 and substitute in equation 7, but this was not right either:

I also tried to substitute for gamma, but the results were not correct. I cannot think of anything else. How would you do that?
The equations that I am looking for:
Equation 28:
Equation 29:


texts: What'll happen to production and consumer distortion loss in a large country with tariffs?

texts: Suppose here $P_0$ is the initial world price, and after tariffs is imposed the world price drops to $P_1$. What would be the production distortion loss and consumer distortion loss? Would it still be D and F (as it is in a small open economy)?


texts: Does the government have a role to play in certifying people's abilities for the labor market?

texts: The nature of information often makes it look like a public good. Is this the case for certification of peoples abilities? Is there a role the government could play in certifying people's abilities? Maybe do people thing that that's one of the roles that public universities play? Spence I guess is the typical reference that suggests that people go to school for certification/signaling of abilities rather than to acquire skills. Maybe that's a reason that there are many public universities?


texts:
I'm not a native speaker so please excuse my English.

When they draw the result that the central bank's monetary supply determine the inflation rate, didn't they suppose many variables sticky?

With money supply matching up with the demand, they start their train of logic as follows. MV = PY, here the Y is fixed since it's exogenous, and V is fixed for the convenience of computation, so M controls the P... Okay I get that part, but what I wonder is that, when you fix the V, doesn't that make the k also fixed, which means kY, the money demand function is eventually fixed.

Then, how can they manipulate the M when they assumed M equals to the fixed demand of money?


texts: Is it proven that prestige gained from sports victories helps the country economically?

texts:
Most of the world's governments support their professional sports teams, both through direct monetarily contributions and through numerous sports schools for children. One of the main rationales for that support is that victories in international competitions help the country gain 'prestige'.

But what exactly is the practical benefit of this 'prestige'? Does it help the country grow economically by attracting tourists or investment? Or perhaps it's merely a matter of national 'pride', without any monetary gains?

I'm looking for academic research on this topic or official statements by government institutions.


texts: What is the empirical price elasticity of demand for insulin?

texts:
A lot of textbooks say that demand for insulin is perfectly inelastic. I don’t think this is quite true (and I am a type 1 diabetic). It’s clearly very inelastic, but not perfectly so. There are things you can do to reduce your insulin intake, e.g. eat less carbohydrates.
I’m curious if any studies have actually gone out and measured this…


texts: Why is fiscal deficit always shown as a percentage of GDP?

texts: If the probable reason is because it must reflect the government's ability to pay back the deficit, wouldn't government income be a better indicator, rather than GDP?


texts: Difference between Outflow of capital and Flight of capital

texts:
I may sound stupid to ask this question but pardon me for that. What's the different between Outflow of capital and Flight of capital? I googled about both terms but couldn't find how they differ from each other.
Edit : Let me quote the definitions from investopedia.

Capital outflow is the movement of assets out of a country. Capital outflow is considered undesirable and results from political or economic instability.
Capital Flight is a large-scale exodus of financial assets and capital from a nation due to events such as political or economic instability, currency devaluation or the imposition of capital controls.

From these two definitions what I can conclude is that Capital flight is a large scale  capital outflow means these two are same things, the difference is just of the scale.Am I correct or is there any other difference ?


texts: Does reducing taxes generally lead to better economic performance? Does it lead to slowdowns in the economy?


texts: How to derive formula for marginal probability of choosing nest in nested logit model?

texts:
I am trying to understand all the details of the nested logit and what confuses me is the formula for marginal probability of choosing the nest. In more details: the joint probability of individual n choosing alternative j can be factored as the probability of individual n choosing nest k, multiplied by the probability of individual i choosing j conditional on having chosen nest k.

As I understand we are decomposing the decision process into two models: upper and lower. In the upper model decision maker chooses a nest and in the lower - alternative within the nest. Say utility of individual n choosing alternative j in the nest k is

$$ U_{njk} = W_{nk} + Y_{nj} + \epsilon_{nk} + e_{nj} $$

where $e_{nj}$ is EV I with scale parameter $\lambda_k$ and $\epsilon_{nk}$ is such that composite error term is EV I with scale parameter 1.

The lower model is trivial, it is a simple logit. However, the upper model is not clear for me. The expected utility of individual n from choosing nest k is

$$ EU_{nk} = W_{nk} + \lambda_kI_{nk} + \epsilon_{nk}$$

where $\lambda_kI_{nk}$ is expected utility that n will get from choice within the nest. And the marginal probability of choosing nest k is

$$P_{nB_k}=\frac{e^{W_{nk}+\lambda_kI_{nk}}}{\sum_{l=1}^K e^{W_{nl}+\lambda_kI_{n}}}$$

My question is how does this probability have a logit form if $\epsilon_{nk}$ is not extreme value? Or is it? Because as far as I understand the sum of two extreme value variables is not an extreme value.

Thank you!


texts: How does a liquidity guarantee for Asset-Backed Commercial Paper used to finance a Conduit work ?

texts:
A liquidity guarantee was what a lot of banks used to insure outside investors payments if an asset in a Conduit defaulted. The way they were doing it was not really dispersing the risk evenly throughout the economy to outside money markets.

Can someone explain a liquidity guarantee and the process of how it works economically in more simpler terms ?


texts: Is protectionism more suited to large economies?

texts:
Large economies like the US and China use tariffs as trade weapons while retaining competitiveness because they have the critical mass to encapsulate supply chains and avoid the cost of cross-border inefficiency.

Smaller economies cannot avoid the domestic costs associated with cross-border trade because they cannot avoid depending on cross border trade for supply chains.

Are these statements correct?

If so, does this lead to divergent trade strategies different sized economies?

Do smaller countries typically lean towards much freer trade out of necessity, while the largest economies like China and the US can afford and possibly even benefit from protectionism?


texts: Log-linearization of an intertemporal budget constraint

texts:
I'm trying to recreate the paper "Learning about Monetary Policy Rules when
Long-Horizon Expectations Matter" by Preston.
At one point he says that he log linearizes the intertemporal budget constraint
$$W_{t}^{i}=\sum_{j=0}^{\infty} R_{t, t+j}\left[P_{t+j} C_{t+j}^{i}-P_{t+j} Y_{t+j}^{i}\right]$$
where $W_{t}^{i} \equiv\left(1+i_{t-1}\right) B_{t-1}$, $\bar{\imath}_{t}=\beta^{-1}-1$ (denoting the steady state of $i$), $\hat{i}=\log [(1+i) /(1+\bar{i})]= log \frac{R_{t,t+1}}{R}$  in order to obtain
$$\hat{E}_{t}^{i} \sum_{T=t}^{\infty} \beta^{T-t} \hat{C}_{T}^{i}=\varpi_{t}^{i}+\hat{E}_{t}^{i} \sum_{T=t}^{\infty} \beta^{T-t} \hat{Y}_{T}^{i}$$
with $\varpi_{t}^{i} \equiv W_{t}^{i} /\left(P_{t} \bar{Y}\right)$.
I tried a houndred times to linearize the budget constraint but i can't really figure out what he did.
Since $ln x_t = ln x -  \hat x_t \rightarrow x_t = x  e^{\hat x_t}$ i wrote the the intertemporal budget constraint as
\begin{align}
W_t^i =&\sum_j^{\infty} R e^{\hat R_{t,t+1}} P e^{\hat P_{t+j}} \left[ ( C e^{\hat C_t+j}) - (Y e^{\hat Y_t})\right]\\
W_t^i=& \sum_j^{\infty} RP e^{\hat R_{t,t+1} + \hat P_{t+j}} \left[ ( C e^{\hat C_t+j}) - (Y e^{\hat Y_t})\right] \\
W_t^i \approx & \sum_j^{\infty} RP (1+ \hat R_{t,t+1}+ \hat P_{t+j}) \left[  (C(1+\hat C_{t+j})(Y(1+ \hat Y_{t+j})\right]
\end{align}
ANd then i don't know how to procede. Where do the steady state values of $R$ and $C$ disappear?


texts:
For example, we could imagine an arrangement like this:

There are currently \$0 in the economy.
A business takes out a \$50 loan. The bank sets there bank account to \$50 - \$50 debt = \$0 net.
The business now pays it workers \$40 to make stuff (through the bank).
The workers in turn pay back \$45 to the business to buy stuff (through the bank).

(We can imagine there being a lot more steps)

Etc...
We can use bank notes instead of currency

What is the purpose of base money then?


texts: What happens if the "control variables" are also endogenous?

texts:
I work in Political Economy, and a lot of the models include "innocent" control variables such as population, inequality, colonial legacy, etc. so that the author can claim unbiasedness on their independent variable of interest.

But if any of these control variables are endogenous to some omitted variable, doesn't this contaminate the unbiasedness of ALL the independent variables?

If that's true, then what can we do? Leave those control variables out and they lead to omitted variable bias themselves. Include those in and they will contaminate everything in the model.

Example: A researcher wants to know if inequality leads to violence, and he controls for a few things:
\begin{equation}
Violence = Inequality + Growth + Development + \epsilon
\end{equation}
Seeing that Inequality is likely to be endogenous (because of the omitted variable Level of altruism), he will try to find a instrumental variable for Inequality. But aren't Growth and Development likely to be endogenous (i.e. correlated with Level of altruism) too?

This example may look silly, but my point is in Political Economy / Development work, there are so many factors at play (yet omitted) that I'm afraid many variables included on the LHS are endogenous. Yet often, the researcher only looks for an instrument for his pet independent variable only.


texts: Extract residuals from Uhlig's rejection method - Lag selection

texts:
I wanna determine the number of lags for a Baysian VAR/FAVAR model, which I implement based on R's VARsignR package. To compute the AIC/BIC I'd need the residuals of the model estimation. How can I extract these to compute the two selection criterion? There is no such object provided as part of uhlig.reject.
model <- uhlig.reject(Y= data, nlags=3, draws=200, subdraws=200, nkeep=1000, KMIN=1,KMAX=2, constrained=constr, constant=FALSE, steps=25)

Later I wanted to compute the criteria according to:
BIC <- function(model) {

  ssr <- sum(model$residuals^2)
  t <- length(model$residuals)
  npar <- length(model$coef)

  return(
    round(c("p" = npar - 1,
          "BIC" = log(ssr/t) + npar * log(t)/t,
          "R2" = summary(model)$r.squared), 4)
  )
}

Any thoughts on this? Is there maybe a smarter way for lag selection in this context? Papers are pretty vague here.


texts: Isn't Bull Put Spread's Maximum Loss = Spread Credit + Loss from sold call + Profit from bought call?

texts:
I don't grasp the blue difference below. If $P \ge 48$, isn't the investor's

Maximum loss = spread credit + $\color{red}{\text{Loss from his sold 44C}} - \color{limegreen}{\text{profit from his purchased 48C}}$.
= spread credit + $\color{red}{P - 44} - \color{limegreen}{(P - 48})$
= spread credit + $\color{limegreen}{48} - \color{red}{44}$.

=   The last line is wrong anyways, because $3 -4 = -1$.

  Bear Call Spread Example

  Investor is bearish on stock XYZ when it is trading at \$50 per share and believes the stock price will decrease over the next month. The investor sells (writes) \$44 call and buys a \$48 call for a net credit of \$3. Best case scenario is if the stock price ends up at or below \$44 then the options expire worthless and the trader keeps the spread credit. Worst case scenario is if the stock price ends up at or above \$48 then the trader is down the spread credit minus (\$44 - \$48) amount.

  Break even point = 44 strike + spread credit = \$44 + \$3 = \$47

  Maximum Profit = Spread credit = \$3

  Maximum Loss = Spread credit $\color{CornflowerBlue}{- (\$48 - \$44)}$ = \$3 - \$4 = \$1


texts: Is this a realistic solution to world poverty?

texts:
The idea: By convincing the U.S. that ending world poverty would actually return so much money back to the U.S. that it would more than compensate for the cost of providing the resources needed to end poverty.

Example: The influence of terrorist groups in the Middle East could be dramatically decreased if we hire the locals there to be soldiers, and this could be far cheaper than risking the lives of our own soldiers and more importantly, more effective because we could afford more of them.

Anyway, the proposal is here:
http://genexie.com/the-most-realistic-solution-poverty-yet/2015/03/31/


texts:
I am trying to replicate the Fama-French three-factor model. I am having issues in the dataset.

1) Using the CRSP/COMPUSTAT merged dataset for firm fundamentals from WRDS, and then dropping data on financial and non-US firms, I have much fewer firms than what FF have in the dataset in French's website. Any suggestions on why this is happening?

2) I am unable to obtain data as far back as 1926 from WRDS.

Any suggestions would be very helpful.


texts: Russian ruble drop in value due to low oil prices

texts:
http://www.americanactionforum.org/research/impact-falling-oil-prices-russian-financing/

Based on the above article, the author states that "For budgeting, this favors the oil exporter, because a drop in oil revenues weakens the exporter’s economy—and consequently their currency". It makes sense that if oil prices are lower and traded based on USD values, it will hurt top line revenues for Russia since they produce oil. However, why does the second part of that statement have to be true? Why does the ruble depreciate against the USD?
The article as states "Since Russia sets its budget in rubles, not dollars, financing sources from foreign currencies are exceptionally strong relative to ruble". What does this mean for budgets to be finance in one currency vs another? Arnt all countries budgets in their own native currency? Why does this matter? What are the implications?


texts:
I need an example of a

Convex, non-monotonic preference
Non-convex, monotonic preference

I figured that an example of non-convex, monotonic utility preference could be $U(x,y)=x^2+y^2$.
For convex, non-monotonic preference, I cannot think of a standard example. As far as my understanding goes, lexicographic preferences are convex, but I don't think these are non monotonic.
Please help me figure out the examples so that I can conceptually understand monotonicity and convexity.


texts: Best way to measure inflation in real time?

texts: I'm looking to measure inflation in real time preferably minute to minute. What would be different feasible approaches to this? I know that the CPI measures inflation quite accurately but this is only on a month to month basis with the Bureau of Labour releasing their findings with a few month lag. The metric should be able to reflect a sudden inflationary spike like in the case of hyperinflation for example. Would much appreciate your help and thoughts!


texts: Show that this income tax is effectively a lump sum tax

texts:
This is a standard income, leisure tradeoff model.
$$ \max_{c,l}  \min\{c; l\} $$

$$s.t. \space c = w(1-t)(1-l)$$
$l$ is leisure (where total time is 1),
$w$ is wage, $c$ is consumption, and $t$ is the labor income tax.

I was asked to show that this income tax is effectively a lump sum tax.

The definition for lump sum tax is as follows: A tax whose value is independent of the individual's behavior.

Individuals can do nothing to avoid the lump sum tax, and there are no relative price changes. I guess that the utility function had something to do with it, but I do not see how the tax can be viewed as a lump sum tax.


texts: Why does a higher risk aversion leads to a lower intertemporal elasticity of substitution?

texts:
Mathematically, a higher risk aversion leads to a lower intertemporal elasticity of substitution (there is an inverse relationship). But why?
If I become more risk-averse, I would like to smooth my consumption. So I will increase my participation in the financial market to avoid or reduce the risk. But how does that lower my intertemporal elasticity of substitution? Like why would I become less responsive to changes in the interest rate if I become more risk-averse? What's the intuition here?
Or because I just wanna smooth my consumption, I don't really care about changes in the interest rate?
Risk-lovers, on the other hand, although also participate in the financial market, do not care about smoothing their consumption? Like if the interest rate increases, they can drastically reduce their current consumption for more consumption in the future, but risk-aversers do not care about the higher interest rate?


texts: What is the name of the economics free trade "punnett square"

texts:
I remember doing these in High School.It was a 2x2 square, where you could work out the math to show that countries were better off focusing on their efficiency/competitive advantage, and that free trade made both better off.

Not looking for an analysis of if the logic is right or wrong or whatnot, just what is the name of the square (assuming it has one)


texts: Why does demand curve shift in, in a monopolistic competitive market?

texts: In a monopolistic competitive market, demand curves shift in, if more firms enter the market. I can't seem to wrap my head around it. Demand remains the same, supply has increased. Shouldn't entry of more firms change the supply curve, rather than demand curve?


texts: Existence of pure strategy Nash equilibrium

texts: I understand the reason why mixed strategy Nash equilibrium exists. But what are the conditions for the existence of pure strategy Nash equilibrium?


texts:
Economists are fond of posing "puzzles", for example the "annuity puzzle" (why don't more people buy annuities).

I wonder if any economists (or other social scientists) have, in similar spirit, studied the "adblock puzzle" (i.e. why don't more people use adblockers)?

Some charts from eMarketer:


texts: List of commercial banks by country in Europe

texts:
How do I find a list of all operating commercial banks by country?

I am only interested in commercial banks. Not building societies nor community banks.

I expected that that list should be made available on EuroStat
or from consolidated banking data by ECB
but it's not as they don't differentiate between commercial banks and other credit institutions.

For example, for UK at some point in that past, that list would look like this.


texts:
There are a couple of questions I have about imposing penalties on repo fails.

Is the repo fail penalty imposed only on the seller of securities if
it does not buy the securities back or also on the buyer if it does
not return the collateral?
I read that a lack of penalties sets the repo floor at 0%, I don't get why this is so.


texts: Inverting the production function - Okun's Law: Fit at 50? (BALL; LEIGH; LOUNGANI, 2012)

texts:
Consider the following equations:
$$ \tag{1}
E_t - E_t^* = \gamma \cdot (Y_t - Y_t^*) + \eta_t, \gamma > 0,
$$
$$ \tag{2}
U_t - U_t^* = \delta \cdot (E_t - E_t^*) + \mu_t, \delta < 0
$$
where $E_t$ is the log of employment, $Y_t$ is the log of output, $U_t$ is the unemployment rate ,and $^*$ indicates a long-run level.
We can then derive Okun's Law by substituting $(1)$ in $(2)$:
$$ \tag{3}
U_t -U_t^* = \beta \cdot (Y_t - Y_t^*) + \epsilon_t, \beta < 0
$$
where $\beta = \gamma \cdot \delta$ and $\epsilon_t = \mu_t + \delta \cdot \eta_t$.
I now quote the authors:

Past research provides guidance about the values of the parameters in equations (1)-
(3). To see this, suppose first that changes in output and employment are movements along a
neoclassical production function: more labor produces more output. For the United States,
economists believe that the elasticity of output with respect to labor is about 2/3, based on
factor shares of income. If we invert the production function, we get equation (1) with γ = 3/2
= 1.5.

How does one go about 'inverting the production function' and getting equation $(1)$? I am quite lost and would appreciate any help.


texts: Tax revenue formula maximization- whats the name of this formula?

texts:
I have been teaching intermediate microeconomics and have come across a formula a number of times relating the tax rate at which revenue is maximized if elasticities are constant. This formula is defined as follows:
$$T_{max}=\frac{\varepsilon}{\varepsilon-1}\left(\frac{1}{\eta}+\frac{1}{\varepsilon}\right)$$
where $\varepsilon$ is our price elasticity of demand and $\eta$ is our price elasticity of supply.


texts: Why would regression coefficients be different on a subsample?

texts:
If I'm running a linear regression for example, and I take out some points, wouldn't the same line/plane still fit the data? If not, wouldn't that show that the data doesn't have a linear relationship?
Example: https://ocw.mit.edu/courses/economics/14-382-econometrics-spring-2017/lecture-notes/MIT14_382S17_lec1.pdf. On page 10, in the gender wage gap example, it finds a predictive effect of ~20% in the full sample and ~7% in the never married sample. But then if dWage/dGender depends on Marital Status, how can the functional form be right?


texts:
I have a hypothetical situation and couple of such questions.
Imagine a situation like this:
You need 1000€ a month in order to survive.
There are three loan providers you can borrow the amount of 1000€ for a month with a fee of 1€ a month (you're always repaying money on time).

I borrow money from the first loan provider.
I spend the money.
I borrow money from second to repay the first.
I now owe money only to the second provider.
I borrow money from the third.
I spend the money.
I borrow money from first to repay the second.

And so on and so on, you can see the pattern. It's maybe a stupid question but could loan circulation work as a way of earning monthly money.


texts: How can increasing debt boost potential returns?

texts:
May 26 2020. Why Even Carl Icahn Couldn't Save Hertz From Chapter 11 - Bloomberg

  Hertz’s debt binge began when it was acquired by private equity firms from Ford Motor Co. in 2005; the new owners quickly took out a \$1 billion dividend. Piling on debt juiced the potential returns for the owners and helped pay the inflated \$2.3 billion price tag for the Dollar and Thrifty brands in 2012, which Hertz struggled to integrate.

Doesn't the embolded sentence above contradict the one below? Wouldn't debt lower potential returns, if you can't re-pay it and the interest?

Oct 16 2006. Hertz share sale raises \$1.32 billion - The New York Times

  Hertz Global Holdings has raised \$1.32 billion in one of the largest initial public offerings of the year, less than 12 months after private- equity firms bought the company, according to an underwriter.

  The offering of more than 88 million shares, which represents about a 27.5 percent stake in the company, sold Wednesday for \$15 per share. Hertz said last month that it hoped to sell shares for \$16 to \$18 each.

  Clayton Dubilier & Rice, Carlyle Group and Merrill Lynch put up \$2.3 billion of the \$15 billion including debt that they paid for Hertz in December. The firms rattled potential investors by adding debt, raising the company's interest costs and pushing down profit.

  "The offering wasn't in high demand, or they wouldn't have had to lower the price in order to get it sold," said Kevin Miller, a partner at Alston & Bird in New York. "This thing isn't going to pop."


texts: Second order condition for symmetric game

texts:
Denote by $i \in \{1, \ldots, n\}$ an economic agent.
Let $\mathbf x \in \mathbb R^n$ denote a vector of actions and $x_i  \in \mathbf x$ a typical element.
Let further $f_i : \mathbb R^n \to \mathbb R$ denote the objective function.
The vector $\mathbf x^*$ constitutes a Nash equilibrium if the following holds
\begin{align}
\forall i : f_i(\mathbf x^*) = \max_{x_i} f_i(x_i, \mathbf x_{-i}^*)
\end{align}
where $\mathbf x_{-i}^* := (\ldots, x_{i-1}^*, x_{i+1}^*, \ldots)$ are the equilibrium actions of the opponents.
The $n$ first order conditions read
\begin{align}
\frac{\partial f_i(x_i, \mathbf x_{-i}^*)}{\partial x_i}\Bigg|_{x_i = x_i^*} = 0.
\end{align}
The second order conditions read
\begin{align}
\frac{\partial^2 f_i(x_i, \mathbf x_{-i}^*)}{\partial x_i^2}\Bigg|_{x_i = x_i^*} < 0.
\end{align}
Assume symmetry such that $x_j^* = x^* ~ \forall j$.
Since the problem is quite complex I cannot derive the second order partial derivative.
I was thus thinking to define the first derivative in a single argument (the symmetric equilibrium actions)
\begin{align}
\forall i : f'(x^*) = f'_i(x^*) := \frac{\partial f_i(x_i,\mathbf x_{-i}^*)}{\partial x_i} \Bigg|_{x_j^* = x^* ~ \forall j}
\end{align}
and then take the derivative of the the simplier first order derivative
and check wether it's negative.
In order to make the simplifictaion in between I must somehow make sure that no information gets lost and that's why I'm wondering if the follwoing relation holds in general
\begin{align}
\text{sign}\left[f''(x^*)\right] ~~ \substack{? \\ =} ~~ \text{sign}\left[\frac{\partial^2 f_i(x_i,\mathbf x_{-i}^*))}{\partial x_i^2} \Bigg|_{x_j^* = x^* ~ \forall j}\right].
\end{align}

I was thinking that there may exists a general theorem from optimization for symmetric actions.

Example
Consider text book Cournot duopol with $i,j \in \{1,2\}$, $i \neq j$ and
\begin{align}
f_i(x_i, x_j) = (1-x_i-x_j)x_i.
\end{align}
Now we readily get the following partial derivatives
\begin{align}
&\frac{\partial f_i(x_i,  x_j^*)}{\partial x_i}\Bigg|_{x_i = x_i^*} = 1 - 2x_i^* - x_j^* \\[2mm]
&\frac{\partial^2 f_i(x_i,  x_j^*)}{\partial x_i^2}\Bigg|_{x_i = x_i^*} = -2\\[2mm]
&f'(x^*) = 1-3x^*\\[2mm]
&f''(x^*) = -3\\
\end{align}
So the sign is the same, but the values differ.

Solution
It seems that the idea was published in the latest Theoretical Economics and the approach is valid. The author actually discusses the super simple Cournot example as well.

The following statement is adapted from Theorem 1 of Hefti (2017): "Equilibria in symmetric games: Theory and applications", Theoretical Economics 12, pp. 979–1002

Suppose $f_i(x_i, \mathbf x_{-i})$ is strongly quasiconcave in $x_i$.
Define $f'(x)$ as above.

  Let $x^* \in \mathbb R$ solve $f'(x^*) = 0$.
  If $f''(x^*) < 0$ then there exists a unique symmtric equilibrium.

Further Issues In footnote 7 the author argues

  The
  assumption of a strongly quasiconcave payoff function in own strategies is mainly for convenience, because it is a sufﬁcient condition for the existence of a (possibly differentiable) best-reply function. However, many results require only differentiability of best replies (and do not otherwise hinge on quasiconcavity), and some results do not require that best replies are everywhere differentiable.

This statment is particular useful, because I have a problem in mind where I cannot say anything about (quasi)concavity of the objective function. I'm, however, not sure if I can apply Theorem 1, because the author does not specify when quasiconcavity is imposed for a result.

How would I know wether the theorem is applicable?

Note that I cannot(!) derive a best response function $x_i^* = \phi_i(\mathbf x_{-i}^*)$, but only the symmetric equilibrium actions $x_j = x^* ~ \forall j$.


texts:
In a paper I was reading, a budget constraint for the Euler equation for the consumption asset was described as:-

$$
W_{t+1} = (W_t - C_t) R_{c, t+1}
$$

Here $ R_{c, t+1}$ is the 'return to the consumption asset'. What does this mean?

Paper: Volatility, the Macroeconomics, and Asset Prices


texts: I think hot weather alters firms' desire to sell at some given price because hot weather increases the demand for ice cream. (Mankiw's book)

texts:
I am reading "Principles of Economics" by N. Gregory Mankiw.
I think hot weather alters firms' desire to sell at some given price because hot weather increases the demand for ice cream.
Am I wrong?

Notice that when hot
weather increases the demand for ice cream and drives up the price, the quantity
of ice cream that firms supply rises, even though the supply curve remains the
same. In this case, economists say there has been an increase in “quantity supplied”
but no change in “supply.”
Supply refers to the position of the supply curve, whereas the quantity supplied
refers to the amount producers wish to sell. In this example, supply does not
change because the weather does not alter firms’ desire to sell at any given price.
Instead, the hot weather alters consumers’ desire to buy at any given price and
thereby shifts the demand curve to the right. The increase in demand causes the
equilibrium price to rise. When the price rises, the quantity supplied rises. This
increase in quantity supplied is represented by the movement along the supply
curve.


texts: Value Function For Durable-Good Monopolist with General Distribution

texts:
It is known that with a unit mass of consumers, each of whom has a value distributed between 0 and 1, one can think of the monopolist solving
\begin{equation}
\max_{p} \ p[1-F(p)]
\end{equation}
when marginal costs are 0 and where $F$ is the CDF of the consumers' valuations.
This yields the solution
\begin{equation}
p^*=\frac{1-F(p^*)}{f(p^*)}.
\end{equation}
$\textbf{Question}$: How would one write the value function (optimal profit function) of the monopolist in this case, given that the solution is implicitly (?) defined?

Can one just say that it is
\begin{equation}
\text{optimal profit function}=\frac{[1-F(p^*)]^2}{f(p^*)}
\end{equation}
or is this incorrect?

Many thanks.


texts:
I encountered this question in Microeconomics by Pindyck and Rubinfeld.

The question says that "Suppose Jones and Smith have each decided to
allocate $1000 per year to an entertainment budget
in the form of hockey games or rock concerts. They
both like hockey games and rock concerts and will
choose to consume positive quantities of both goods.
However, they differ substantially in their preferences
for these two forms of entertainment. Jones prefers
hockey games to rock concerts, while Smith prefers
rock concerts to hockey games."

We are asked to draw indifference curves for both of them.

A solution manual showed that the indifference curves should be convex to the origin with different degrees of steepness. However, I believe that the curves should be concave to the origin as convex curves show a tendency to diversify one's bundle, which is certainly not the case here. Also, convex curves at some point will say that one of them is ready to leave more of what he prefers more to get just $1$ unit of what he prefers less. That too seems a contradiction to me. I am of the belief that here the indifference curves should be concave to the origin with different degrees of steepness for the both the consumers.

Kindly help me reach the right answer.


texts: Is the capital-output ratio in developing countries low or high?

texts:
For a developing economy, I've seen sources claiming that the capital-output ratio (more commonly known as ICOR) is high (e.g. here and here), while other sources claiming that it's low, like below (the answer is A):

I suppose I can come up with reasons why the ICOR or a developing country might be low: low rate of saving -> little investment on capital -> low returns -> low ICOR. Then again, the ICOR is a ratio, so even if both nominal investment and output are low, there is no guarantee that they're values are therefore low relative to each other, if anything the ICOR can easily be high, as explained in the two sources that claim the ICOR is high for such economies.


texts: How does locking down a country cause its economy to suffer?

texts:
As of time of writing, many countries have been in lockdown for weeks or months, and the economic data coming out of that is usually quite grim. I'm wondering how being in lockdown relates to poor economic data. As I understand it the standard chain of reasoning goes like this:

Country in lockdown means people stay at home, which means they spend less.
In turn this means the services they would otherwise have bought get less revenue, which means less profit, which means they suffer and might have to lay off employees.
Therefore unemployment increases and more people have no money.
Therefore we get an economic crisis and recession.

However, #1 also means that people have more money. Some of them might earn less, but as a whole unless money is actually being taken out of the economy (and how would that happen?), the amount saved across the entire economy ought to balance the amount not earned. Therefore what actually happens is more "income inequality" (quotation marks here because it's the amount of money that each person has that becomes more unequal, not income itself). And if that is what happens and income inequality is the root cause of economic crises, why am I not seeing that in the media?

I don't get it, so hoping someone can explain.

Related: Who has the unspent money? which is about similar things, but doesn't go as far as this question does.


texts:
High demand for goods drives up prices, and also encourages firms to hire more; and likewise high employment raises demand.
Then why stagflation?
According to above explanation,  it should not exist.


texts: Is there a go-to resources on the use of the scientific method in economics?

texts:
I once had a physics teacher who said (paraphrased):

for any formula or principle you use on an exam, you have to be able to provide a real world test that would demonstrate the theory's validity. In other words, the test must show the theory accurately describes some real world phenomena.

I would like to better understand how economist think about "testing" their theories. For instance, psychology undergrads at my local university take a psych research methods course. I would like something along these lines for economics. But more than this, I want something that goes beyond just discussing research methods and actually assesses what makes high quality economic science. In contrast to psychology, many claims in economics are hard to test because doing so is either impossible, intractable, or impractical. Therefore, I think a good understanding of how to do economic science is crucial to learning it to figure out whether a given author is adhering to the scientific method.

Remark:

By science, I mean

CLAIM: the earth's acceleration is $g$

TEST:

We will drop a ball and measure how long it takes to hit the ground.

(1) measure a height $d$ off the surface of the earth

(2) time the ball as it drops from $d$ to the surface

(3) compute the acceleration from $d = v_0t + \frac{1}{2} a t^2$

and I will find the acceleration of the earth is $g$.


texts: Understanding the gradient of the social cost curve in a market failure/ negative externalities diagram

texts:
Why does the social cost supply curve in a negative externalities diagram have a steeper gradient than the private cost to firms?

I assumed it should only be shifted upwards as the negative social costs are directly proportional to the production quantity?

Any explanation is greatly appreciated.


texts: How would Trump's tariffs affect an American multinational company? Would the goods that they produce be considered imports?


texts: Shifts in IS in a fixed exchange rate mechanism

texts:
First, we assume we are in a fixed exchange rate mechanism. In this system, I deduce that the expected exchange rate would be fixed, at the market rate.
In a floating system, with open capital markets, when the expected exchange rate changed, or the foreign interest rate changed, the uncovered interest parity (UIP approx. version: $i_H=i_F+\frac{E^e-E}{E}$) would shift the IS curve accordingly. If the expected exchange rate rises ($E^e$ increases), or the foreign interest rate ($i_F$) rises, then we would have a shift of the IS curve by means of the  current exchange rate $E$.
However, in a fixed exchange rate system, where $E^e=E$ (and hence $i_H=i_F$), is there a shift in IS when the foreign interest rate changes?
I ask this, because in chapter 18, and 19 of Feenstra and Taylor book, some 'examples' of fixed exchange rate systems with shifts in the IS curve due to changes in the foreign interest rate are given... But they don't explain how they are possible.


texts:
In the Wikipedia article on annuity, different formulas are given, and their difference is due to whether the first payment is made in the first period or not, whether we compute the present or future value, whether the annuity is a perpetuity or not, etc.

In macroeconomics, e.g. page 8 here, I often recognize something of the following terminology: "If the interest rate is $r$, then the annuity of $x$ (which may be initial wealth) is $\frac{r}{1+r}x$." Now, the problem is that I do not understand why we would say that the annuity of $x$ is $\frac{r}{1+r}x$ in any sense given in the article on Wikipedia. What am I missing here?

Let me mention some examples.

If the interest rate is $r$, then the present value of an annuity-immediate for $n$ periods with "rent" $x$ is $x\frac{1-(1+r)^{-n}}{r}$. If $n=1$ here, then we have $x\frac{1}{1+r}$ (I pick $n=1$ to somehow get the expression $\frac{r}{1+r}x$).
For the future value way of writing an annuity-immediate, we have $x\frac{(1+r)^{n}-1}{r}$ which is $x$ for $n=1$.
For an annuity-due, we have the former expressions in 1 and 2 multiplied by $(1+r)$.
For a perpetuity I get $x\frac{1}{r}$ for first payment in second period.
For a perpetuity I get $x\frac{1+r}{r}$ for first payment in first period.

So, in no case do I get $\frac{r}{1+r}x$. I feel there is something I am missing in my understanding of the concept of an annuity.

Looking at 5, I think that they mean by the "annuity value of $x$" the annuity value of some present value $x$. So in 5, the present value is $x=y\frac{1+r}{r}$ for some other rent $y$, and thus the annuity value of $x$ is $y=\frac{r}{1+r}x$?


texts:
If there is less money, its value increases.
There is less liquidity when there is less money.
Does a negative interest decrease the money supply?

Especially when people don't need money: they saved it up but nobody needs it -- nobody needs to borrow it from them so they saved up for their pensions and now they want to buy a pension but nobody really needs their money. So a negative interest rate is established to entice them to spend it: a little late because they are buying pensions but OK. They are too old to spend it well. They think the washer will outlive them. So they leave the money in the incinerator of negative interest bank accounts. Then there is less and less money. Now somebody wants to sell something (liquidate it) but there isn't that much money there at the moment. It was burnt. The money becomes a kind of commodity that people are willing to pay more assets for. The asset price in currency is lower. People think, hey cool: Let as much people as possible have their money burnt so that my cash becomes more valuable. Run on the bank. But then it turns out that the CB really can print money...

Here's a story. I guess it can be what happened in the repo market recently.


texts: expected payoff of an American put option

texts:
I am reading about the American option and sources got me confused in the part where the American put option is considered on a non-dividend paying asset.

I understand that the payoff of an American put option at maturity is given by $$\max\left\{K-S(T),0\right\}$$ where $K$ is the exercise price and $S(T)$ is the price of the underlying at maturity.

Some sources state that considering n-arbitrage, the American put option problem aims to find the option value $$P(S,t)=\sup_\tau EG_\tau$$ where $G_\tau$ is the gain function and E is expectation.

In my understanding, the gain function is equivalent to the payoff function, hence $$V(S,t)=\sup_\tau E[max\left\{K-S(\tau),0\right\}]$$ for all stopping times $\tau$.

However, I also stumbled upon sources that say that $$(S,t)=\sup_\tau E[e^{-r(\tau-t)}\max\left\{K-S,0\right\}]$$ for all stopping times $\tau$.

What could be an explanation behind this?


texts: Why is increased productivity infinitely good

texts:
From investopedia:

  Supply rises with productivity, dropping real prices and increasing
  real wages; it lifts people out of poverty and allows them to focus on
  efforts beyond mere survival.

I thought I was naive so I asked google why productivity was always good in economics and this is "google's answer."  Does economics really assume that whatever work a human does, doing it less and something else more is always better for them?


texts: Is there any pressure to keep currency exchange rates around 1?

texts:
I notice that for any pair of currencies, the exchange rates seem to stay around 1 (as opposed to, say, 1,000,000). This is no longer the case if one country experiences an economic crisis that results in a very high inflation, but otherwise, rates don't seem to deviate very much from 1.
As you may have guessed I have very little knowledge in finance, so correct me if any of my assumptions are wrong, my aim here is to learn.
An example I'm thinking of is the Leu in Romania. It was revalued several times, the latest in 2005, when 10,000 old Leus were converted to 1 new Leu. That made the exchange rate with euros, for instance, closer to 1, given that 1 old Leu ≈ 0.00025 Euros, then 1 new Leu ≈ 0.25 Euros.
Why is this? Is this something most countries do? Does this principle have a name?


texts: When does the law of diminishing returns apply?

texts:
Law of diminishing returns does not always apply:

The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant, will at some point yield lower incremental per-unit returns.

I interpret "productive process" as a process that creates a product other than money.

Many productive processes can be done in parallel.

I see how it is true for any process with a central control, because that is limited by the interaction with the instances, so at some point adding a new instance requires additional changes.

But A productive process does not need to be centrally controlled.

If I run a snowball factory, I can add more workers, invest in required infrastructure like gloves, and send them out to build snowballs autonomously.

The central work does not only scale linearly, it even scales constant! The total effort summed up over all instances scales  linearly.

To be strict, it scales exactly linearly because adding a later instance can not add less productivity than an earlier, because the earlier instances are not in communication with the central point at the time. The first instance does not differ from any other, because their creation does not differ.

If I would insist to earn money, the money transport is limited in  bandwidth. We have freight trains, that's good enough. But there is also a limit in snowball to money conversion by market interaction, as a market is finite.

So, producing money is limited final market size, there can be a snowball I can not sell. Adding instances does not increase production of money.

But the production of snowballs seems to be limited only by the availability of snow and homo sapiens - by climate change.

What's wrong with that?

Of course, "law" does not mean it strictly applies always. Is it that I just constructed an example outside its validity? Where is it valid, if that is well defined? Or is the argument above wrong?


texts: Maximization problem FOC and Euler equation

texts:
Can someone please help me with the Lagragian and the derivation of the following objective function ? Beneath I provide the objective function, the constraint and the Euler equation that results from the maximization. Your help is very much appreciated !!

Thanks !


texts:
I looked around in the forum but I have not found this question yet. I would like to approach the topic of bargaining models in the spirit of Rubinstein, Ariel. "Perfect equilibrium in a bargaining model." Econometrica: Journal of the Econometric Society (1982): 97-109.
I have studied game theory but never actually worked with these kind of models (see for example: Chae, Suchan, and Paul Heidhues. "Buyers' alliances for bargaining power." Journal of Economics & Management Strategy 13.4 (2004): 731-754.)
I have done some timid google scholar searches, but I have found so much material that I cannot skim it on my own. Could you suggest a reading list of the main references that are a must read for these kind of models?
Thanks a lot.


texts: Deriving the optimal path of consumption

texts:
Question:
A consumer has wealth ß0 > 0 and wants to find the best way of consuming
this wealth. Preferences over consumption c(t) are given by
$\int$$\infty$0 e-pt((c(t)1-$\sigma$-1)/(1-$\sigma$))dt
where 0 < $\rho\ < 1$ is an intertemporal discounting and $\sigma$ > 0, ß $\neq$ 1. Let ß(t) denote the amount of wealth at time t. ß does not spoil over time, that is, its value does
not decrease if it is not consumed. On the other hand, it does not receive interest. A
unit of consumption decreases wealth by the same unit. You can view ß0 as a cake
and the problem of the consumer as the problem of eating the cake over time in the
optimal way.
Formulate the problem and find the optimal path of consumption over time.

(My queries in bold)

Solution:

The problem is max $\int$$\infty$0 e-pt((c(t)1-$\sigma$-1)/(1-$\sigma$))dt subject to $\int$$\infty$0 c(t).dt = ß0

Or $.{B}$ = -c with ß0 given. The Hamiltonian of this problem is:

H (c, ß, $\mu$) = ((c(t)1-$\sigma$-1)/(1-$\sigma$))-$\mu$c

1) What do we mean by the Hamiltonian? Is it a constraint of some sort?

where $\mu$ is the costate variable attached to the constraint .{B} = -c. The conditions for the optimum are $\partial$u/$\partial$c = 0 and .$\mu$ = $\rho$$\mu$ - $\partial$H/$\partial$B together with the constraint. The transversality condition is:

limt$\longrightarrow$$\infty$+e-$\rho$t$\mu$(t)ß(t)=0.

2) When we use a transversality condition, does this define the boundaries of consumption in this case?

These conditions imply:

c-$\sigma$ = $\mu$, .$\mu$ = $\rho$$\mu$

Notice that H does not depend on the state variable and so the second optimality condition is very simple.

3) Why are we using a second optimality condition?

c-$\sigma$ = $\mu$ implies -$\sigma$(.c/c) = $\rho$ $\Rightarrow$ .$\mu$/$\mu$. Together with the second equation:

-$\sigma$(.c/c) = $\rho$ $\Rightarrow$ .c/c = -($\rho$/$\sigma$)

Therefore, the optimum path involves setting consumption to the path c(t) = c0e($\rho$/$\sigma$)*t. To find c0, we can use the transversality condition. Another way of finding c0, more
direct and more intuitive, is by the constraint $\int$$\infty$0 c(t).dt = ß0. According to this constraint, given the optimal path of c:

$\int$$\infty$0 c0e($\rho$/$\sigma$)*tdt = ß0

$\Rightarrow$ -(c0e(-$\rho$/$\sigma$)*t)/($\rho$/$\sigma$)|$\infty$$0$

As a result, the path for consumption, now fully characterised, is given by:

c(t) = ($\rho$/$\sigma$).ß0.e-($\rho$/$\sigma$).t

We see that consumption decreases gradually over time, that consumption is higher if ß0 is higher, and that $\rho$ and $\sigma$ affect the optimal path for consumption.


texts: Why are things usually cheaper in absolute terms the poorer a country is?

texts:
I think something like this can be seen with something like the big mac index: http://www.economist.com/content/big-mac-index, there you can see that at the cost of one big mac in switzerland you could buy 10 in Venezuela if price is taken in dollars.

In a globalized economy like the one we have right now, I think it would make more sense for any consuming good to have aproximately the same price everywhere, (if they have the resources for making the consuming good in their own country it would be then cheaper), then depending on how rich is the country the salaries would be according (salaries would be as much higher for one country to the other as how much richer is that country).

I don't know about economy, but I'd like to know why that happens. so I'd like in explanation in layman terms if possible.

Thanks for your attention.


texts: Relationship of continuous and discrete time models

texts:
I am trying to understand two comments from a colleague. I have no clue about continuous time models. He said something like "just replace $\delta$ with $e^{-rdt}$ the Poisson process becomes a Bernoulli process."
Suppose I have a discrete time setting with discount factor $\delta$. A buyer receives a constant value $v$ for each period in which he uses a good.
Then, for example, my total value today of using the good for two periods is $v(1+\delta)$. Would the value from having the good over a time interval $[0,d]$ be $\int_0^d v e^{-rt} dt$, or how does it work?
Next, if in one period of length $d$ in expectation $\lambda_d$ buyers arrive and the number of arrivals is Poisson distributed, how do I get to the Bernoulli process? What exactly is the probability? Whatever I wrote down seems to converge to zero.
Do you have a recommendation where I can read up on these basics?


texts: Why do the income and substitution effects cancel for log preferences? Trouble reconciling Slutsky decomposition

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I've read (pg 10) in Gourinchas' notes on consumption that the income and substitution effects cancel for log preferences, and I tried to prove this to myself doing the Slutsky decomposition for the simple case of $U(x,y) = \ln(x) + \ln(y)$ s.t. $p_x x + p_y y = I$. I get that the Hicksian and Marshallian demand functions are $x^* = \frac{p_y}{p_x} y = \frac{I}{2 p_x} $ respectively. Plugging these in gives me this for the decomposition:

$$ \frac{\partial x^*}{\partial p_x} = - \frac{p_y}{p_x^2} y - \frac{1}{2 p_x} \frac{p_y}{p_x} y $$

which is definitely not zero. Am I misunderstanding?


texts: Why do graphic card prices rise due to bitcoin miners?

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I thought it would mean more sales thus more production and more profit, so why does nvidia and amd simply dont ramp up production if the trend has been now quite a long one?

And as far as I can see it's the retailers that are upping the prices, not the manufacturers so the manufacturers could easily adapt to demand within a month or two.

Am I missing something?


texts: Derive the cost function for a Homothetic production function

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I'm having trouble understanding the steps in showing that a Homothetic production function's cost function must be expressible in the form $C(w, q) = a(w)b(q)$.

Since the production function is homothetic, I know that the optimal cost minimizing input ratio given the same input costs must be exactly the same for different quantities of output i.e.

$$
\frac{H^j(w,q)}{H^i(w,q)} = \frac{H^j(w,q')}{H^i(w,q')}
$$

Rearranging this we arrive at the ratio:

$$
\frac{H^i(w,q)}{H^i(w,q')} = \frac{H^j(w,q)}{H^j(w,q')}
$$

This makes sense because in order to the maintain the input ratio constant, we would need both cost-minimizing inputs to increase by the same factor when going from $q$ to $q'$. However, the proof then states that "for the above to true it is clear that the ratio must be independent of w, thus, setting $q' = 1$"

$$
\frac{H^1(w,q)}{H^1(w,1)}= \frac{H^2(w,q)}{H^2(w,1)} = \cdots =\frac{H^m(w,q)}{H^m(w,1)} = b(q)
$$

and so

$$
H^i(w,q) = b(q)H^i(w, 1)
$$

The steps after this to get to $C(w, q) = a(w)b(q)$ is pretty understandable and straightforward for me.

However, what I don't understand is how you can clearly see that the ratio must be independent of w. Surely the ratio just states that for a given w the inputs must increase by the same factor/ratio. But how does that imply that the ratio has to be exactly the same for all w?

Edit: for those who are asking, this comes from an exercise question in Frank Cowell's textbook: Microeconomics: Principles and Analysis.


texts: Why do vacationers spend more on food and essentials than the locals?

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I cannot think of an answer to this question from the chapter on elasticity in Tyler Cowen and Alex Tabarrok's Modern Principles of Economics, Second Edition:

How might elasticities explain why people on vacation tend to spend more on food and necessities than the local population?

I am assuming Cowen and Tabarrok want me to say, "Vacationers' demand for food and necessities is more inelastic." I don't know why this should be true. For a given change in the price of food, the quantity demanded would barely budge for both vacationers and locals (there are, after all, no substitutes for it).
I first thought vacationers want food of just one kind, i.e., food commonly found in the place they came from, but this doesn't explain why the demand for necessities should be inelastic.


texts: Partial differential equations in economics

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Where, in economics, are partial differential equations used?

I'm particularly interested in micro theory applications, but would also be keen to know of other applications.


texts:
If someone has the attitude that they want to maximize their worst possible outcome (so they are maximally risk-averse), what does the utility function for that look like?  Can this attitude be expressed as a utility function?

Maybe as a function defined by a limit?


texts: How does the monopoly's deadweight loss affect market surplus and the economic pie?

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Source: p 312, Principles of Microeconomics (7 Ed, 2014) by N G Mankiw

  Welfare in a monopolized market, like all markets, includes the welfare of both
  consumers and producers. Whenever a consumer pays an extra dollar to a producer
  because of a monopoly price, the consumer is worse off by a dollar and the
  producer is better off by the same amount. $\color{red} {[1.]} $ This transfer from the consumers of the
  good to the owners of the monopoly does not affect the market’s total surplus—
  the sum of consumer and producer surplus. In other words, the monopoly profit
  itself represents not a reduction in the size of the economic pie but merely a bigger
  slice for producers and a smaller slice for consumers. Unless consumers are
  for some reason more deserving than producers—a normative judgment about
  equity that goes beyond the realm of economic efficiency—the monopoly profit is
  not a social problem.

  The problem in a monopolized market arises because the firm produces and
  sells a quantity of output below the level that maximizes total surplus. $\color{green} {[2.]  \text { The
deadweight loss measures how much the economic pie shrinks as a result. }} $ This
  inefficiency
  is connected to the monopoly’s high price: Consumers buy fewer units
  when the firm raises its price above marginal cost. But keep in mind that the profit
  earned on the units that continue to be sold is not the problem. The problem stems
  from the inefficiently low quantity of output. Put differently, if the high monopoly
  price did not discourage some consumers from buying the good, it would raise
  producer surplus by exactly the amount it reduced consumer surplus, leaving
  total
  surplus the same as could be achieved by a benevolent social planner.

On p 311, Mankiw discusses the deadweight loss (hereafter DWL) of a monopoly, which 2 above concerns. So what does 1 mean? It appears to contradict 2. DWL reduces the total market's surplus, and so the size of the economic pie.