texts: How is the Euler Equation for Consumption derived from from intertemporal budget constraint and lifetime utility function in basic macroeconomics

texts:
I suspect that what I'm actually asking here is just a basic calculus question, which I have overwrought, but I wanted to ask it here to make sure before taking it to SEMaths.

In the Jones Introductory Macroeconomics textbook, he says that we don't really need to know the calculus for HOW Euler's Equation is derived, which is true, but I'm having a hard time moving on without it.

We start with the lifetime utility function:

$U= u(c_{today}) + \beta u(c_{future})$

$c$ is a quantity consumed, $u()$ is a utility function, $\beta$ is a ratio parameter to account for impatience.

Then we use the intertemporal budget constraint to express $c_{future}$ in terms of $c_{today}$.

$U= u(c_{today}) + \beta u[(1 + R)(\bar{X} - c_{today})]$

$R$ is real interest rate, $\bar{X}$ is total lifetime wealth

The next step is the one I don't understand, and probably just comes down to my own poor calculus. We are told to take the derivative of the previous equation with respect to $c_{today}$ in order to arrive at

$u'(c_{today}) + \beta u(c_{future})(1+R)(-1)=0$ OR
$u'(c_{today}) = \beta (1+R)u'(c_{future})$

I understand that we've applied the sum rule of differentiation, meaning we take the derivative of $u(c_{today})$ and $\beta u[(1 + R)(\bar{X} - c_{today})]$ separately. And since in the context of this problem the utiltiy function is a black box, we just express it as $u'(c_{today})$. No problem.

However, when I look at the second part, $\beta u[(1 + R)(\bar{X} - c_{today})]$, I do not understand what rule has been applied. It appears to be the chain rule, but if I'm reading it correctly, then $(1 + R)(\bar{X} - c_{today})$ is the argument of the utility function. The chain rule, as I understand it, would only apply to the value of the function. After performing the differentiation, some values have somehow moved from being arguments of a function to being part of the equation. Considering that, for this exercise, the utility funciton is a black box with an unknown relationship, how are we allowed to apply any of our differentiation rules to the arguments?


texts:
No idea if this is the right stackexchange for this,  feel free to point me elsewhere!

I'm teaching business calculus and one of the problems the students have is to figure out the present value of a continuous income stream $\$$$A$ per year earning $r$ interest rate.  The integral comes to $$P.V=A\int_0^te^{-rz}dz=\frac A {-r}(e^{-rt}-1)$$
I've noticed as a heuristic that for relatively short values of t ($t<10$) and small values of r ($r<.04$) (the parameters the learning software uses),   the present value comes to be just a bit less than $A\cdot t$. (usually within about 10 percent)  Does anyone know an economics rational why this is the case,  and would it hold for larger values of $r$ or $t$?


texts: Would the military be more efficiant if they were unionized?

texts:
I hear about the extremely long work hours in the army. I understand it hardens them for readiness for combat situations. With the technology and increase of intelligence need to operate it would a more normal work schedule be more efficient and less mistakes?

How much more would it cost the military to have union like rules?


texts: I'm looking for a reviewed source on the amount of money in the world

texts:
As in title, I'm looking for a paper estimating the amount of all money in the world, sum of value of all national currencies or something like this.

When I google it, I find only pop-science curiosities, but I need hard data to quote.


texts:
This question is not backed by serious economic research but mainly by a very simple attempt to look at how the world economy has changed.

I am asking whether and why the world has, over the past 50 or so years, become less productive (not used in the strict economic sense here) and therefore people have less money to do stuff/buy things.

Several reasons why I believe this to be the case (I am open to be corrected):

Real wages in developed economies have not risen for a long time
Financial crisis now been going on for many years (almost 10)
Unemployment in the EU is very high
Tax rates are ever-increasing (it seems) relative to median wages
More and more people are reliant on welfare (from what I gather, unfortunately I don't have a source at this point
Growth in developing countries (China) has decreased
National debts are ever-increasing

This has left me with the feeling that in many situations, there is simply 'less' money to go around and be spent. I can observe this, for example, by the seemingly constant need of companies and countries (even where I live, in wealthy Switzerland) to save money and reduce expenses (I don't know if it only seems this way because of some biases or it is actually the case).

Again, not sure if this is actually happening or if it only seems so to me (Also apologies for not being able to express this in very 'economy' terms).

Several reasons that I could explain to myself why it would seem like we have less to spend and are less productive than we used to be:

Rising inequality (the rich keep getting more so the majority has less)
Less incentive for technological progress (apart from in IT). In many industries, there is no reason to keep making everything better, only to make it cheaper and more profitable. We have most of what we need and don't see a point in improving it (cupboards, beds, kitchen utensils etc.)
Lethargy of people. Many people are happy with what they have and do not want to work more/harder
We have most of what we need, and the things that are left to buy are luxury items (which we maybe didn't think about before)

Again sorry for the very vague way of asking this question without any evidence, but if someone could help me make it more concrete I would be very open to that.

I guess what I want to say is do people have less money and less to spend than they used to, and if so, why?


texts: Elasticity when the demand function is given

texts:
Given the demand function, $ q = kp^{-\epsilon} $, how do I calculate the elasticity? As a result, I do know that the elasticity when the demand function is in this form is $ - \epsilon $. But I'd like to know how. I also found a derivation online that proceeded like this:

(1) Take logarithm on both sides
(2) Differentiate on boths ides
(3) You'll get: $$ \frac {\text{d} \ln(q)}{\text{d} \ln (p)} = - \epsilon $$
(4) The LHS of the above equation is simply elasticity.

How does $$  \frac {\text{d} \ln(q)}{\text{d} \ln (p)} $$ represent elasticity?


texts: Do the efficiency savings of mergers indicate a type of waste or inefficiency in a market?

texts:
In this BBC News article about the merger of Tata Steel and Thyssenkrupp, the following figure is reported:

  The merged group anticipates it will make costs savings of between £350m to £440m a year.

Presumably some or all of these savings would be achieved by eliminating redundant duplication of departments across the two organizations.

Are the cost savings mentioned in the article indicative of a fundamental inefficiency caused by a competitive market, that wouldn't be present in, say, a nationalized industry (or total monopoly)?


texts: When only half of the independent variables are non stationary, does it make sense to run a cointegration test?

texts:
I have the following regression equation (panel data):
$Y = f(X_1, X_2, X_3, X_4)$

After obtaining CIPS and CADF statistics, $X_1$ results to be stationary for both intercept and intercept + trend, whereas $X_2$ is stationary only for intercept + trend. $X_3$ and $X_4$ are contrariwise non stationary in neither case.

Because of these results, I was wondering whether running a co-integration test makes sense (since if I'm not wrong, all the variables should be $I(1)$).

Also, I was wondering whether to proceed with using a first difference for $X_2$, $X_3$ and $X_4$, or only for $X_3$ and $X_4$.

Thank you very much.

Kodi


texts: Any suggestion for a good intro to the theory behind economic evaluation of healthcare programmes?

texts:
I'm looking for an introduction to economic evaluation of healthcare systems.

So, maybe the most obvious answer is Methods for the Economic Evaluation of Health Care Programmes by Drummond et al. but I'm waiting with ordering until the release of the latest edition on the 24th of September.

In the mean time I would like to start reading a bit. Are there any suggested (review) articles (journals / web) which can serve as a good introduction? My main focus is on cost-effectiveness analyses.


texts: What is the economic meaning of multiple internal rates of return?

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Recall that the internal rate of return (IRR) is the discount rate such that the net present value (NPV) of a project is 0.

One interesting complexity of the internal rate of return (IRR) is that it does not have to be unique. For example, consider the following project with cash flows spanning 5 years:

What is the economic meaning of this phenomenon? Beyond the economic meaning, what are the project financing implications? Say your IRR hurdle rate is 10%. Should you do this project or not?

I know there is a related issue, where the IRR doesn't exist. That doesn't seem like as big a deal, because if the NPV of a project is positive for all discount rates then that seems like a very good project (and if always negative then it is a very bad one). Is there a modified IRR decision rule that handles the situations where the IRR is non-unique or non-existent?

Some claim this is a reason to use NPV instead (Jan (2016)). But I don't see how that helps. What do we make of a project like this, one that has a positive NPV with a discount rate of 10% (\$1,429.94) and a negative NPV for a discount rate of 5% ( -\$1,008.15)? Are we really saying that this is a project that if profitable if your cost of capital for the project is ten percent but unprofitable if your cost of capital in five percent? Doesn't that seem off and maybe even wrong? Normally, having a lower cost of capital is an advantage!


texts: Please explain in simple terms. How exactly does it function?


texts: Can $u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$ be solved by Kuhn–Tucker conditions?

texts:
Consider

$\max_{x_1, x_2, x_3, x_4} u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$

s.t. $\; p_1x_1 + p_2x_2 + p_3x_3 + p_4x_4 \le w$

I know we can solve the max problem through separately considering case(i): $x_1, x_2 > 0$ and $x_3 = x_4 = 0$; and case (ii) $x_1 = x_2 = 0$ and $x_3, x_4 > 0$.

But is it possible to solve the whole optimization problem through the Kuhn–Tucker method?

We can write down the Lagrangian $L(x,\lambda)=\sqrt{x_1x_2}+\sqrt{x_3x_4}+\lambda(w-p_1x_1-p_2x_2-p_3x_3-p_4x_4)$

with the complementary slackness conditions:

$\frac{\partial L}{\partial x_1}=\frac{1}{2}\sqrt{\frac{x_2}{x_1}}-\lambda p_1 \le 0,\quad x_1 \ge 0, \quad \text{and}\quad  x_1 \frac{\partial L}{\partial x_1}=0$.

$\frac{\partial L}{\partial x_2}=\frac{1}{2}\sqrt{\frac{x_1}{x_2}}-\lambda p_2 \le 0,\quad x_2 \ge 0, \quad \text{and}\quad  x_2 \frac{\partial L}{\partial x_2}=0$.

$\frac{\partial L}{\partial x_3}=\frac{1}{2}\sqrt{\frac{x_4}{x_3}}-\lambda p_3 \le 0,\quad x_3 \ge 0, \quad \text{and}\quad  x_3 \frac{\partial L}{\partial x_3}=0$.

$\frac{\partial L}{\partial x_4}=\frac{1}{2}\sqrt{\frac{x_3}{x_4}}-\lambda p_4 \le 0,\quad x_4 \ge 0, \quad \text{and}\quad  x_4 \frac{\partial L}{\partial x_4}=0$.

However, when guessing say, $x_1 = 0$ and $x_2,x_3,x_4>0$, $\lim_{x_1 \to 0}\frac{\partial L}{\partial x_1} \to \infty$, which does not satisfy the complementary slackness $x_1 \frac{\partial L}{\partial x_1} = 0$.

I do not know whether we can use the Kuhn–Tucker method to solve this optimization problem? And if not, what are the reasons?


texts:
Does anyone know of journals related to welfare economics?
If not, what is the next best alternative to find articles (preferably open access) related to current research in welfare economics?

Thanks


texts: Research around the free-rider problem when the resource is taken away?

texts:
Today, Wikipedia is again running a donation drive in an attempt to raise more money. Their requests seem to occur more frequently each year. I would guess that 99.99%+ of Wikipedia users never donate, and yet continue to use the service. The existence of Wikipedia as a resource certainly isn't "free," as servers cost money. I wondered what all of the free-riders would do if Wikipedia were to run out of funding and not exist as a resource anymore.

Can anyone share some insight/examples around what happens in a given microeconomy in which the "free" good - the existence of which results in the free-rider problem - is taken away? Is there a sudden rush from the free-riders to pay, and then after some time, donations regress to their original mean?


texts: :History: Industry threatening to leave if social change takes effect

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With growing inequalities and salary gap, left-wing politicians are asking for social reforms in some countries (I am thinking of France).

Social reform include: equal pay for women, maternity leave, increasing minimum wage, higher taxes on multinationals, lowering retirement age, etc.

In all these countries, people are threatening that if these changes come into effect, "the money will leave".

I seem to recall similar threats: Ford threatening to close its plants in the UK after the 1968 strike if the women pay were increased, some French based companies after the 35h-week reform (all worked hours above 35 in a week are considered extra and payed more), and currently politicians in the US when people speak of holidays or maternity leave.

My questions are:

1: is there any historic precedent of these threats to "leave" being actually carried out and

2: does it even make sens from an economics point of view ? I can understand manufacture going to Asia, but Starbucks, McDonald, and all these companies that have to stay in France to make profit and, with a clever manipulation, do not pay taxes on the companies in France (impôts sur les sociétés), would they really leave ? Starbucks makes 2 billion benefits in France, so if social reform and it paying taxes would mean it would only make 1 billion benefits, wouldn't that be still worth it ? And even if the benefits are less than that, wouldn't McDonald stay in France, if only to maintain the hegemony (leaving would mean taking the risk of someone taking its place, like Burger King or something, and that would mean losing the monopoly, which I would think is a bad thing for such a company). And even if they do leave, couldn't France just introduce a 5 years tax-free period for any new start-up replacing  them ? It's not getting its taxes anyway, better give it up for 5 years than for ever... no ? Am I being naïve ?


texts: Post-redistribution Lorenz curve comparison with reranking in R

texts:
Using R, assume the population income for N= {1.. 7} looks like $X_1$= c(1,3,5,7,7,19,21). Use the Lc() function from the "ineq" package to plot the corresponding Lorenz curve $L_{X_1}(p_1)$.

Next, rerank $n_2$ and $n_6$ so that $X_2$= c(1,18,5,7,7,4,21) while mean is same ($\mu = 9$). Plot the Lorenz curve $L_{X_2}(p_2)$ using Lc().

Next, rerank $n_4$ and $n_5$ so that $X_3$= c(1,18,5,6,8,4,21) while mean is same. Plot the Lorenz curve $L_{X_3}(p_3)$ using Lc(). Note that this redistribution violates strict horizontal equity.

Questions:

Using the Lorenz curves above, may I say that all strictly increasing, concave social welfare functions will prefer $L_{X_2}(p_2)$ and $L_{X_3}(p_3)$ as dominant over $L_{X_1}(p_1)$?
Can we discuss the "equalizing effect" of the redstribution even though reranking has caused $p_1$ to change?

I ask because Lambert (2001, 37-42) treats the total tax ratio > 0 and the mean post-tax income < mean pre-tax income, and shows that the "concentration curve for post-tax income with respect to pre-tax income" is the same as the Lorenz curve if there is no reranking. In my example, however, the total tax ratio = 0, the mean post-tax income = mean pre-tax income, and there is reranking. I think my confusion relates to the "concentration curve" as an intermediary to our real goal, the comparison of Lorenz curves.

All clarification appreciated.

Lambert. 2001. The Distribution and Redistribution of Income.


texts: Government debt and Fiscal Theory of Price Level

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I am trying to understand the Fiscal Theory of Price Level (FTPL) and how it explains inflation. I've been reading several papers by Eric Leeper and I am slightly confused about some of his claims. For example in this paper he argues:

  Suppose that higher deficits do not create higher expected surpluses and that central
  banks either peg short-term nominal interest rates or raise them only weakly with inflation.
  Because a tax cut today does not portend future tax hikes, individuals initially perceive the
  increase in nominal debt to be an increase in their real wealth. They try to convert higher
  wealth into consumption goods, raising aggregate demand. Rising demand brings with it
  rising prices, which continue to rise until real wealth falls back to its pre-tax-cut level and
  individuals are content with their original consumption plans.

I understand that he is explaining 'non-Ricardian' policies. However, if the government increases its deficit by issuing bonds, would that not decrease AD in the period the bonds are sold? Say that the government increases its deficit in period $t$ by selling bonds. Private agents buy these bonds and thus give up consumption goods. So in period $t$, should AD not decrease? And when the bond matures and the agents receive their payoff, they will spend it as long as the government is credible enough in not raising taxes. I might be overcomplicating things about this is just a thought I have had.

And lastly;

  By preventing nominal interest
  rates from rising sharply with inflation, monetary policy prevents debt service from growing
  too rapidly, which stabilizes the value of government bonds.

I understand the reasoning that keeping interest rates stable will stabilize the debt servicing. However, suppose that interest rates rose. If the interest  rate is higher than the growth rate of the economy, the government will have to monetise its debt in order to pay the interest component, this will obviously be inflationary. Or, they can issue more debt. If they choose the roll over on the debt (i.e paying the interest by issuing even more debt), will this be inflationary or deflationary? Using the same reasoning as above, I would think this is deflationary because by selling bonds to private agents, they have to give up consumption goods, thus reducing AD.

I'm trying to understand the intuition behind fiscal and monetary authority interaction. So if my questions can be answered by academic literature, I would gladly give it a read.

Thanks in advance!


texts: Why can we finance government deficit by having a trade deficit?

texts:
I encountered an example question regarding government deficit as follows:

$G-T=(S-I)-(X-M)$

where $G$ is government spending, $T$ is net tax (tax minus transfer payment), $S$ is total private sector saving, $I$ is investment, $X$ is export and $M$ is import.

Suppose deficit $G-T=\$84249$, $S-I=\$58558$, so $X-M=-25661$.

The example question states that: to finance the deficit, private saving must exceed investment by $\$58558$, and to finance the rest of the government deficit, foreign imports ($M$) must exceed exports ($X$) by $\$25661$.

My question is, if there is a trade deficit (import is greater than export), that means the government buys imported products more than it sells the exported products; the government spends more than it earns, then how can it finance the government deficit?

This really confuses me. Thanks for any help!


texts: Is UK house price spiral connected to debt based monetary system?

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(cross-posted from Personal Finance & Money)

Is the monetary system's debt basis* driving government policy on housing and property, and how could this ultimately affect personal housing affordability?

The UK has an ongoing 'situation' with property.  A recent topical example is the government's promise of a 'right to buy' for housing association properties, to acclaim and criticism.  The government seem generally keen to get citizens mortgaged up, or are they just aiming to satisfy the public's home-owning aspirations?

These are some typical headlines:-

UK housing crisis 'in breach of human rights'

UK has world's second-highest house prices beaten only by millionaire's playground Monaco

Is the monetary system's debt requirement driving this property bubble?  And if so, what are the characteristics of it.

Edit

For example, the US subprime debacle, considered by some to be caused by pressurised lending, possibly driven by a monetary system that needs to grow by increasing the debt pool.  If this is the case, it could be viewed that government would support the taking of mortgages and increasing debt, in order to keep the money pool growing and stave off recession.

*Ref: What is a debt based monetary system?


texts:
I was reading a note on Solow model in continuous time, and it said we can derive K, C, and Y from the key equation. But the steps were omitted, and I have no clue with it. How can I derive these variables?

Many thanks!


texts: Why was the Bank of England nationalized after World War 2?

texts:
After the Second World War the new Labour government nationalised the Bank of England.

Did this give the British Government any new capabilities? For example, could the Government print money before this?

What was the purpose of this move?


texts:
I'm taking kind of a crash-course in convex analysis to complement my mathematical skills and was wondering if anyone knew about nice ways in which this kind of tools were used in Economics.
To be more precise, some of the things I've seen so far are not strictly in the area of convex analysis but are very related, like dual spaces, weak topology, subdiferentials and Hahn-Banach theorem.

The only example I know of is the duality between the UMP and EMP in consumer theory (and of course the firm maximization and cost minimization problems). I also think that Hahn-Banach is used in the proof of the first welfare theorem.

Has anyone here used this kind of mathematical concepts in their work or has seen any interesting recent usage of them?


texts:
Would appreciate some guidance on a matter of recursive substitution, where we have the AR model:
$$y_t = \alpha +\theta_1y_{t-1}+ u_t$$
And
$$E(y_t)= \mu_t$$
Where:
$$\mu_t = (1+\theta_1 + \theta_1^2+..+\theta^{t-1})\alpha+\theta^ty_0$$
It follows by recursive substitution we get:
$$y_t = \mu_t +(u_t +\theta_1u_{t-1}+\theta^2u_{t-2}+...+\theta^{t-1}u_1)$$
And subsequently:
$$E[y_t] = E[\mu_t]+ E[(u_t +\theta_1u_{t-1}+\theta^2u_{t-2}+...+\theta^{t-1}u_1)]= \mu_t$$
Would someone be able to explain how the step concerning recursive substitution is obtained, moving from line 2,3,4?


texts: What benefits does Bitcoin (i.e. cryptocurrency) offer?

texts:
I really, really like moderate inflation. I live in Sweden where the interest rates just went negative because we are on the brink of deflation, and the rate of inflation we have now is far too low. We have huge problems attracting foreign attention and the swedes don't want to take out loans to invest since paying them back ten years down the road hurts just as bad as paying them now (and there's a real risk it might take more to pay them back later, if we go into deflation). It's a real head ache that's all the talk in our financial world.

Getting a hold of Bitcoin is very, very hard and expensive. The value of it has deflated dramatically from when it was introduced, and despite occasional crashes, it could very well just keep climbing in value. It also has a cap, which to me looks like it would unleash a deflationary spiral that would only end once we find a new currency (like the Great Depression was alleviated when we stopped using the gold standard).

But, I'm a computer scientist and I just can't stop finding bit coin supporters everywhere. It has thousands of evangelical missionaries using blogs and magazines to tout it as a means to liberate us from the bankers. I don't know, can't computer scientists be just as corrupt? It looks like dot coms with access to good cryptographic algorithms and server farms who can work in parallel could game the system even more, and once they've swept up all the bit coins they would wield more power than nation states.

Am I missing something? What does bit coin bring to the table that is worth disregarding deflation? Does it bring positive GDP growth? Ease of investment? Monetary power to the people? How? And, I keep coming back to this, wouldn't all these positives be completely wiped out once the 30s come knocking deflation style?

Why does this currency have so many supporters? Are everyone mad?


texts:
I'm following Woodford's Interest & Prices to derive the microfundations for a New Keynesian model with staggereed prices.
I defined the utility function and disutility function (1.1 at page 144) as
$$ u= \frac{\xi_t C_t^{1-\sigma}}{1-\sigma}, v= \frac{h_t(j)^{1+\eta}}{1+\eta}, $$
where $\xi$ is a consumption disturbance.
Then I have defined the production function ( 1.7 at page 148) as
$$ y_t(j)= A_t * h_t(j). $$
With this functional forms we can write the real marginal cost (1.10 at page 149) as
$$ s_t(y,Y,\xi) = \frac{v_h(f^{-1}(y_t(j) /A); \xi)}{u_c(Y_t; \xi)A} \frac{1}{f'(f^{-1}(y_t(j)/A))} = \frac{y_t(j)^\eta \cdot C_t^{1/\sigma}}{A_t  \cdot\xi_t } .$$
Woodford says that with flexible prices we can write the natural rate of output as (1.14 at page 151)
$$s(Y^n, Y^n, \xi)= \mu^{-1}.$$
Therefore I get that the natural rate of output is equal to
$$ Y_t^n =( \mu^{-1} * A_t * \xi_t )^{\eta/ \sigma}. $$
However the problem with this definition is that in the steady state where the shocks($\xi$ and $A$) are zero also the natural rate of output will be zero.
Is this formulation correct? Is there another way to express the natural rate of output?


texts:
I'm confused because my textbook says  the higher interest elasticity of money demand is , the flatter slope of the LM curve is.

If the interest changes, then isn't it the movement along the curve in the money demand curve?

I can't understand how interest elasticity of money demand is related with the slope of the LM curve. Can someone explain this GRAPHICALLY?


texts: Nominal versus real wages in panel data modes

texts: Assuming dependent variable is log of wage, do we need to convert nominal wages to real wages in analyzing panel data sets when using random and fixed effects models? Is that also applicable for pooled OLS when not controlling for years?


texts: What's the difference between loans, notes, bonds and mortgages?

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Long-Term Investments

Multi-year investments in:

Debt securities: loans, notes, bonds, mortgages
Equity securities: shares of other companies

These assets are normally not intended to be sold (and converted to cash) within one year

Can anyone explain what's the difference between loans, notes, bonds and mortgages?


texts: Why is fuel more expensive on the high way in Europe?

texts:
In Europe it's usual, that fuel prices are 10-20% higher on the highway, than in the city. This is not only my personal observation, but also mentioned on travel sites (eg here and here). I don't have much expertise in economics, but as I understand this should not be possible in a competitive market, since what would stop a petrol station to lower their prices to the same level as the ones in the city, and get all the customers?

One solution could be, that they are different companies, but even the big ones like Shell and OMV have higher prices on the highway.

My question is: what is the reason for this situation, and what stops petrol stations from lowering their prices?


texts: Deflate level and flow variables using PPI and CPI

texts:
What do statements like

Flow variables (such as dividend growth and returns) are deflated using the CPI index.

or

Level variables are deflated using the Producer Price Index (PPI).

mean?

What are level varibales?
I guess both indices correct for inflation but why would dividend growth/returns need to be adjusted?
How does one actually implement this deflation of variables? Is there a time series of the CPI and PPI available only and one simply has to multiply a particular variable with the index?


texts: Optimal decision for perfect substitutes utility function ?

texts:
Given $u(x_1,x_2)=4x_1+14x_2$ and $m=\frac{1}{2}x_1+\frac{3}{2}x_2$, I shall choose the optimal decision among:
$a)(2m,\frac{2m}{3})$
$b)(2m,0)$
$c)(\frac{m}{2},0)$
$d)(0,\frac{2m}{3})$
The correct answer is $(d)$

But not sure how to find this, what I did:
$$m=\frac{1}{2}x_1+\frac{3}{2}x_2 \Leftrightarrow x_2=\frac{2m}{3}-\frac{1}{3}x_1 $$
And the marginal rate of substitution is $-\frac{2}{7}$,so we have :

Obviously $a)$ isn't the right one and $c)$ doesn't seem to be the best one... but really don't know 'how to think', some explaination would be great.
Thanks in advance


texts: Analytically tractable Ramsey model: how to solve ODE for optimal trajectories

texts:
In Brunner and Strulik (2002) the authors claim, that the solution of
\begin{align}
\dot c &= \frac{c}{\sigma}(\alpha k^{\alpha-1} - \delta - \rho)\\
\dot k &= k^\alpha - \delta k - c
\end{align}

is given by (see eq. 27)
\begin{align}
c(t) &= \left(1 - \frac{1}{\sigma}\right) k(t)^\alpha\\
k(t) &= \left[\frac{1}{\delta\sigma} +\left(k(0)^{1-\alpha} - \frac{1}{\delta\sigma}\right)\exp(-\delta(1-\alpha)t) \right]^{\frac{1}{1-\alpha}}
\end{align}
if $\alpha\delta\sigma = \delta + \rho$.
I can verify the solution for $c(t)$ (see eg. this thread). However I'm not sure how to solve for $k(t)$. We can plug in $c(t)$ into $\dot k$, which gives
\begin{align}
\dot k &=  \frac{1}{\sigma} k^\alpha - \delta k.
\end{align}

How would one proceed?

Solution

With respect to Alecos answer we may solve the following ODE

\begin{align}
\dot z + (1-\alpha)\delta z = \frac{1-\alpha}{\sigma}.
\end{align}

The genereal solution is given by
\begin{align}
z(t) &= \frac{1}{\exp(\int (1-\alpha)\delta dt)}\left[\int \exp\left(\int (1-\alpha)\delta dt\right) \frac{1-\alpha}{\sigma} dt + C \right]\\
&= \frac{1}{\delta\sigma} + C\exp((\alpha-1)\delta t).
\end{align}

With $z(0)$ given we pin down $C$
\begin{align}
C = z(0) - \frac{1}{\delta\sigma}
\end{align}

which yields the desired result
\begin{align}
z(t) &= \frac{1}{\delta\sigma} + \left(z(0) - \frac{1}{\delta\sigma}\right)\exp((\alpha-1)\delta t) \\
\Longleftrightarrow \quad k(t)^{1-\alpha} &= \frac{1}{\delta\sigma} + \left(k(0)^{1-\alpha} - \frac{1}{\delta\sigma}\right)\exp((\alpha-1)\delta t)\\
\Longleftrightarrow \quad k(t) &= \left[\frac{1}{\delta\sigma} + \left(k(0)^{1-\alpha} - \frac{1}{\delta\sigma}\right)\exp((\alpha-1)\delta t)\right]^{\frac{1}{1-\alpha}}.
\end{align}


texts: Pooling equilibrium in akerlof's lemon market with certification cost

texts:
Consider a market for 300 used cars where 1/3 of all cars are good quality cars and the rest are bad quality cars. All these cars are owned by (potential) sellers to begin with and each seller owns only one car. Suppose the value of a bad car is 20 to the buyers and 10 to the seller The valuation of a good car, however, is 100  for a buyer and 50 for a seller. Assume the number of buyers on the market exceeds the number of sellers and as a result seller and the bargaining power(the price of any car in the market will be its value to the buyer)
Question: Suppose there exists a certification test costing C that can identify good cars with certainty. However, bad cars can also pass the test with probability 1/4 (and fail with, remaining probability). Consider the possibility of a pooling equilibrium, in which both sellers of good cars and bad cars choose to undertake the test. Find out the range of certification test cost C for which such a pooling equilibrium exists.
My attempt: without certification buyers are willing to pay the average price i.e. is $$140/3=46.67$$The price of a good certified car in the pooling equilibrium will be $$200/3=66.67$$ assuming that buyers know that test can certified lemon as a good car with probability 0.25
and that of lemon is 20.
Therefore, $$0< C <16.67$$
i.e C can be anything between what buyers are willing to pay less valuation of good cars to seller $$(66.67-50)$$
I am having doubts in my attempt. I am not sure if it is correct or not.
It would be of great help if someone helps me with this.
Thank you.
Edit: After certification, lemon will be sold for an average price of 40.
Rationale of my attempt: Suppose C=17, then the net benefit to a seller after certification is 23>20(=value of a bad car to seller) for lemon and 49.67<50(=value of good car to the seller) for a good car. Therefore, the seller of good car will opt out of certification.


texts: The characteristics of market liquidity, accoridng to Kyle, are tightness of the market, depth of the marekt and resiliency of prices. By referring to tightness, it descriebes the cost of turning around a position over a short period of time. Does this mean the cost to change your position in a risky security from short to long in the short term? The depth reflect the size of an order flow inovvation required to change prices a given amount, and this means the order flow necessary to induce prices to rise or fall by $1\$$. But what is the intuition behind resilienc of the market? It confuses me a little in the way Kyle sets this.


texts: Is utility function used in customer data/profile analysis? What alternatives in practice?

texts:
Utility function is great theoretical concept but is it used in customer data analysis or in building customer profile (e.g. from Big data or cash register/checkout data, ecommerce history) or in predicting future sales and future proposals that customers can be eager to accept? If utility function is not used in these areas what other tools (conceptually similar to utility function) is used in customer data analysis?

Are there attempts to discover customer goals, intentions and personality, build utility function from these conceptually high level data and use such framework in sales prediction or modelling the desirable features of new product? I have read about behavioral economics but it have strong focus on stock market modelling and little is said about consumer goods and services.


texts: Would a Federal Job Guarantee hurt the economy?

texts: I've been reading about how a job creation program would disrupt the private sector. One of the main things I kept seeing was that the a FJG will result in the elimination of thousands of jobs. So, consequently it would hurt the economy. But a FJG would create jobs that pay higher than minimum wages as well. Wouldn't that increase consumer spending, cancelling out the negative impact?


texts: Is an income tax always more favourable for consumers compared to ad valorem/quantity tax?

texts:
I'm studying the optimal choice of consumers with regards to taxation.
I read that for consumers, income tax is generally (for Cobb-Douglas preferences) preferred compared to ad valorem tax:
If the budget constraint is generally $p_1x_1+p_2x_2=m$, then an ad valorem tax $t$ will change it to $(p_1 + t)x_1+p_2x_2=m$.
If the income tax is the same amount, we get $p_1x_1+p_2x_2=m-R*$, where $R*=tx_1$ is the amount of taxes for both variants.
Now, the following figure demonstrates how an increased price of good 1 will lead to a preference of an income tax over ad valorem tax:

I wonder if this is the case for all indifference curves or if there are certain indifference curves where consumers might prefer an ad valorem tax. I doubt this, but I think the chapter in H. Varian lacks a mathematical (algebraic or analytical) explanation for this which I feel would help me understand.


texts: Relation between Nash equilibrium , subgame perfect equilibrium, backward induction, perfect Bayesian equilibrium

texts:
My claims are

1- Backward induction solution is Nash equilibrium solution.

2- Not all Nash equilibria are sequentially rational

3- All Backward induction solutions are sequentially rational

4- SPNE solutions are Nash equilibria

5- SPNE solutions are sequentially rational if game has at least one
proper sub game. If only has improper sub game then it may not be sequentially rational.

6- PBE solutions are Nash equilibrium and SPNE

7- PBE solutions are sequentially rational no matter what.

8- WPBE solutions are Nash equilibria. And sequentially rational no matter what.

Are these true? What do you think? Anything want to add?


texts: When the global optimal is outside of the constraint set, what will be the demand?

texts:
$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex.
$a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that connects $a$ and $b$.
Given: $$x^*=\arg\max_{x\in[a,b]}u(x)$$
Let $b'$ be a point in the segment $[a,x^*]$. That is: $b'=\lambda a+(1-\lambda)x^*$ for any $\lambda\in[0,1]$.
Prove that:
$$b'=\arg\max_{x\in[a,b']}u(x)$$
Graphically this result is very straight forward but I don't know how to mathematically prove it.
I think we could start of proving that $u(\lambda a+(1-\lambda) x^*)$ is monotonically decreasing with $\lambda$.
Are there named theory related?


texts: Does it matter if your decision might not matter?

texts:
I have read several experimental papers which ask people to make decisions which only matter with a certain probability. For example, individuals might be asked to submit bids in an auction, but told that their bids only 'count' with a certain probability $p$ (with probability $1 - p$, their payoff is 0 regardless of what they do). Alternatively, if we wanted to learn whether an individual's valuation for a good exceeds £10, we could offer to sell her that good for £10; but tell her that the good will be sold to her (and the payment taken) only with a certain probability. In both cases, the idea is that individuals should act as they would if $p = 1$ (i.e. the mechanism is 'incentive compatible') which then allows researchers to run these experiments more cheaply than they would be able to otherwise.

Is there any evidence about the general validity of this approach? More concretely, is there evidence as to whether the outputs of such experiments vary with $p$? Intuitively, I would have expected that subjects become inattentive if $p$ is very low (since in absolute terms, it doesn't matter much what they do), which could then add noise to the elicited estimates.


texts: What is Application of Vector Algebra in Economics?

texts:
I through one tutors heard that vector is used in economics .
But on searching about it on internet could not find anything

Recently I studied about Vectors in Mathematics

So I was wondering how could Vector be used in Economics ?


texts: Binding and slack constraints in adverse selection problem

texts:
When I am dealing with a constrained maximization, once I face constraints with inequality sign, I have to understand which one are binding and which others are slack.

If I find that a constraint is binding, I can easily substitute it in the objective function, but what if I find that a constraint is slack (it holds with inequality)? Should I keep it in the maximization problem or can I get rid of it?

I am asking it since my professor gives us two methods in order to understand if a constraint is slack: one is to compute the Lagrangian, using slackness conditions; the other is trying to understand if the constraint is implicitly satisfied, given the other constraints. In this last case, it seems I can get rid of implicitly satisfied constraints since they seem redundant to me.

I'll give you this problem as an example: there two types of person $\theta_L, \theta_H$ with $\theta_H>\theta_L$. To make the problem interesting, we suppose $\psi > \beta$.

\begin{gather*}
max_{c_H,c_L,q_H,q_L}\ \psi(c_L - v(\frac{q_L}{\theta_L})) + (1-\psi)(c_H - v(\frac{q_H}{\theta_H}))
\end{gather*}
\begin{gather*}
\beta(q_L-c_L)+(1-\beta)(q_H-c_H) \geq 0\  (BC)
\end{gather*}
\begin{gather*}
c_L - v(\frac{q_L}{\theta_L})\geq 0 \ (IR_L)
\end{gather*}
\begin{gather*}
c_H - v(\frac{q_H}{\theta_H}) \geq 0 \ (IR_H)
\end{gather*}

In perfect information at the optimum, I know from the solutions that both $IR_H$ and $BC$ are binding, whereas $IR_L$ is slack.


texts: How does elasticity impact market efficiency?

texts:
I am wondering how the price elasticity of demand (or supply) impacts market efficiency. A more specific question - can we say that in a monopolized market elasticity will be low, and that in a competitive market the competition allows the elasticity of demand to increase? Said another way, a lack of competition places a ceiling on the elasticity of demand, when there is good competition, the elasticity is not bound and reaches the correct market equilibrium value.

Can a regulator use low elasticity as evidence there is a lack of competitiveness?

Can an increase to price elasticity of demand increase consumer surplus while reducing producer surplus?

Would be great to hear some layman thoughts,a s well as references to academic literature (I didn't find much on the topic in my search).


texts: Why is it a problem if a considerable amount of currency is hoarded by the enemy of the issuing government?

texts:
During WWII and after Pearl Harbor, the United States issued the Hawaii overprint notes because they feared the possibility that if the Japanese captured Hawaii they would also control a considerable amount of USD bills [1].

I found this piece of trivia not only interesting but also made me wonder why this could be an issue? Does this mean it is also an issue if say today China starts hoarding stacks of American dollars?

https://en.wikipedia.org/wiki/Hawaii_overprint_note


texts: Dynamic Optimization: What if the second order condition does not hold?

texts:
Consider the following dynamic optimization problem
\begin{align}
&\max_u \int^T_0{F(x,u)dt}\\
\text{s.t.}~& \dot{x} = f(x,u)
\end{align}

FOCs

The Hamiltonian is given by
\begin{align}
H(x,u,\lambda) = F(x,u) + \lambda f(x,u)
\end{align}
The necessary condtions for optimality are given by the maximum principle
\begin{align}
\frac{\partial H}{\partial u} &= 0\\[2mm]
\frac{\partial H}{\partial x} &= -\dot{\lambda}
\end{align}

Suppose $u^*=\arg\max_u H(x,u,\lambda)$ is a maximizer, i.e. $H_{uu} < 0$.

SOC

The Arrow Sufficient Theorem states, that the necessary condtions are sufficient if the maximized Hamiltonian
\begin{align}
H^0(x,\lambda) = \max_u H(x,u,\lambda)
\end{align}
is concave in $x$, i.e. if $H_{xx} < 0$.

Problem

Suppose the FOCs hold, but the SOC fails to hold.

What can be said about the optimality of the solution?


texts: Could eliminating all taxes and only creating new money theoretically work?

texts:
Imagine you had the opportunity to found a new country from scratch (in 2020).
Value exchange would be digital, where only the state can create new currency units.
Instead of relying on income tax and/or indirect taxes, there would be no form of tax but instead the government would rely on increasing the overall supply of the currency to perform welfare redistribution, such as providing Universal Basic Income.
(note: UBI was my choice in this example since it simplifies welfare redistribution, making the question clearer)
An example:
Year 1: Initial currency units: 100. Government creates 10 more units (10%) and pays it out as UBI
Year 2: Init. units: 110. Government creates 11 more units (10%) and pays it out as UBI
Year 2: Init. units: 121. Government creates 12.1 more units (10%) and pays it out as UBI
...
Each year the value of the currency is lessened due to inflation, so more money has to be generated.
Would this work if the country was completely isolated?
If so, would it still work if international trade were a factor?
FOLLOW-UP QUESTION:
As far as I know, money was initially created as a means of value exchange, not necessarily a means of storing value.
Since most existing answers highlight (rightfully so) that high inflation rates lead to people not using a currency to store value, but resorting to USD or similar, wouldn't it be plausible that they would still use the currency for everyday transactions, simply because it is universally recognised, thus leading to higher ease of use?


texts: Elasticity of intertemporal sustitution with composite CRRA function

texts:
In the usual CRRA $\frac{c^{1-\sigma}-1}{1-\sigma}$ function we have that the intertemporal elasticity of sustitution  $\partial\frac{c_{t+1}}{{c_{t}}{\partial r}}$ is $\frac{1}{\sigma}$.
But how can i calculate the IE of S when the CRRA function is the composite:
$\frac{(c-G())^{1-\sigma}-1}{1-\sigma}$
Thanks in advance


texts: primary impact on real estate prices/taxes

texts:
Are my housing prices/taxes more influenced by the $40M beach house a few miles away from my home or those in the lower-class well beyond my county line?

Assuming a few basics:

there are differing economic classes
each lower one (ideally) graduates to the next higher one
we are, rather I am, somewhere at the upper-end of well-off
Area: SoCal, near the beach

Full disclosure, this question is to satisfy a disagreement; in order not to taint the question, my side of the dispute will not be identified.

The 2 differing assertions are:

my home prices are more affected by a fewer number of wealthy homeowners near my neighborhood.
my home prices are more affected by a vastly greater number of poor/blue collar renters/homeowners nowhere near my home.

The supporting argument for assertion #2 is that those people at the lowest end of the spectrum are renting/buying in such great quantities that the supply is exhausted. Subsequently, all home prices, even those hundreds of miles away in higher-classes, are affected through a "ripple effect".

Extra kudos for those with more understandable answers. The final assumption, I'm not an economist.


texts: How does the size of the largest cryptocurrency compare to the largest traditional currency?

texts:
'Money' has evolved throughout economic history, and has included moving from:

barter economies (i.e. no 'Money' - simple trading of final goods/services)
commodity money - money whose intrinsic value - e.g. the gold/silver/copper/alloys it was made from - has real value
fiat money (e.g. where the paper a bank note is made from isn't actually worth much/anything)
digital currency equivalents of fiat, as computing became common place where the 'Money' is a record in several banks' computer systems
to crypto currencies where the 'Money' is bits in a distributed ledger
probably more I've missed (e.g. bank issued notes).

Question
Bitcoin is the largest of the class of currencies/assets known as 'cryptocurrencies', and the USD is the largest in the class of traditional currencies, what is the 'size' of bitcoin relative to the USD?
That is, how does bitcoin compare to the US Dollar in terms of any/all of:

Total estimated annual transaction volume on final goods and services
Total value (e.g. if all BTC were converted to USD at the current market rate, or vice-versa, how would their values compare?)
Other measures?

Sensible assumptions in measuring the above are welcome.
Note: I thought about also including comparison of the total number of accounts, bit I think that's useless since creating accounts in cryptocurrencies is so trivial that one person could create billions, making comparison fairly uninformative. I also thought about comparing the number of (human) users, but suspect that could be difficult since it's not possible to know how many human users there are for most of the large crypto currencies.


texts: Do house prices increases affect inflation?

texts:
In this book, page 202, the authors develop the idea that when the central bank increases the interest rates to get the CPI inflation back to target inflation, it will not necessarily cut off an eventual house price bubble, or the financial accelerator. And to justify this assertion, in a footnote they state: «The elements of housing costs included do not influence the overall price indices that enter the inflation target to a high degree. To see this plot the US Consumer Price Index against the US Consumer Price Index less Shelter(Data available from US Bureau of Labor Statistics)». (What I understand from this is that since the housing related costs that enter into CPI computation are negligible, the central banker will perceive an inflation different from what if it included housing prices directly. Did I understand correctly?)

So, I plotted the graph.

I included an extra series, "All items less Food". It behaves exactly like the CPI.

How can I deduce from the graph what the authors of the book are saying?

Any help would be appreciated.


texts:
The Demand Curve
The Supply Curve
Monopoly: How to Graph It

In videos (1) and (2), we see that the supply and demand curves do not touch the axes.
In (3), we see that the demand curve touches the Y-axis but doesn't touch the X-axis. MR curve touches both axes. On the other hand, MC and ATC curves do not touch any axis.
When do the curves touch the axes and when don't they?


texts: Mortgage loans from foreign banks at lower interest rates

texts:
I had a thought - what if I live in a relatively poor country like let's say Russia and I would like to buy a house. In order to do that, I need to take a mortgage loan. In Russia however, interest rates are pretty high, lets say the best offer from a bank is 15 % annually. That's a lot but due to high interest rates, unlike in rich EU countries, the housing prices relative to income are not that high.

What does stop me from taking a loan from a bank in a rich EU-country to build or buy a house in a poor country like Russia, while having EU-level interest rates below 3% instead of the Russian 15%?


texts: Effect of a productivity shock on the real exchange rate within a two period model

texts:
So if we have a two period model, tradable goods and nontradable goods, where consumers tend to maximize utility, then we have the following Euler equation:
$$\frac{ u' (c_1) }{P_1} = (1+r)\beta \frac{ u'(c_2) }{P_2}$$
And $P$ is the Price level in period 1 and period 2.
If there is a productivity shock in period 1, such that consumers need to borrow money in order to smooth consumption and repay this debt back in period 2. But how does this affect the price level in case of Cobb Douglas production function, i.e:
$Y_i = A_i K_i^\alpha L_i^{(1-\alpha)}, \;\;\;\; i = {tradables, nontradables}$
and  nontradables is labour-intensive and tradables is capital intensive?


texts: Multiplier in the two-sector Keynesian model

texts:
Which of the following is most likely to reduce the size of the multiplier in the simple (2-sector) Keynesian model?

Increased taxes on savings
Reduced access to government funded medical care
Reduced compulsory superannuation contributions for workers
Increased competition in the banking sector, leading to lower borrowing costs

Answer given by the lecturer was 2. Could some please explain why? I thought that it was 3 (Employees have to save more of their earned income for retirement because firms no longer supplement super contributions for their workers, which increases the marginal propensity to save and decreases the multiplier.) How could it be 2 if we are in the two-sector Keynesian model? Doesn't that condition imply that there is no government spending to begin with as we are only considering the interaction between households and firms?


texts: Derive a cost production function give prod f, only K

texts:
In this question, only K is included and L is excluded how would I go about deriving it?

Total cost= Fixed costs + Average costs.

Since the variable input costs r per unit, the variable costs is r times the number of units rQ, hence $VC= rK^\alpha$.

Thus $C(Q)= c_0 + rK^\alpha$

Is the above solution correct?
IS there a more mathematical way of doing it, one that involves grpahs etc.


texts:
Is there a measure of similarity for economies?

For example, I would like to find the world economies most similar to the UK.


texts: Are the primary dealers obliged to buy treasuries no matter what?

texts:
It is said that treasuries are the highest quality debt because the government can always "print money" to pay the debt.
But, isn't so that the ones printing the money to loan to the government are the primary dealers.

If so is the reason it is said that the government can always pay their debt because the primary dealers are obliged to always loan to the government?

Is there a case in which the primary dealers could refuse to buy treasuries?

In general, are the primary dealers incentivized or compelled under the law to always bid for the treasuries?


texts:
I am currently reading Woodford (2010) and I have understood it for the most part. However, as I am new to solving these kind of models I have a question regarding a specific type of monetary policy rule. Namely one where the domestic central bank pegs domestic rates to foreign interest rates (due to e.g a currency peg).

The examples I have working with involved a Taylor rule of the form:

$i_{t} = \bar{r} + \phi \pi_{t}$
I then use the method of undetermined coefficients and assume a solution on the form:

$i_{t} = \bar{r} + \gamma_{i} \hat{g}_{t}$, $\pi_{t} = \gamma_{\pi}$ $\hat{g}_{t}$ , $y_t = \gamma_y \hat{g}_t$

and do the appropriate substitution in to the IS function:

$\hat{y_{t}} = E_t \hat{y}_{t+1} + \sigma^{-1}(i_{t} - E_t \pi_{t+1} - \bar{r})$

So the term inside the brackets become:

($\phi$ $\gamma_{\pi}$ $\hat{g}_{t}$ - $\gamma_{\pi}$ $\hat{g}_{t+1}$) and after assuming a functional form of $g_{t}$ I am able to solve the model.

However, now when the monetary policy rule is to peg the interest rate I am unsure how to guess the form of the solution.

My monetary policy rule is:

$i_{t} = i_{t}^{*}$ where $i_t^*$ is the interest rate of the foreign country. My initial thought was to do something like:

$i_{t}^* = \gamma_{i^*} \hat{g}_{t} $ but then when I try to solve it I end up with two equations (PC and IS ) and three unknowns ($\gamma_\pi,\gamma_i^*,\gamma_y$). TO clarify what I mean, consider again the term in brackets from the IS function:

$(\gamma_i^*\hat{g}_t - \gamma_\pi \hat{g}_{t+1})$, it's the $\gamma_i$ that is causing me problems. With the Taylor rule I was able to deal with it because the policy rule implies:

$\gamma_i = \phi \gamma_\pi$

Any ideas where I am going wrong?


texts: Utility functions and positive monotone transformations

texts:
We let $g(z)$ be a strictly monotonous function so:
$$\frac{dg(z)}{dz}>0$$
Consumer 1 has preferences given by the utility function $u(x_1,x_2)=ln(x_1)+2ln(x_2)$, while consumer 2 has preferences given by n $v(x_1,x_2)=g(x_1x_2^2)$.
Then I have to show that consumer 2 got same preferences as consumer 1.
I think I have to use MSR on $x_1x_2^2$ and on $v(x_1,x_2)$. For MSR on $x_1x_2^2$  I get:
$$MRS=-\frac{\frac{\partial }{\partial x_1}}{\frac{\partial }{\partial x_2}}=-\frac{x_2^2}{2x_1x_2}$$
But How can I find MSR on $v(x_1,x_2)$ (I think I got the same MRS if I use the chain rule, but I'm not sure?), and how can I use this to conclude that the ranking of the two indifference curves is the same when $g(z)$ is monotonous?
I hope that someone can help me?


texts:
I'm looking for scholarly articles or summaries on the subject of markups. More importantly, for empirical evidence whether they're pro- or counter cyclical, and on theoretical papers on their conclusions.

For Example, Nekarda and Ramey, The Cyclical Behavior of the Price-Cost Markup, who show that some methods which provide empirical counter cyclicality are not robust, and look at the implications for Neo Keynesian models.


texts: When everyone sells at an event of a recession, who buys?

texts:
I'm trying to walk through and understand the basic events of the great depression. I understand that at one point (Black Thursday) the news of a downfall of stock prices hit investors, so they obviously wanted to get rid of their shares.

Given the very high pace investors started to sell, there needs to be an equally big number of buyers, or -- more likely -- a not that big number of buyers, who bought that huge number of shares.

Is this a valid assumption?
If it is, I don't see who bought those shares.


texts: How does private benefit exceed social benefit?

texts:
I've done economics for 3 months only, so bear with me.

If Social Benefit = Private Benefit + External Benefit

Then how is it physically possible that private benefit could ever exceed social benefit?

Someone told me that if there is an External Cost this reduces the social benefit, but why? If the Social Cost already takes the External Cost into account, why would the Social Benefit do the same?

If the Social Benefit and Social Cost are two different things then why do they both take into account costs and benefits?

I really do not understand the logic behind it and do not understand my teacher's explanation. Much help is needed.

Thank you.


texts: Statistical tests/models to use for Macroeconomic and Financial Research

texts:
I am a student, new to research and have chosen a challenging field to perform my research in. While I have been reading about similar research's, as part of my literature review, I observed various researchers using various models in their study. I am having a tough time understanding why researchers use different models/tests and how they choose it, although its the same kind of research being performed.

My research is about the impact that macroeconomic variables have on Stock indexes. I have 6 indexes and 5 variables x 2 countries (Quarterly data). Each of the index/variables have about 60-70 observations.

What I am planning to find -

Which of the MV's could potentially explain the movements of the index prices. Which of the MV's impact the Stock prices.
Is there a variable/combination of variables that specifically create a downward/upward movement.

Should you have any suggestions of statistical tests/models for the above, I'd be pleased to learn and know more about them.

Thanks in advance.


texts: House allocation: Data notation correction with Top Trading Cycles (TTC) example

texts:
I am trying to understand TTC algorithm for house allocation. I have got a small problem. I am trying to understand the following example:

  IE=[i1 , i2 , i3 , i4], IN=[i5], Ho=[h1 , h2 , h3 , h4], and Ho=[h5 , h6 , h7]

The above example is using the Ho variable twice (which is not correct). Somebody please guide me what could be the other variable:

I got the following image:

The link of the paper is:

House Allocation with Existing Tenant

Somebody please guide me.


texts: What does it mean for a firm to have a 0.95% dividend?

texts:
Here's an Apple's dividend:

What does this 0.95% mean? Is it 0.95% of share capital? If not, what does it mean?


texts: STATA: Impulse Response Function after ARDL?

texts:
I am working with an ARDL model in STATA but am unable to figure out how to run the impulse response functions with the estimated coefficients. Numerous papers talk about ARDL and IRF, but not a single one I've found actually outlines the process.

Can anyone point me in the right direction?


texts: Is a mixed strategy ever the best response to a pure strategy?

texts: Suppose you are playing a game against an opponent whom you know only uses pure strategies.  My question is, is there any such game in which using a mixed strategy in response is better than all the pure strategies you have at your disposal?


texts: How to determine a corner solution? Growth Model

texts:
I'm working on a paper called "Fertility clubs and economic growth" of Ahituv and MOav (linked below) and arrived at this point:

The paper shows three optimal conditions respect to consumption (ct), intergenerational transfers (st+1), solved in the images and the educational level (et+1).
Following the paper, I shall use the rt+1 equation derived on the images to get the et+1 optimal level, but, there is a note that says the following:

According to the corner solution showed in the note and replacing the value of rt+1 that I get in the first two images I get the result, but is not a good answer, because I need to know how to get that condition.
I tried to solve the general model detailed on Moav (2001), and I get the result showed, but in this case it doesn't includes the intergenerational transfers and the interest rate. In the next image you could see the general model solution respect to et+1

As Moav (2001) says, the extended model is just a case where Teta is =1, but I can't just justify the development of the model with that answer, I need to solve it.
Am I doing something wrong? If I have to compute the corner solution in the note, how should I do it?
THANKS A LOT!!
Ahituv Moav Paper: http://scholar.google.com.ar/scholar_url?url=https://www.cesifo-group.de/dms/ifodoc/docs/Akad_Conf/CFP_CONF/SC_CONF_1999-2006/GRI_2001X2002/PAPERS2/gri02-moav__221461_en.pdf&hl=es&sa=X&scisig=AAGBfm0HqRpnafuT244j5-Exa5QjPYhtbA&nossl=1&oi=scholarr
Moav (2001) Cheap Children an persistence of poverty (sorry, I couldn't find the link)


texts:
Consider the following version of KPR preferences (with $l$ being leisure):

$$ U(c,l) = \left(\left(c\right)^\gamma l^\omega\right)^{1-\sigma}$$

I'm after the Frisch elasticity:

$$ \frac{\partial(1-l)}{\partial w} \frac{w}{1-l}$$

Note that $\frac{\partial(1-l)}{\partial w} = -\frac{\partial(l)}{\partial w}$.

In general, one can compute the first component as $$  w\frac{\partial l}{\partial w} = \frac{u_l}{u_{ll} - \frac{u^2_{lc}}{u_cc}}$$

Hence, the Frisch elasticity is given by

$$  \eta = \frac{u_l}{\frac{u^2_{lc}}{u_cc} - u_{ll}}\frac{1}{1-l}$$

With the given preferences, I have that

$$ u_l = \omega l^{\omega-1} c^\gamma K\\
u_c = \gamma c^{\gamma-1}l^\omega K\\
u_{cc} = (2\gamma-1)\gamma c^{\gamma-2}l^\omega K\\
u_{ll} = (2\omega-1)\omega l^{\omega-2}c^\gamma K \\
u_{cl} = 2\gamma c^{\gamma-1} \omega l^{\omega-1}K
$$

and then the Frisch elasticity boils down to

$$ \eta = \frac{1}{\frac{4\omega}{2\gamma-1} + 1 - 2\omega}\frac{l}{1-l}$$

It makes sense to some degree: as $\sigma$ is the inter temporal elasticity of substitution, it does not appear here. However, the relative curvatures on $c$ and $l$ appear, which is fine. However, the elasticity is not independent of $l$. As I'm somewhat in the KPR environment (despite adding curvature to $c$), I didn't expect this.

Are my result correct? Does anyone have more insights on this matter?


texts: Could anyone give me a detailed description on how the US dollar serves as the "safe haven" of assets when there are market stresses?


texts: Why Are Cargo Ships Backed Up If The US Economy Is Struggling Due To The Pandemic?

texts:
Since the start of the present pandemic, the US Congress has authorized over \$5 trillion in various forms of economic aid (Business Insider), including the just-signed $1.9 trillion American Rescue Plan. So things are pretty bad, right?
Then why are cargo ships queuing up outside the ports of Los Angeles and Long Beach (Axios)? The articles I've read (such as CNBC and WSJ) say the backup is caused by the combination of surging consumer demand and COVID-19 disruptions. I'm looking for data to corroborate that interpretation, because a "surging customer demand" narrative seems to contradict the "the economy is in a bad way" narrative.
So is consumer spending surging? If I am reading these FRED graphs right, personal spending on durable and nondurable goods spending are roughly 10% above pre-pandemic levels. (I'm eyeballing these on a smartphone.) So yes, demand could be described as "surging."
So then why the need for \$1.9 trillion in new government spending? My belief and understanding was that the economy is struggling right now, but then how are we all paying for so much more stuff that our ports are clogged? (I know the pandemic has disproportionately hurt service industries; is that the answer? Spending on goods is fine but the lack of spending on services is dragging the economy down?)
(The COVID-19 disruptions part of the explanation also confuses me but that's less important, and less relevant to this forum. But from that CNBC article, 800 of 15,000 longshoremen have been "out of work due to COVID;" so if 5% of Longshoremen call in sick, the ports grind to a halt? There's got to be more to the story that I'm missing.)


texts:
Assume that in country A college tuition is 10,000 per year, citizens save 5% of their income for retirement, and there is a mandatory retirement age of 60 years old. In country B, the tuition for college is $5,000 per year, citizens save 10% of their income for retirement, and there is no mandatory retirement age. According to human capital theory, in which country will citizens be more likely to go to college? Explain how the presented facts determined your response.

Here is my attempt:

Younger workers should invest more in human capital than older workers because longer time to recoup investment and earn returns so younger workers invest more in human capital.

Increases in the differential between high school and college earnings will increase college enrollments. The bigger the difference in earnings, more go to college.

There is an inverse relationship between the discount rate and human capital investment; costs upfront, future earnings so size of discount rate make it + or – value; increase costs of education, decrease PV; lower discount rate, more investment in education
Increases in the cost of education should decrease the amount of investment in education; how much earn w/ different schoolingwage-schooling locus, decreasing marg. Prod. Of education

Investments such as education and on-the-job training that improve the productivity of human labor. More education leads to higher earnings
Earnings increase at a decreasing rate with more years of education
Some returns from people learn somethings useful in school and more productive (returns from human capital) but some returns from schooling; studies suggest if all the return due to human capital theory, same return as get from return from high school; implications is that if add up returns for all courses and rate of return of 6% and rate of return from completing h.s. is 12%, 6% of return is knowing something (pass classes), 6% due to graduating from h.s. (credential of graduating)

The human capital model suggests human capital investments such as education provide a way out of poverty and low incomes. Highly educated workers earn more than less-educated workers. For example, more educated workers have higher average annual earnings than less educated workers of the same age group. Education increases earnings because education increases productivity or education serves as a signal of a worker’s innate ability. Earnings rise over time, but at a decreasing rate.

The wage increase suggests that a worker becomes more productive as the person accumulates labor market experience, perhaps because of on-the-job or off-the-job training programs. The rate of wage growth slows down as workers get older. Younger workers add more to their human capital than older workers. The age-earnings profiles of different education groups diverge over time. Earnings increase fastest for most educated workers. The steeper slope of age-earnings profiles for the most educated suggests a complementarity education and postschool investments. This complementarity might arise if some workers have a knack for acquiring all types of human capital.

So my question is, Is there a better answer?


texts: What is the subgame perfect pricing policy for seller?

texts:
Suppose there is a seller S who is selling to 3 different potential customers H, M, L

The good is a durable good and it's utility in terms of dollar equivalent is as in the picture below:

So if H buys in period 1 it's total payoff will be 1500+700-p1 where p1 is the price paid to seller in period 1.

If any buyer buys in 1st period they will be out of the game for the second period.

So if H buys in period 2 it's total payoff will be 700-p2 where p2 is the price paid to seller in period 2.

If any customer does not buy they get a payoff of 0.

The game starts with S announcing the price p1 the H, M and L simultaneously and independently decide whether to buy or not. Whoever buys in period 1 is left out in period 2 and all the players are observable to everyone involved.
Then S announce price in p2.

Given this what will be the subgame perfect pricing policy for seller S and strategies for all players involved.

My attempt:

Below image shows the possible pay off matrix for each period.

From all three possibilites we can see that H will always buy in period 1. Given that H will always buy in period 1 the best possible case is Case 2 for S which maximizes the payoff of S to 2697.
Therefore the subgame perfect pricing policy is set p1 = 1199 and p2 = 299


texts: Trouble Deriving Indentification Scheme in Gertler-Karadi (2015) AEJ

texts: I'm having trouble following a derivation that Gertler-Karadi (2015) AEJ http://pubs.aeaweb.org/doi/pdfplus/10.1257/mac.20130329 do in their paper on Footnote 4 on the bottom of page 52. I've tried many attempts in deriving their equation 17 and 18 but to no avail. In particular, I can easily match elements of the matrix in (15) with that of (14) in order to get (16) but cannot move any further. I've concluded that this case is only true if s12 and s21 are scalars. I've attached a copy of the derivation thus far. Any advice would be greatly appreciated.


texts: A differentiation step in a economic growth model

texts:
I started studying Olivier Blanchard and Stanley Fischer's Lectures on Macroeconomics, but I couldn't follow the reasoning behind a differentiation step (at least I think it is something involving differentiation) in the chapter 2 (Consumption and Investment: Basic Infinite Horizon Models), page 38.
There, it is exposed by a simple production function the idea that output is either consumed or invested:
(1) $Y_t = F(K_t, N_t) = C_t + \frac{K_t}{dt}$
Then, as one of this production function's properties is homogeneity of degree one, everything is divided by $N_t$ for us to get the per capita form of this production function:
(2) $f(k_t) = c_t + \frac{dk_t}{dt} + nk_t$
And that is my question: I suppose that the $nk_t$ term is originated by the $N_t$ division of equation 2, since $\frac{d\frac{K_t}{N_t}}{dt}$ can be determinated as a multivariate chain rule, since both $K_t$ and $N_t$ are functions of $t$. But when I proceed like that, I always end up with:
(3) $f(k_t) = c_t + \frac{dk_t}{dt} - nk_t$ instead of a positive $nk_t$.
After some hours of trying to figure it out, I realized that my approach might not even be appropriated, since when we divide equation 1 by $N_t$, it makes more sense that equation 1 gets a form:
(4) $\frac{Y_t}{N_t} = \frac{C_t}{N_t} + \frac{\frac{dK_t}{d_t}}{N_t}$
Instead of what I originally thought:
(5) $\frac{Y_t}{N_t} = \frac{C_t}{N_t} + \frac{d\frac{K_t}{N_t}}{dt}$
And then I am kinda stuck. It is a basic question, but if someone could shed some light on it, I would be really, really grateful.


texts: How to calculate substitution and income effect when only 1 bundle is given?

texts:
I was given information of a consumer that initially consumed 4 units of both good x and good y with the initial price of $5 for both goods (px = py = 5).
The initial budget constraint is 40 = 5x +5y
Then the price of x increases by 1 and the price of y falls by 1.
The question is to Compared with the initial situation, what can you say about the substitution and income
effects of the simultaneous change in two prices in (i) on the amounts consumed of each of x
and y?
I have drawn the budget constraint graph, yet no other information about utility or MRS is given in order to calculate other points.
How do I go about calculating the substitution and income effect without the other bundles?
Is there a way to calculate other bundles?
Thank you in advance


texts:
Greece: signs of growth come as austerity eases

  Last month the Greek parliament approved a stimulus programme
  involving highway construction that is quite large. According to the
  ministry of infrastructure, transport, and networks, total spending on
  this project will be €7.5bn over the next year and a half. This
  amounts to about 2.7% of GDP during this period.

Portugal Sets New Stimulus After Setback

Italy approves fresh multi-billion-euro stimulus plan

Ireland stimulus package aims to create up to 13,000 jobs

Spain Prepares $8.6 Billion Economic Stimulus Package

Did this all happen? What effect did it have?


texts: Who first used the term "externality" in economics?

texts:
Who first used the term externality in economics, as the term is currently used in its modern sense?

(I believe it was already used in philosophy to mean something else and the economics version of this term came into use later.)

The earliest instance I've found so far is Bator (1958). However, he uses it without any introduction and as if it's already a well-known term so I suspect someone else may have used it before.


texts:
I was wondering whether someone can explain the household production function (HPF). Specifically, the variant presented in Patanayak et al (2005). The paper uses the HPF to determine household willingness to pay for improved water supplies. The HPF model theorizes that averting expenditures (coping costs) are lower bound to willingness to pay (WTP). However other people (e.g. Orgill-Meyer et al (2018)) talk about how including sunk costs (expensive tank assets, pumps, etc) when calculating coping can reverse this relationship causing coping costs to be upper bound to WTP. However, Patanayak et al, 2005 includes amortized sunk costs in his coping cost calculations and the HPF premise still holds.

This is confusing me a bit.

I know the question is elementary but I am really not an economist. Can someone please clarify this?


texts: Have Bernanke, Geithner, Paulson, or the Fed ever responded to Laurence Ball's accusations about Lehman?

texts:
Ben Bernanke, Hank Paulson, and Timothy Geithner have repeatedly stated that they wanted to save Lehman Brothers but couldn't do so legally because Lehman didn't have enough collateral.
Laurence Ball says that this is not true and was something they made up weeks after the Lehman bankruptcy (2016 paper, 2018 book). From the paper:

The people in charge in 2008, from Ben Bernanke on down, have said repeatedly that they wanted to save Lehman, but could not do so because they lacked the legal authority. ...

There is a substantial record of policymakers' deliberations before the bankruptcy, and it contains no evidence that they examined the adequacy of Lehman's collateral, or that legal barriers deterred them from assisting the firm. ...

If legal constraints do not explain the non-rescue of Lehman, then what does? The available evidence supports the theories that political considerations were important, and that policymakers did not fully anticipate the damage from the bankruptcy.

Quote from MarketWatch interview of Ball (2018):

what irks me is that they have not owned up at all to any kind of mistake and they've invented this alternative history of what happened on the Lehman weekend that just isn't accurate.

Slate interview (2018):

what irks me is that they have just dug in their heels and insisted. They've just said the same thing over and over, more and more insistently. That we knew it was going to be a calamity for Lehman to fail. We absolutely did everything we possibly could do. It was simply illegal and we didn't want to break the law, so with great sorrow, as Bernanke put it at one point, we realized Lehman had to fail. That is what these days is called an alternative fact. And that's just not the way it happened.

Have Bernanke/Paulson/Geithner ever responded to Ball's accusations? Specifically, have they ever addressed the arguments made in Ball's paper/book?


texts: What would happen to nominal income and wages if the money supply were fixed (100% reserve banking). Would real wages increase, even though nominal wages would stay the same or even decrease?


texts: What's unique about the Chicago School's Methodology?

texts: What is the methodology of the Chicago School and what makes it unique among economic schools of thought?


texts: How to show the production function is concave in K and L but not strictly so?

texts:
Suppose we have a production function with constant returns to scale. Let us denote it by $F(A,K,L)$ where $A$ is the technology, $K$ the capital and $L$ Labor. Further assume the first partial derivative of $L,K$ are both positive and the second partial negative. How to show the production function is concave in $K$ and $L$ but not strictly so?

This problem is from Acemoglu's Intro to Modern Economic Growth. I don't quite understand what it means to say the function is concave in $K$ and $L$. Do I need to show that $F(K,L)$ (treating A as constant) is concave? or do I show $F(K)$ and $F(L)$ are concave (treating L,A or K,A as constants)?

If it is the latter, it seems the problem seems trivial by the second derivative test.


texts: Can the current account go into deficit with zero capital mobility?

texts:
So, can it? The supposition is that this has been caused by an increase in domestic residents' marginal propensity to import.

My thought would have been: no, it cannot, but my answer seems too simple for me to believe it (it forms part of an assignment).

In the IS-LM-BP model I am considering,

$BOP=NX-NFI=0$

where NFI (net foreign investment) depends on the degree of capital mobility and foreign and domestic interest rates, and where NX (net exports) depends on foreign income, domestic income, the exchange rate, and foreigners' and domestic residents' marginal propensity to import.

But  if there is zero perfect mobility, surely $NFI=0$, and, as a result, $NX=0$, too? Indeed, it hardly seems intuitive to me that there could be a current account deficit in this case, since the only way imports could be bought would be by exporting goods--hence meaning $NX=0$.


texts: If governments can accurately do your taxes for you, why would it overwithhold people's income?

texts:
Here's What Would Happen if No One Paid Taxes

But don't the majority of people get refunds? And wouldn't that mean it wouldn't be quite so much of a disaster if no one filed?
$\color{red}{\text{There are more refunds; people are overwithheld.}}$ So for those folks, it works as a kind of forced saving. You get a lump sum that you can then spend for some item you may not have been budgeting for on a weekly or monthly basis. A bunch of economists have argued, pretty persuasively, that with modern computers, the government could do your taxes for you with no problem. The computer could do that stuff with the blink of an eye. They would have all your information, so you would either get a check or a bill in the mail.

Overwithholding Definition

Who wouldn't want to get a big tax refund check from the Internal Revenue Service (IRS), right? But think again: When you get a big refund, you’re just getting your own money back; but with no interest. In effect, you're letting the IRS use your own money for most of the year without paying you any interest.

If governments can accurately and automatically do your taxes, why would people be overwithheld and there be more refunds? Can't the government's supercomputers can factor in and compensate you the interest?


texts: Does Not Having a Fractional Reserve System Cause More Inflation?

texts:
It is my understanding that countries without fractional reserve requirements still have capital requirements, but what I do not understand is how equity can be used to satisfy these requirements without causing large amounts of inflation in the housing market.

If banks are not required to have currency reserves, then what is to prevent them from extending themselves effectively unlimited credit based on their equity?  In the short term, they may be limited by debt to equity ratios, but in the long term, wouldn't this lead to a consistent rate of near constant inflation?

Every time a bank issues credit to buy a house, (in aggregate, of course) the price of housing increases, which increases equity, which allows them to issue more credit..

Does anyone else not see a problem with this?


texts:
You plan to use the following specification for an empirical study:
$$e_i = \alpha_i + \sum_{j=1}^{n} \beta_{ij}p_i + \gamma_iy +\delta_i,
i=1,...,n$$
where $e_i$ is the consumer's expenditure on good $i$, $p_i$ is the price of good $i$, $y$ is the income and the $\alpha_i, \beta_{ij}, \gamma_i, \delta_i$ are parameters.

You want the specification to be consistent with standard consumer theory and three friends offer the following opinions:

1) “the equation will work for any values of the parameters;”

(2) “you need to impose the  $\beta_{ij}=0,\sum_{i=1}^{n}, \delta_{i}=1$";

(3)“you need to impose restrictions such as $\beta_ij = -\gamma_i\alpha_j, \gamma_i \geq 0,\sum_{i=1}^{n}, \gamma{i}=1,\delta_i=0 $

(a) Explain which of the friends gave sensible advice.
(b) Why should you really not listen to the advice of the other friends?


texts:
I can't understand how it makes sense. From what I've read, corn producers (for example) sell their corn at current price but deliver the corn later, in order to protect themselves from decline in corn prices.
On the other hand, those who buy corn agree to current price in order to protect themselves from potential increase of corn prices.
But in the end, one of them is going for profit from this (corn producer if prices fall, buyer if prices raise).
Let's say price of corn rose. Essentially, the producer of corn didn't protect himself - he just lost money on that trade.

The only way I see this work for the producer is if there is >50% chance that price of corn will decline, but if that's the case then buyers of corn wouldn't agree to that trade.

So in the end, doesn't it all even out? Sometimes the producer will make money sometimes he will 'lose'.


texts: What are "the fundamental categories of economics"?

texts:
I had an introductory class in marketing last week, and the professor wanted to test our previous knowledge of economics (we are juniors).
He asked us this simple question: "What are the fundamental/basic categories in economics?"

Confused by the vagueness of the question, most of us said labor, capital, profit, markets... All sorts of things, but none were apparently correct. In the end, he said that the correct answer is:

cost
result (as in profit or revenue)
time

He continued to say that we define everything in economics on the basis of these three categories.

My questions now are: is this true? Do I really have such a significant knowledge gap that I somehow missed this crucial piece? Where can I find the confirmation of his statement?

If this is not true, can you please refer me to where I can find the answer to this question?

Thanks


texts: Can monopolistic dead weight loss persist without government intervention? If so how? I am researching monopolies and find dead weight loss proposed as an evil of monopolies but i can not find any examples or understand the reasoning behind it. I have seen the graphs and understand them but why would new businesses not enter the market if there are profits to be earned.


texts:
I'm recently new to Game Theory and I've recently started teaching myself about Bayesian Nash Equilibirum. I've stumbled across a problem set that I can't seem to wrap my head around concerning Bayesian Nash Equilibrium.

The problem set is shown below:

For question 3, I initially tried to solve the first problem using Mixed Bayesian Nash Equilibrium but that doesn't make sense since both Player 1 and Player 2 have weakly dominated strategies, so why would they mix? Also when I combine the matrices I find no Pure Strategy Bayesian Equilibrium.

Is there something I'm missing here? How would I go about solving this question? Some example's would be very helpful

For question 4, I have no idea where to even start solving this question. I haven't come across any questions or tutorial on how to solve for Bayesian Nash Equilibria when BOTH players have don't know what game they're playing. Any and all help on how I would solve this problem would be greatly appreciated.


texts: Difficulty Understanding CPI (Consumer Price Index)

texts:
Here's a question about CPI in my microeconomics text (Pindyck), which I don't seem to understand:

  The price of computers has fallen substantially over the past two decades. Use this drop in price to explain why the Consumer Price Index is likely to overstate substantially the cost-of-living index for individuals who use computers intensively.

In my opinion, the CPI is a universal thing, and the way we calculate the real price in some year with respect to a base year is also fixed, i.e. multiplying nominal price by the ratio of CPI of base year and the year in consideration.
So how exactly can CPI overstate or understate the cost of living in any circumstance?

Please help me out, I'm an engineering student and I'm very new to Economics (I've taken up a little course since I find it interesting)

P.S. Here's the solution that's given (which I hardly can make sense of)

  The Consumer Price Index measures the cost of a basket of goods purchased by a typical consumer in
  the current year relative to the cost of the basket in the base year. Each good in the basket is assigned
  a weight, which reflects the importance of the good to the typical consumer, and the weights are
  kept fixed from year to year. One problem with fixing the weights is that consumers will shift their
  purchases from year to year to give more weight to goods whose prices have fallen, and less weight
  to goods whose prices have risen. The CPI will therefore give too much weight to goods whose
  prices have risen, and too little weight to goods whose prices have fallen. In addition, for nontypical
  individuals who use computers intensively, the fixed weight for computers in the basket will
  understate the importance of this good, and will hence understate the effect of the fall in the price of
  computers for these individuals. The CPI will overstate the rise in the cost of living for this type of
  individual.

Thanks!


texts: Normalisations in the wage equation with firm-worker fixed effects

texts:
where
$$
Y_{it}=\alpha_i+\psi_{j(i,t)}+\epsilon_{it}
$$
for $i=1,...,N$ (individual index), $t=1,...,T$ (time index), $j=1,...,J$ (firm index), and $j(i,t)$ is the firm employing worker $i$ at time $t$. $\alpha_i$ is called worker $i$'s fixed effect. $\psi_{j(i,t)}$ is called firm $j(i,t)$'s fixed effect.
By stacking observations over individuals, the equation above can be rewritten as
$$
\underbrace{Y_i}_{T\times 1}=\underbrace{D_i}_{T\times N}\underbrace{\alpha}_{N\times 1} +\underbrace{F_i}_{T\times J} \underbrace{\psi}_{J\times 1}+\underbrace{\epsilon_i}_{T\times 1}
$$
Assume that:
[A1] We have a sample of observations $\{Y_i, F_i\}_{i=1}^N$ i.i.d., for $N$ large and $T$ small.
[A2] $E(\epsilon_i| D_i, F_i)=0$ for each $i=1,...,N$.

As shown here, the identification of $\alpha$ and $\psi$ passes through dividing the sample into connected groups. In turn, under A1-A2 and for each of these groups $g=1,...,G$, $\alpha_g$ and $\psi_g$ are identified if and only if

One element of the vector $(\alpha_g, \psi_g)$ is set equal to a known constant (for example, zero).

$N_g>1$ and/or $J_g>1$, where $N_g$ (resp. $J_g$) are the numbers of individuals (resp. firms) in group $g$.

MY QUESTIONS:
(Q1) Is the element of $(\alpha_g, \psi_g)$ to be normalised picked arbitrarily? That is,
suppose the vector $(\alpha_g, \psi_g)$ has length $5$. Then, from a purely mathematical perspective, am I totally free to fix its third element equal to $0$ or, equivalently, its fifth element equal to zero?
(Q2) Suppose $G=2$ and that the two groups have the same number of firms and workers. It is often said that the estimates of the fixed effects cannot be compared across groups due to the normalisation. However, if I am totally free to normalise the value of any element of the  vector $(\alpha_g, \psi_g)$ - subject to the answer to Q1 -, I could set in both groups the first element of the vector $(\alpha_g, \psi_g)$ equal to zero. Would I then be allowed to make comparisons?


texts: How can this be proved? (Convex optimization)

texts:
Consider the following maximization problems:

$\max_{x} x -\gamma p(x)$
subject to $x \in \Omega_1$

$\max_{x} x-\gamma (p(x) + q(x) )+K$
subject to $x \in \Omega_2$

where $\Omega_1 $ and $ \Omega_2$ are convex sets, $p(x) \geq 0 $ and $q(x) \geq 0$ for all $x\in \Omega_2$. Also, $p''(x)>0$ and $q(x)$ is linear in $x$ and $K>0$ is a constant.
If for given $\gamma = \bar{\gamma}$, the optimized objective value for problem 1 was greater than the optimized objective value of problem 2, does the optimized objective value for the problem 1 always greater than that of problem 2 for all $\gamma > \bar{\gamma}$?
Prove or provide counter example for (1) $\Omega_1= \Omega_2$ and (2) $\Omega_1 \subset \Omega_2$.
Since the higher penalty proportional to $\gamma$ is imposed to the objective function of problem 2, this claim seems right. I tried using contradiction, in which assuming there exists $\gamma'>\bar{\gamma}$ such that optimized value for problem 2 is greater than that of problem 1, but struggling. How can this be proved?


texts: Can government just print a little of money to purchase some foreign resources?

texts:
We know that government shouldn't just print money, because it's gonna be bad. Bad what if to do it in a small scale, just a little, for example to hire some scientist (probably nothing gonna happen because of printed salary for just one or three men) or get one oil tanker (to get a little of oil)?
And it both those cases it looks like a good investment that will return money.


texts:
There are competing definitions of regressive taxes out there:

On Wikipedia:

  A regressive tax is a tax imposed in such a manner
  that the tax rate decreases as the amount subject to taxation
  increases.

In a textbook I use (Case, Fair, and Oster's Principles of Economics):

  A regressive tax is a tax whose burden, expressed as a percentage of income, decreases as income increases.

By the Wikipedia definition, a sales tax would technically be a proportional tax as the rate is fixed regardless of how the base (consumption) changes.

However, by the textbook definition, and assuming that households with lower income consume a greater percentage of that income than households with higher income (i.e. have lower savings rates), a sales tax with a fixed rate would be regressive.

You might be inclined to suggest that the textbook was defining it specifically for income taxes where the Wikipedia article is defining it generally. Actually, though, the authors of the text make it clear they mean their definition to be general. They say that they define it in terms of income because "all taxes are ultimately paid out of income." I think that statement is a bit imprecise, but whatever. They go on to show an example that demonstrates that sales taxes are regressive (conditional on lower-income households saving less).

I agree with them on an intuitive level that sales taxes are regressive. But then why has Wikipedia decided on a definition that is independent of income, with one consequence being that sales taxes are proportional?


texts: Could food storage prevent a depression?

texts:
In Genesis chapter 41 Joseph interpreted the dreams of Pharaoh about 7 years of plenty and 7 years of famine which resulted in saving Egypt from famine, among other things.

I think this is a great economic feat to say the least. But it brings up so many economic questions about the scenario and how it might play out under different economic models and policy decisions.

First off, nowadays can a big enough food storage keep a city or a nation from going into an economic depression? Which economic models might I use to analyze the situation? The Great Depression included the Dust Bowl, and a lot of hunger, and it makes me wonder what difference a gigantic food storage could have done.

Egypt in that Bible story was experiencing a famine though, and economic depressions don't seem to be caused by famines necessarily. So is food storage only applicable during a famine?


texts: Microeconomics, deriving demand equations from utility unction

texts:
Utility function: U=X+XY and I=XPx+YPy
Good Y is a composite good, so Py= 1

What would be the demand function for good X?

I got Mux=1+y and Muy=x and since Mux/Px=Muy/Py

1+y/Px=x/py

so that I=XPx+(Xpx-1)Py---> X=(I+Py)/(Px(1+Py)

Is this correct? Or am I supposed to set Py= to 1 in the calculations so that it would instead be X= (I+1)/2Px?

Also, would it be correct to say that these are substitutes? And good X is a normal good?


texts: How price and quantity of ice cream sold changes when the price of yogurt reduces?

texts:
I am a newbie at economics and would appreciate help from the community.

Question

Use the model of supply and demand to explain
how a fall in the price of frozen yogurt would
affect the price of ice cream and the quantity of
ice cream sold. In your explanation, identify the
exogenous and endogenous variables.

My Answer

A fall in prices should cause the supply of the frozen yogurt to increase so a higher quantity of frozen yogurt demanded at a lower price. Here I assume supply curve shifts to the right and demand curve doesn't change.

The fall in yogurt prices should cause demand for ice-cream to decrease(here i assume that they are somewhat replaceable), do the demand curve should shift to the left and cause lower quantity of ice-cream to be demanded at a lower price.

Is my analyis correct or did I miss something or I can improve it in some way.


texts: Misleading vertical axis in foreign exchange graphs analyses?

texts: The market for a currency typically has the y axis labelled as (currency1/currency2) where currency1 is the currency in which the demand and supply is for. If this is the case, wouldn't it mean that a vertical movement upwards along the vertical axis mean that the currency is in fact depreciating rather than appreciating? For example, if a point on vertical axis is originally at £3/1USD and a movement upwards along the vertical axis to a point where £5/1USD, does this not mean that the pound has depreciated? I'm curious all of a sudden because I've always been told and analysed the currency market as one where any upwards/downwards movement on the vertical axis represents appreciation/depreciation, but the example I've just given seems to conflict with this. I've also found various sources where a movement upwards along the vertical axis shows an appreciation, such as in the pic below, which is how I've always viewed the market until just now.


texts: Do Fines Imposed by Regulators Improve Performance?

texts:
After receiving a fine, do companies immediately seek to recoup their loses or do they take it on the chin?

I'm just wondering if it's the most efficient way of deterring complacency or non compliance with industry standards? If a company raises prices to cover regulator imposed fines are they in the consumers interest?
Wouldn't it be more useful to prevent them paying shareholder dividends or management bonuses/pay rises for a number of years instead of potentially reducing their operating capital?

DISCLAIMER - I'm brain dead and unemployed so I apologise if this question is moronic.


texts: Questions regarding 'Efficient Trade with Interdependent Values' by Marek Pycia and Peng Wang,2015

texts:
This question is with reference to the paper 'Efficient Trade with Interdependent Values' by Marek Pycia and Peng Wang,2015(See here).

At page no. 4 of the paper, the authors describe $v_i$ as the private signal observed by each agent. Are these signals i.i.d random variables (the paper says that the signals are drawn independently from the same distribution $F$, I'm not sure whether it translates to the i.i.d case or not)?

Also, it is given that the agents report their private signals. So, as far as calculating the transfer and allocation profile for the mechanism is considered, wouldn't it be more relevant if the valuations are submitted instead of the private signals?


texts:
I am having a dumb doubt in writing some slides for an undergraduate class.
I want to be consistent with the use in microeconomics but this easy thing is really bugging me:

Mas-colell pag. 54

$ MRS_{lk} = \frac{\frac{\partial u}{\partial x_l}}{\frac{\partial u}{\partial x_k}} $

"tells us the amount of good k that the consumer must be given to compensate her for a one-unit marginal reduction in her consumption of good l"

Reny advanced micro pag. 18

$MRS_{ij}(x) ≡ \frac{\frac{\partial u}{\partial x_i}}{\frac{\partial u}{\partial x_j}}$

" ..MRS_{ij}(x) is again a positive number, and it tells us the rate at which good j can be exchanged per unit of good i with no change in the consumer’s utility"

I know also how to derive this result with the total differentiation but one thing really confuses me:

$du = \frac{\partial u}{\partial x_i}*dx_i+\frac{\partial u}{\partial x_j}*dx_j$

$ 0 = \frac{\partial u}{\partial x_i}*dx_i+\frac{\partial u}{\partial x_j}*dx_j $

$ \frac{\partial u}{\partial x_i}*dx_i = -\frac{\partial u}{\partial x_j}*dx_j$

$ \frac{dx_j}{dx_i} = - \frac{\frac{\partial u}{\partial x_i}}{\frac{\partial u}{\partial x_j}}$

The last equation expresses the differential increase in $x_j$ correspondent to a marginal increase in $x_i$ just as the two formulas above. Where does the minus go in the two books? Am I neglecting something?
Thanks.