texts: Consumer Theory - Relationship between compensating variation (CV) and the equivalent variation (EV)

texts:
John consumes two products – X and Y and his preferences are represented by an unknown utility function – u(x,y) (we may assume his indifference curves are well-behaved). His income is m, while the product prices are Px and Py.
John was made an offer to sign up for a rewards card. This card would allow him to purchase x at a 10% discount. He would, however, have to pay A dollars to sign up for this card. John is indifferent between accepting and declining the offer.
John’s mother has offered to pay the signup price. Alternatively, she’s willing to give John B dollars instead (in which case, John would be prohibited from signing up for the card). John is indifferent between the two options.
What can one say about A and B?

A > B
A = B
A < B
We can’t know the relation between A and B, however if X were known to be a normal good, we could.
The above answers are incorrect.

I'd appreciate it if someone could direct me to info about the relationship between the compensating variation (CV) and the equivalent variation (EV) and their sizes, dependent on income elasticity (classification of the good as normal\neutral\inferior.


texts: Who took utimatum game and dictator game as the evidence against Homo Economicus assumption of individual utility maximization?

texts:
Wikipedia and this McGill University page states that the two games "have been taken as both evidence for and against the Homo economicus assumptions of rational, utility-maximizing, individual decisions"

This argument makes some senses; however I am having trouble finding one famous economist, mathematician, or scientist who explicitly states that the assumption of individual utility maximization is "wrong" because of the findings in these games.


texts:
I have following dynamic optimization problem
$$V(k_0)=\max \sum_{t=0}^{\infty} b^t((1-a)ln c_t+a ln(l_t))$$
Subject to $l_t+e_t=h$ and $y=Ak_t^pe_t^{1-p}$ and $k_{t+1}=i_t+(1-x)k_t$
Where c is consumption, i is inverse,ent, y is output, k is phisical capital per capita. $l$ is leisure time , e is working time. V is value function. x is depreciation rate. A is total factor productivity.

The question I asked to you is that when a is zero, the economy would accumulate more physical capital? Or not? If yes, Why?

I think that
Capital accumulates according to $k_{t+1}=i_t+(1-x)k_t$
Since investment $i_t=y_t-c_t$
So
$k_{t+1}=y_t+(1-x)k_t-c_t$
When a=0, the utility function becomes $u(c_t)=ln(c_t)$
That, househoulds get more utility from consumption with this new utility function in comparision to the previous utility function given. So consumption level increases, which decreases one period forward capital stock.
But the things that I said seems to be wrong to some extent. What do you think ? Do you have any other wise idea about this?


texts: Why utility rather than expected utility in Cochrane's "Asset Pricing"?

texts:
Cochrane "Asset Pricing" Chapter 1 p. 6 says

We model investors by a utility function defined over current and future values of consumption,
$$
U(c_t,c_{t+1}) = u(c_t) + \beta \mathbb{E_t}[u(c_{t+1})]
$$
where $c_t$ denotes consumption at date $t$.

Later, this utility is maximized subject to a sort of a budget constraint

$$
\max_{\xi}\ u(c_t) + \mathbb{E}_t[\beta u(c_{t+1})]$$
where
\begin{aligned}
c_t &= e_t - p_t \xi, \\
c_{t+1} &= e_{t+1} + x_{t+1}\xi.
\end{aligned}

I am used to maximization of expected utility rather than raw utility. Moreover, the expression on the right hand side of $U(c_t,c_{t+1})$ looks just like expected utility where the expectation is conditional on the information available at time $t$:
$$
u(c_t) + \beta \mathbb{E_t}[u(c_{t+1})] = \mathbb{E_t}[( u(c_t) + \beta u(c_{t+1})].
$$
Question: Why does Cochrane not call $U(c_t,c_{t+1})$ expected utility then?


texts: Government using tax to cover for spending without increasing inflation

texts:
If, at full employment, the government wants to increase its spending by 100 billion without increasing inflation in the short run, it must do which of the following?

Raise tax by more than 100 billion
Raise tax by 100 billion.
Raise tax by less than 100 billion.

Official solution:  1. Reason:  If the government does not want to increase inflation, it must increase taxes so that the policies are completely offset.  Remember, changes in government spending have a direct effect, whereas changes in taxes have an indirect effect.  Changes in taxes affect aggregate demand by changing incomes and, thus, consumer spending.  However, people don’t spend all of their income (they do save some portion of it).  Thus, the actual change in consumption is equal to the marginal propensity to consumer (MPC) times the change in taxes.  So, in order for no inflation to occur, the government is going to have to raise taxes by more than the $100 billion (which is the amount that they increased government spending by).

My thought: I think 2. is correct because the saving mentioned in the reasons should are also counted in aggregate demand as they become investment money and will also increase demand with money multiplier.


texts: Under what BLS line do "people who want a job but haven’t searched in the last 12 months" show up?

texts:
I'm trying to understand how this CNN math was derived:

  This category — jobless people who “want a job now” but “did not search for work in the previous year” — has hovered around 3 million workers per month for most of the last decade, but it suddenly more than doubled to 6.9 million in April. Because these workers didn’t search for new jobs in the last 12 months, they were not counted in either the unemployment rate or the U6 underemployment rate.

But where are these 6.9 million reported by the BLS? I see BLS says "discouraged workers" are actually included in U6...

So where are these 6.9m "people who want a job but haven’t searched in the last 12 months" reported by the BLS?


texts: Can the effect of different prices of gasoline at different gas stations be measured?

texts:
I am looking for studies in which the effect on demand of different prices of gasoline at different gas stations  in the same area is measured or estimated (on the same day or hour).

This question has to do with price elasticity. Since gasoline is strongly needed on a daily basis in equal amounts by many people, its price elasticity is quite low and estimated to be in the range of -0.02 to -0.04 in the short term.

But I want to look a bit deeper: Can (and were) the effect on demand of different prices of gasoline at different gas stations in the same area be measured?


texts: Why does capital flight cause inflation?

texts:
Context: I was watching a video about Venezuela, and, it all started with capital flight due to poor confidence in the government. The government tried to stop it, and in the process it created a bubble in the exchange market, causing smuggling and exportation into neighboring countries highly profitable in order to buy the dollar outside Venezuela and to sell at high prices in the bubble inside Venezuela. I can see how that causes inflation (same money supply chasing less domestic goods).

But then, the video said: if the foreign exchange market is open in order to end the bubble once and for all, allowing the currency to depreciate to its normal levels, thus allowing capital flight to happen in the first place, it would trigger more and more inflation (in hyper levels). And that's when I bugged me. I started searching in other sources, for instance this one, and several of them said that capital flight can indeed trigger inflation. But why?

Let's focus on capital flight: It is my understanding, that capital flight shifts the supply curve of a given currency in the exchange market, causing its depreciation with respect to, say, the dollar. But then.....:

(1) Shouldn't it cause a deflation? Currency is less and less available (due to flight) for the purchase of domestic goods, thus.. deflation. That is, a smaller amount of currency chasing the same goods.

(2) But also, capital flight is done with saved money, instead of money reserved for purchases, and that means aggregate demand is not affected much, meaning, purchases are done as normal, and normal life follows. Surely, that doesn't mean a deflation, but it doesn't mean an inflation either.

(3) Consider this: Assume for whatever reason, interest rates has fallen. This means, borrowing money is cheaper, and that is likely to cause a shift in aggregate demand and domestic consumption, possibly boosting the economy, and causing some inflation in the process. However, with capital flight, there's less and less investment done inside the nation, so, the supply of investment shifts, causing an increase of interest rates -- which again, should tend to cause a deflation due to a decrease in the money supply (basically, the reverse reasoning of lower interest rates).

My question: Why does capital flight can trigger inflation? What is wrong with my reasoning in these three situations?

I am not an economist.. so... forgive me if this is such a simple question.


texts: What would the determinant of the input-output matrix represent? What is the intuition?

texts: I know that the determinant of a 2x2 matrix represents the oriented area of the parallelogram represented by the vectors in the matrix. For 3x3 or higher order matrix it represents the oriented volume. I am trying to get such an intuitive understanding of the determinant of the input-output matrix used in macroeconomics. What could it represent? Does it represent the size of the economy? We usually measure the size of the economy by measuring it's GDP. If it represents the size of the economy, could this determinant be a better measure of the size of the economy than GDP?


texts:
I'm struggling to think of a way to violate the transitivity axiom. I was thinking about the following scenario:
Let's say that you're voting on three different choices, A, B and C.
If you pit A vs. B, A wins 3 - 1 so A > B
However, if you pit A vs. C, they're indifferent and neither wins
But just because A = C, does that necessarily mean that pitting C vs. B would either yield C > B or B > C since we do not know the relationship between B and C?
This is the question I'm trying to answer:
How can tie votes violate transitivity? Does this violate WARP or SARP?
I'm thinking this violates SARP this the preferences are strict preferences.


texts: Existing metric for personal productivity hours needed per life hour?

texts:
With about 50 hours of productivity a week, including work, cooking, etc. I can complete the tasks and pay the expenses necessary to live about a week. Subtract maybe 5 hours of labor that goes into personal savings, and 45 hours of weekly work affords me 168 hours (1 week) of life.

Thus the number of hours of "life" that a single productivity hour buys me is about 3.7. I'd imagine in parts of the developing world, this can get as low as 2 or even 1.5, while for the best earners in the cheapest markets, this may exceed 1000, though obviously with very high earners, the meaning of "life expenses" is very much up to interpretation. But I just made this metric up.

Is there a formalized, existing metric for how many hours one gains from a single hour of "work"?


texts: Value of Mexican Peso vs US Dollar in 1920s -- is silver content complete determiner?

texts:
I am rewatching The Treasure of the Sierra Madre which is set in Mexico in 1925 and they seem to use the term peso and dollar interchangeably -- for example, the trio of prospectors need another 100 bucks in order to launch their expedition and Dobbs wins 200 pesos in a lottery. Clearly the peso at that time was worth much more than its current value vs the dollar but whether it was worth exactly a dollar I can't find data on for the 1920s.
What I do know is that the peso coin was made of silver (not pure) and I think its total silver content was about half that of a US silver dollar. But I don't know if silver content completely determined the exchange rate. If it did, maybe Dobbs 200 peso prize was just about exactly what they needed.
Dobbs keeps begging peso coins from the man in the white suit and he can, for example, buy a meal and a pack of cigarettes and still have 20 centavos left over (which is how Dobbs bought the 1/20th of a lottery ticket). I know that depression-era prices were ridiculously low and even 50 cents was more than enough for a meal but 1925 was pre-depression.
We also find out that either 2.5 dollars or pesos was not enough to pay for a single bed in a passable hotel although 50 cents (or was it centavos?) was enough for a bed in the hotel Oso Negro which was full of rats, scorpions and cockroaches. During the depression, the Waldorf Astoria was charging 3 bucks a night for a room so again, the prices of the depression are not a guide.
I suspect the film makers did not worry too much about details like exchange rate.


texts:
I have recently encountered (in a few applications), the Dixit-Stiglitz Pricing index. Consider a Constant elasticity of substitution form of utility $$U=\left(\sum_{i=1}^{N}c_{i}^{1-\frac{1}{\sigma}}\right)$$

This index basically aggregates prices to give a general term as a function of prices that yields a unit cost of utility. How is the index derived?


texts: (AD-AS model) How is it possible for firms to spend less, but supply more at higher price level, assuming no increase of the SRAS?

texts:
According to the interest rate effect theory higher prices will lead to lower GDP demanded because firms will spend less due to loans being more expensive.

It seems at odds with what the SRAS curve tells us about how suppliers (i.e. firms) react to changes in prices in the short term. At higher prices they supply more GDP in the short run.

We get quite strange situation. At higher prices firms will spend less, but at the same time supply more. Assuming that the SRAS didn't increase, how is it even possible?


texts: How does inflation impact the welfare of the economy?

texts:
When the government causes inflation through printing money, the individuals who saved their money in the bank are poorer.
Is there a way to determine how different inflation rates impact the welfare of the economy?
I tried answering this question myself using the production function, and, though I was able to come up with some conjectures, I was unable to come to a definite conclusion.


texts:
Would someone be able to check my solutions to this basic problem? This is a practice test with no solutions provided, and I have no idea if I am going in the right direction.
Problem:
https://ibb.co/KhgwLcX
Solution (apologies my LaTex is rusty):
$\underset{c,l}{\text{max. }} c^{\alpha}l^{(1 - \alpha)}$
s.t. $c = w(24-l)$
rewritten as
$\underset{c,L}{\text{max. }} c^{\alpha}(24-L)^{(1 - \alpha)}$
s.t. $c = wL$
First order conditions:

$\alpha c^{(\alpha - 1)} = \lambda$
$(1 - \alpha)(-1)c^{\alpha}(24 - L)^{(1-\alpha)}=(-1)\lambda w$
$c = wL$
Solving this:
$L = 24\alpha$
$c = 24w\alpha$
So the labor supply is perfectly inelastic, which makes sense (you work to the extent that you value consuption over leisure).
For the markets to clear,
$b\sqrt{L} = c$
$b\sqrt{24\alpha} = 24w\alpha$
$w = \frac{b}{\sqrt{24\alpha}}$
b. Adding education in, let $\beta = \frac{L-T}{L}$, i.e. the share of labor time spent actually working. Then the firm's problem is:
$\underset{L,\beta}{\text{max. }} b\sqrt{L} - wL$ if $\beta = 1$
$\underset{L,\beta}{\text{max. }} 2a\sqrt{\beta L} - wL$ if $\beta \in [0,1)$
This is where I get a little unsure of why I'm allowed to do what I'm doing. Taking the labor supply as constant, I optimize for $\beta$ to get:
$\beta = a^2L$
Then the firm's problem becomes:
$\underset{L}{\text{max. }} 2a^2L - wL$
Here is where I get really unsure of why I'm allowed to do what I'm doing. If the derivative is constant, the firm will demand as much labor as the household will provide, which is $24\alpha$. Plugging that in, I get:
$\beta = 24a^2\alpha$
For education to be profitable, we need the extra production to be worth it, so:
$2a\sqrt{\beta L} - b\sqrt{L} < 0$
$a^2 < \frac{b}{2\sqrt{24\alpha}}$
But I also want to make sure $\beta \leq 1 $, which results in:
$a^2 \geq \frac{1}{24\alpha}$
So $a$ needs to be between $\frac{1}{24\alpha}$ and $\frac{b}{2\sqrt{24\alpha}}$
Clearing the market to find the wage:
$24wL = 2a\sqrt{24\alpha\beta}$
$w = 2a^2$
and the firm's profit is zero.


texts: Can capital still be paid its marginal product in the absence of a homogeneous capital stock?

texts:
Thomas Piketty's best-selling book on inequality, "Capital in the Twenty-First Century" has attracted a lot of criticism on the right for its data analysis.  Less well-known, however, is the criticism it's gotten from economists on the Left.  Piketty uses an aggregate production function, where capital is represented by a single number K.  This is a fairly standard thing to do in mainstream economics, but back in the 1960's there was a major debate in economics called the Cambridge Capital Controversy, revolving around the fact that capital is heterogenous and thus it may not be legitimate to represent it by a single number.  So some economists argued that many standard conclusions in economists, like the notion that capital is paid its marginal product, are flawed.

Paul Krugman disagrees with this critique of mainstream economics, so in this blog post he defended Piketty from the charge that his conclusions depend on assuming a homogenous capital stock:

  The thing to bear in mind, however, is that you really don’t need to
  reject standard economics either to explain high inequality or to
  consider it a bad thing.

  There are a few economists on the left who seem to believe that:

  You need to believe in the existence of a perfectly well-defined aggregate measure of capital to believe in the marginal productivity
  theory of income distribution;
  If you believe in, or even use, marginal productivity theory, you are conceding that capitalists deserve their income.

  Neither of these things are true. Nothing about marginal productivity
  theory depends on the exact truth of a simple aggregate production
  function with capital defined by a single number. And saying that
  capital gets its marginal product in no way says that the people who
  own that capital deserve what they get.

My question is about the statement in bold, where Krugman says that you can still get the conclusions of marginal productivity theory without assuming that capital can be described by a single number.

So my question is, what is the basis of Krugman's assertion?  Can someone point me to a proof of the statement "capital is paid its marginal product" which doesn't depend on homogenous capital?


texts: What was the impact of the Great Recession on the economics curriculum

texts: O. Blanchard claims that the discipline needs at least 5 types of models. Did the Great Recession have an impact on the economics curriculum? What are the discipline areas that were affected/'reformed'? If possible, present a representative example of what got replaced and what took its place.


texts: Perfectly functioning credit markets and consumer saving

texts: Today in my Macroeconomics lecture, while covering the Real Intertemporal Model with Investment (Chapter 11 of Williamson's Macroeconomics), my professor proponed that a key assumption to not make consumer saving a central choice variable is the existence of perfectly functioning credit markets. This left many students and I slightly confused. Can somebody please help me get a good grasp of this? Thanks!


texts: How to calculate the optimal wage and the optimal rent on capital in an economic model?

texts:
In Dhondt & Heylen (2009)*, they specify a certain production function.

Under some standard model assumptions such as perfect competition and so on, they calculate the optimal wage as

$$  w_t = \frac{\partial y_t}{\partial l_t}  $$

and the optimal rent on capital as

$$  r_t = \frac{\partial y_t}{\partial k_t}  $$

with $k_t $ the capital per capita and $l_t $ the amount of labour per capita and $y_t $ the output per capita.

Now what's the reason of this equality? If it because if you maximize for profit, that the maximum is reached in:

$$  0 = \frac{\partial W}{\partial L}  $$
$$  0 = \frac{\partial W}{\partial K}  $$

and that this must mean, as W = TO-TK, with TO total revenues and TK total costs, that

$$  \frac{\partial TO}{\partial L} = \frac{\partial TK}{\partial L}   $$

and

$$  \frac{\partial TO}{\partial K} = \frac{\partial TK}{\partial K}   $$

?

So in this case, it would be explained if you see ... as ... :

$$  \frac{\partial TK}{\partial K} = r_t   $$

and

$$ \frac{\partial TO}{\partial K} =  \frac{\partial y_t}{\partial k_t}  $$

and

$$  \frac{\partial TK}{\partial K} = w_t   $$

and

$$ \frac{\partial TO}{\partial L} =  \frac{\partial y_t}{\partial l_t}  $$

Is this correct?

*Employment and growth in Europe and the US—the role of fiscal policy composition


texts: How to solve Bertrand Equilibrium with a non-constant MC?

texts:
I know that Bertrand Oligopolies will charge a price equal to marginal cost. But if marginal cost is, say,

  2Q or 4Q^2

(i.e. not constant) then how does one determine where, on the MC curve, the equilibrium lies?

If there are 5 Bertrand firms, then do I just find where MC intersects the Demand Curve and divide the quantity by 5, and then set price equal to MC at that quantity?

Conceptually this sounds reasonable, but I'm not sure that this is correct. If these firms charge this price then it seems to me that one of them will under produce to charge a lower price until (if MC is 2Q for instance) price and quantity = 0. So that no firms will produce because if they do then someone will charge a cent less till we reach 0 again.


texts: Estimate function expression for TC and MC

texts:
I have this

Labor (L)   0   1   2   3   4   5   6   7   8   9   10  11
Output      0   32  72  114 161 204 242 272 292 304 302 288

and I need to estimate function expressions for $TC$, $AVC$, and $MC$.

I have capital $K = 10$, wage $w = 30$, and rate $r = 50$.

I think that total costs are
$$
TC = wL + rK = 30 L + 50 \cdot 10 = 30 L + 500.
$$
and marginal costs are $MC = TC'(Q)$ but my $TC$ doesn't depend on $Q$. Is it $MC = TC'(L) = 30$ instead?

If I'm calculating the marginal cost ($MC_t = \frac{\Delta TC}{\Delta Output}$) in discrete quantities I get

Labor (L)   0   1   2   3   4   5   6   7   8   9     10    11
Output      0   32  72  114 161 204 242 272 292 304   302   288
MC          -   25  20  19  17  19  21  27  40  67    -400  -57

but these numbers seem very wrong.


texts: If Greece defaults, can it still stay with the euro?

texts:
Should Greece default, a forced conversion from euros to drachmas will be a further catastrophe to Greek economy as the drachma will quickly collapse. However, if Greece leaves the Eurozone, but keeps the Euro as a national currency (at least for a year), its value will be kept stable because of the implicit trust in the euro.

There already are precedents of countries using the euro without being members of the Eurozone (Montenegro, Kosovo, Monaco, etc.). Is that possible for Greece?


texts: How can CVS which has about 3 billion in cash on hand buy Aetna for 69 billion?

texts:
How will CVS be able to buy Aetna for 69 billion if CVS only has 3 billion in cash without borrowing a large amount of money?  I understand that a company can trade for a multiple larger than 1 of their assets but how can they buy other companies which cost much more than their assets?  The market cap of CVS is 76 billion.  This is what CVS shareholders currently are worth.  How can they spend 69 billion of this and still own CVS?  Wouldn't they have to give Aetna almost all of their CVS equity in exchange for Aetna's equity?

One way this would make sense would be if it is more of a merger and that Aetna shares will become CVS shares.  So the value of the new CVS shares will be worth about the same as the value of the current CVS shares and the current Aetna shares.  There would simply be more shareholders in the new company - all of the existing CVS shareholders plus all the existing Aetna shareholders.

In this case, I suppose I could buy a large company like Google even if I only had a company with a market cap of 1 million.  Google's shareholders would simply own virtually all of the new combined company.


texts:
Jovanovic (1982) cites Du Rietz (1975) as a source for

Survival Rates of smaller firms are smaller than for larger firms

It's his doctoral thesis, and using Swedish data. Is there any recent evidence on this for the United States?


texts: Separating and supporting hyperplane theorems

texts: I am having trouble understanding  the separating and supporting hyperplane theorems. I've read what I can online but am just not able to develop any intuition. Can someone please give a basic outline of these theorems using economic context? And any graphical interpretations would be extremely helpful.


texts:
GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative.

I wonder if we can naturally relax the $\mathbb R_+$ constraint. i.e. let $x\in\mathbb R$,

GARP: if $p_i⋅x_{i+1}≤p_i⋅x_i$ for $i∈\{1,...,N−1\}$ and $p_N⋅x_1≤p_N⋅x_N$, then those inequalities must be equalities.

At a first glance, the generalization to negative number seems plausible and not problematic.


texts: How to demonstrate that a game always have a subgame-perfect equilibrium in pure strategies?

texts: If I have an specific extensive game, with only a finite set of strategies, how can I demonstrate that the game always have a subgame-perfect equilibrium in pure strategies? My first intuition was to show that in every subgame a pure strategy it's a solution to the problem (maybe not unique) and then there is always a pure strategies equilibrium. But I'm not sure.


texts: How to find sequential equilibria and weak perfect bayesian equilibria quickly?

texts:
I have read several texts on the nature of sequential equilibria and weak perfect bayesian equilibria (called such by Mas-Colell, also called weak sequential equilibria).

I am not looking for computational methods that can be used by computers. I'm looking for a method to quickly find these equilibria in simple games that can be done by hand.

Could you recommend a good text that explains how to do this quickly?


texts: Relation between incomplete contracting and the principal agent problem?

texts:
I have read about incomplete contracts in the context of vertical integration of firms, in which the two contracting parties are relatively "symmetric" (we cannot say that one is the agent and the other the principal. Both take hidden actions that influence the other party)

In principal agent theory, I have not read anything that explicitly talks about "contractual incompleteness" as a source of agency problems. Yet it seems intuitively that they are related.

How is contractual incompleteness related to the principal agent problem?

Are all principal agent problems the result of incomplete contracting?
is incomplete contracting merely one example of a source of principal agent problem?
How, in general, are they related?

EDIT: In particular, the term "admissible contract" or "feasible contract" is used in the context of principal-agent problems. Does "incompleteness" of contracts simply mean that "the set of admissible/feasible contracts is restricted in some important senses"?


texts: exchange rate and domestic money supply part II

texts:
This question is related to the answer to the question
exchange rate and domestic money supply

It is said that the 'CB purchases foreign currency on currency market'.

Is it possible that some of this purchasing is even done within the domestic market (I would guess not but don't really know)? Or are we assuming that in circulation means within the domestic market and foreign market (again I would guess not)? Or is maybe that we assume/know that when in circulation, our currency will find its way back to our market and this will obviously result in more money in circulation. Maybe I am really thinking about it in the wrong way, and in circulation simply means that there are lenders out there now (foreign or domestic) that have more of our currency and will lend at a low interest rate.


texts: Premises on which the Efficient Market Hypothesis is built upon

texts:
The Efficient Market Hypothesis tells us that stocks are "fairly priced" (i.e. not systematically over- or under-valued). That is, stock prices reflect all information that is already known about them. This is because any information from current or past events are already "absorbed" by the market. What is this "asborption" of information by the market supposed to mean? The market is comprised of its participants, buyers and sellers. I would also like to ask if the Efficient Market Hypothesis is built upon the following premises:

All market participants have perfect information at all times, i.e. they know the operations of the companies listed on the stock exchange fully well and that they are also well-equipped with the financial knowledge required to interpret any economic news that may affect the performance of the listed companies.
All market participants respond rationally and make decisions using the marginalist principle.
Market participants are able to assess the circumstances readily at any one time and are able to respond to any new economic information (e.g. government macroeconomic policy changes, changes to corporate earnings etc.) instantly.

I just learnt about this concept and so I would just wish to seek clarification on it.


texts:
I'm not sure if this is the right place to post this, since my question is a bit more general to all of social sciences (indeed sciences in general), but I figured since Economics is a social science and since the question I have is somewhat economics related someone here might have an idea.  I am a statistician but work with a lot of economists who test various economic theories through observational data (not experimentation).  Some of the "studies" I've seen carried out recently concern me because it seems, no matter the findings our outcomes, one particular researcher tries to tie the specific results back to a pet theory of his.  In other words, the hypotheses are not clearly laid out in advance, but he looks at some data and if it shows 1 thing, he's say, Ah-ha, that is because my theory explains it.  But if the same data showed just the opposite finding, he's still say, ah-ha, this is because my theory explains it!  Specifically, let's say he compares 2 items for purchase that are identical in all physical aspects but one.  If the price of item A is higher than price B, he's explain it with this theory.  But if price of item A is lower than B, he'd simply twist his theory to to explain it as well.

Is there a name for this?  It sounds like confirmation bias a bit, but not quite.  I'm just curious if there is a name for this way of manipulating the findings to fit a narrative?  Any ideas would be greatly appreciated.


texts: What is the percentage of free riders in public goods games?

texts: Of all experimental public good games that have been conducted in laboratory & field settings, what is the average percentage of subjects that can be classified as free-riders (as opposed to (strong) cooperators & conditional cooperators)?


texts: Why is the Dollar Index strong after the Fed dropped the Fed Fund Rate?

texts: I have a query about the current forex market. In 16 March 2020, the US Federal Reserve Bank announces to cut the interest rate to 0%. This move supposedly weaken the Dollar Index, but why for a sudden movement it becomes stronger?


texts: Growth theory / Initial GDP: positive coefficient sign

texts:
I estimated growth regressions for several EU countries. In each of them, the sign of "initial GDP"'s coefficient is statistically significant but positive, which contradicts growth theory as well as most of other published papers on this topic. I tried to change the variables, the period, etc. but it remains positive.

I can't find any explanation for this result in the literature, which would imply that there is no growth convergence among European countries.

Did anybody already face this problem? How did you solve this? I can't find the source of this problem. Personally, I replaced "initial GDP" by "lagged (one period) GDP" but it would be better if I could keep "initial GDP" among the explanatory variables.


texts: How did the purported 2008 decoupling of emerging markets pan out?

texts:
One opinion voiced (in The Economist) around the 2008 recession was that:

  Decoupling does not mean that an American recession will have no impact on developing countries. That would be daft. The point is that their GDP-growth rates will slow by much less than in previous American downturns.

In hindsight, how did this pan out?

I seem to recall that some Eastern European countries, e.g. Estonia (and actually all 3 Baltic states) had a much worse recession in the aftermath than the US did (~15% contraction of GDP for 2009 compared to 2.5% for the US). But how did this alleged decoupling from the US economy fare on average for the emerging markets in aftermath of 2008?


texts: Money supply control vs. interest rate control

texts:
In a macroeconomics book I'm reading, the author talks about money supply control vs. interest rate control as two different approaches in monetary policy of a central bank.

With the goal of price stability being the same in both cases, money supply control alters the supply of money and thus effects the interest rates within the economy in either a expansive or restrictive manner. With interest rate control, the central bank defines a central interest rate to increase or decrease the money supply for the commercial banks, which in turn translate this into the economy.

The author claims that money supply control is only a viable option when there is certainty about the money demand. Interest rate control is preferred when there is uncertainty about money demand.

I don't quite understand the difference between these two approaches as in my opinion they are essentially the same. They are not even comparable as two different approaches, they are both part of the same approach from my understanding: Interest rate control in consequence effects the money supply. So interest rate control allows money supply control.

In most media you'll only read about how the central banks in the US and Europe alter the central interest rate to increase or decrease money supply. I never read about direct money supply control. I feel like I might be confusing terms or just misunderstand the author.

Can anybody shed light on this topic?

Thank you in advance!


texts: Effects of Robotics on the overall marginal propensity to consume

texts: Basically we know that poor and middle class workers have a high marginal propensity to consume as compared to rich people. Assuming that all of their jobs will be done by robots, and  only a few consumers with jobs are left, won’t the overall spending decrease and thus result in a sort of recession? This is if we assume that Rich people who know robotics have a lower marginal propensity to consume and a higher marginal propensity to save. What is your view?


texts: Calculating the growth rate of a stock over a year with imperfect information

texts:
I am trying to find the growth rate of a stock over a given year.

Let's say I wanted to find the growth rate from today, June 11, 2015 to June 11, 2014. This is easy enough when you have perfect information and both sets of data exist.

However let's say June 11,2014 stock data does not exist, but June 10th and June 12th do. Which date do I compare to? Do I extend the "year" by a day and go to June 10th, or do I shorten the year and go to June 12th?


texts:
Question: Use the Weierstrass Theorem to show that a solution exists to the expenditure minimization problem of subsection 2.3.2, as long as the utility function II is continuous on $\mathbb{R}$ and the price vector p satisfies p » O. What if one of these conditions fails?

$X(\bar u)$ = $\{x\in$ $\mathbb{R}$$^n$$_+$| $u(x)$ $\geq$ $\bar u$

The objective is to solve:

Minimize $p\cdot x$ Subject to $x\in X(\bar u)$.

I do not understand how to actually apply the weierstrass theorem here. Can anyone solve this exercise?


texts:
Doctors average salary is around \$110,000 a year, whereas NBA stars salary may well cross \$5,000,000 a season.

Why do sports players and television stars make more than doctors and politicians?


texts: What Interest Rate used to calculate opportunity cost?

texts:
What Interest Rate used to calculate opportunity cost (Calculating Future Value/Present Value)?
Usually in the textbook it said that the rate used is government bonds interest rate(since it's risk free), but government bonds interest rates varies depends on the loan term. Which one do we choose? also since the opportunity cost basically calculate the return for risk-free assets, shouldn't we use bonds yield instead?


texts: Why does having a single market price maximize quantity traded?

texts:
From what I have heard, the exchange of goods defined by the intersection of supply and demand generally maximize quantity traded, although this doesn't apply in cases of monopolies, imperfect information etc. I am trying to understand why this is true, and came across what appears to be a counter example:

There are 4 people in a market for eggs, 2 buyers and 2 sellers. The buyers are each willing to pay up to \$10 and \$3 for 1 egg each. The sellers are willing to sell an egg each at \$9 and \$2. The most productively efficient trades are when one egg is bought for some price between \$9 and \$10 and another is bought for some price between \$2 and \$3. What happens according to supply and demand is that one egg is traded for a price between \$3 and \$9.

The fact that there is one price seems, in this case, to reduce the total traded quantity. What am I missing?


texts:
The following diagram is included in my textbook as a means of deriving the IS curve.
Is it not the case that in the top graph, as output increases, interest decreases at a rising rate whereas in the bottom graph, as output increases, interest decreases at a falling rate. How are they compatible?


texts: Which countries have the comparative advantage in Ricardo's example?

texts:
I am a complete beginner here trying to learn through Khan Academy. I found some data that correspond to Ricardo's explanation of comparative advantage. According to Wikipedia "England has a comparative advantage in producing cloth due to lower opportunity cost." Yet, when I work through it I get the opposite, where am I going wrong?

          Cloth Wine
England     100 120
Portugal    90  80

England

100 = 120
100/100 = 120/100
1 = 1.2

For 1 cloth there is an OC to England of 1.2 wine. For 1 wine there is an OC to England of 0.8333 cloth.

Portugal

90 = 80
90/90 = 80/90
1 = 0.8888

For 1 cloth there is an OC to Portugal of 0.8888 wine. For 1 wine there is an OC to Portugal of 1.125 cloth

England should produce wine because its OC is lower (0.8333 < 1.125).

Portugal should produce cloth because its OC is lower (0.8888 < 1.2).


texts:
Suppose a town is building a bridge, and it costs $B$.
There are $n$ villagers.

Each village's valuation of the bridge is private information, $v_i$.

It is common knowledge that this valuation is drawn from a uniform distribution $[0,1]$. $B\in[0,1]$.

Villager can only submit $0$ or $B$.

If one villager submits $B$, then the bridge is built and every other villager pays their submission.

If no bridge is built, everyone gets $0$.

How do I construct an expected payoff a village $i$?

What I got down to is having 2 scenarios: $v_i>B$ and $v_i\leq B$.

But in each case, I have two possible payoffs. For the former case,

  if every other player submits $0$, $i$ should submit B, because $v_i-B>0$.
  if someone pays $B$, $i$ should submit 0, because she gets $v_i$.

You get a similar type of for the other scenario.

But how would I incorporate this into expected payoff of $i$ and how should I go about constructing a social welfare function?

I feel like this is just a variation of all-payout auction with discrete action space for each $i$.


texts: What graph theory textbook should I use?

texts:
I'm doing my Msc dissertation on production networks and business cycles and I want to learn graph theory. I need to be able to model the evolution of the network and identify equilibrium graphs.

Could someone recommend a textbook for me?


texts: Who loses/wins in exchange rate fluctuations?

texts: I recently joined Amazon prime unknowingly and USD99 was debited on my non-USA credit card for an annual membership. I canceled the membership and was refunded USD99 after two days. Due to exchange rate fluctuations, I lost approximately USD10. Where did the USD10 go to?


texts: Textbook covering calculus and probability theory

texts:
Is anyone able to recommend a textbook that covers the following topics at a level suitable for econ undergraduates?

Differential calculus, including the various rules of differentiation and partial derivatives.
At least some integral calculus.
Probability theory, expected values, Bayes' rule.
(optional) basic set theory.

I can find books with a nice treatment of calculus, but am struggling to find a book that also includes coverage of topics in probability.

Failing one book that covers all of these topics, I also welcome suggestions of books that might work well together to give such coverage.


texts: True or False: During the Japan Bubble, one sky scraper in Tokyo was worth more than the entire state of california?

texts:
I have heard a rather outlandish claim that during the peak of the real estate bubble in Japan (I think that was in the 70's and 80's), one sky scraper in Tokyo was worth more than the entire state of California! Seeing as California's economy is larger than even some entire nations, I couldn't wrap my head around how high the bubble in Japan was. Then again, it reminded me of the Dutch Tulip crisis, and we all know how expensive those flowers were... so maybe the Tokyo skyscraper claim was legit? I'm just not sure.

Question: Is this statement true? I wonder if there is any data that is readily accessible; I'd like to plot it on a line graph. Also, if the statement is true, it would be neat to know how long it lasted. Was 1 Tokyo sky scraper out valuing California a momentary apex before it all imploded, or was this the way it was for an extended period of time (months, years)?


texts: Why would minimum rent under franchise arrangements for McDonald's decrease year by year?

texts: I am working on a project regarding the refranchising strategy of McDonald's and came across this piece of data in their 2014 annual report. My understanding of minimum rent is that its a fixed amount to be paid by franchisees to McDonald's as the franchisees are leasing a restaurant location from McDonald's. Hence, I have no idea why its decreasing.


texts: References to learn continuous-time dynamic programming

texts: Does anyone know of good references to learn continuous-time dynamic programming? The references don't have to be books. They could be links to online resources as well. Links to clear, concise discussions of even just the basics would be helpful.


texts:
I would like to know how I could write a value function when there are habits in preferences. I have the following equations:
$$
u\left(C, t, H_{t}, L_{t}\right)=\frac{\left(C_{t} / H_{t}^{\kappa}\right)^{1-\gamma}}{1-\gamma}-\theta \frac{L_{t}^{1+1 / \chi}}{1+1 / \chi}
$$
Habits are external in the sense that they depend on past aggregate consumption, so from the perspective of atomistic households, they are exogenous.
$$H_{t}=C_{t-1}
$$
Resource constraint gives: $Y_t=C_t+ I_t=C_t +K_t-(1-\delta) K_{t-1}$. There is technology $Z_t$ following a standart AR(1) process.
How should I write the policy functions in Matlab's code? Should I write them as 2 dimensional, that is to say, they would depend only on the grid of capital and the grid of technology? Or should they be 3 dimensional, namely they would depend on the grid of capital, the grid of technology, and the grid of $H_t$ ?
Thank you


texts: Relationship between elasticity and interpretation of approximate percentage change

texts:
Let's define elasticity, in a regression setting, as $\frac{\partial \log E(y|u)}{\partial \log x_j }$. How do we relate this definition to the percentage change interpretation, i.e., seeing this elasticity as the approximate change in $E(y|x)$, when $x_j$ increases by 1 percent? I'm reading Wooldridge.

Any help would be appreciated.


texts: What are good books about monopolies and market failures?

texts: Is there a good undergraduate level book specifically about economic monopolies and market failures?


texts: Why would males' shorter pension's savings produce more, and not less, income?

texts:
Source: The European Union: A Beginner's Guide (1 ed. 2012) by Alasdair Blair.

  [p 139:]  Gender has traditionally played a key role in the pricing of insurance policies.
    In 2004 an EU Directive prohibited all discrimination based on
  sex in the access to a supply of goods or services. In principle the
  Directive therefore prohibited the use of gender as a method of
  determining insurance premiums and benefits with regard to contracts that were entered into after 21 December 2007. However,
  the Directive also stated differential pricing could be maintained
  where statistical evidence supported such an approach. Insurance
  companies regarded this as crucial because as women drivers are
  statistically proven to have fewer accidents than male drivers, premiums for female insurance policies have generally been lower. In
  a similar way, because women live longer, men have traditionally

  [p 140:]

  received a higher rate from their pension annuities because their
  life expectancy is lower and as such their pension savings are able
  [1.] to produce  more income over a shorter time [End of 1.].

What have I misunderstood about 1? If male pensioners die earlier,  then their pensions would be shorter, and the principal would generate less interest and fewer payments. So why more income?


texts: Macroeconomics, price setting and wage setting

texts: What happens to prcie setting and wage setting when consumption falls? I already looked at what happens to IS-curve and LM-curve.


texts: How to close the gap between non-Econ background and Macroeconomics

texts: I'm a first year PhD student with mathematical finance background, and am not quite familiar with all the assumptions/setup for macroeconomics. During study I found the math relatively easy but I'm having hard time to grasp the often critical relation between variables. For example capital market clearing implies that the total capital that firms have equal to the total assets that households have. First of all, I didn't even know there's a market clearing until I ask my TA, secondly, there are too many such assumptions I don't know. My professor would probably think it's too dumb to tell students about these because most of my classmates have an Econ background, but I don't and it's really killing me. Is there any good reference I can read, open courses I can watch that could help me with this? Given limited amount of time, I hope it won't take as much time as a full course. Thanks in advance.


texts: Statistics of links between public debt and recessions

texts:
When the debt of a country gets above a certain level, is there a bigger chance for an economic crisis, recession or even civil unrest?
I know things are different today.
But did anyone bother to study the relation between debt levels and such problems along history?


texts: Why are some natural monopolies protected by the law from competition?

texts: It just doesn't make sense. Any try to challenge a natural monopoly is fruitless (at the best) or an economic suicide (at the worst). Why would you forbid companies from doing such stupid move? It's like forbidding inhabatants of skyscrapers from jumping out of windows.


texts: Is there a way to eliminate shilling, spiting, and overbidding in second price auctions?

texts:
In a 2nd price option, if all the player choice their bids independently, the optimal strategy is to bid their valuation. However, in some situations, their decisions can effect each other.

For example, an over bidder could announce that they will bid \$1000000 for a painting worth \$1000. This would cause all the bidders to not bid (since now there is no point), and the over bidder pays $0 since there were no other bids.

A solution to the over bidder is a spiter, who predicts the bid of and underbids the highest bidder by 1 cent, forcing them to pay their bid. However, the spiter presents a new problem. If the players know their is a spiter, they will bid like they would in a first price auction, since they know they will end up paying whatever they bid. Even worse is a shill, someone who colludes with auctioneer to underbid the highest bidder by a cent. If they accidentally win (if they overestimated the highest bid), the auctioneer can secretly refund the purchase. If they succeed, however, they can share the extra revenue with the auctioneer, meaning that they have an incentive to succeed.

My question is, are there any modifications you can make to the auction to solve this? Of course, you could just say "no over bidders, spiters, or shills allowed", but I would prefer a mathematical solution.


texts:
Let´s discuss a little!

When the direct effect of a tax or transfer policy (compared to what would happen in the absence of the policy) is a reduction in inequality, it is called progressive policy. If a policy’s direct effect is a rise in inequality it is called regressive. Policies that are neither progressive nor regressive are called distributionally neutral.

In the book on the website https://core-econ.org/the-economy/book/text/19.html#1910-redistribution-taxes-and-transfers there is an exercise 19.10.

There are question such as

1) Suppose you learn that the richest 10% of people pay 30% of income tax. Does it mean that the tax system is progressive?
2) Some governments of developing countries give scholarships for some of their best students to go to graduate school abroad. If there are no eligibility restrictions, is this policy likely to be progressive or regressive? What might justify this policy?

My answers
1) From the information given we can not say whether tax system is regressive or progressive. First of all we do not know what percentage do the lower-income earners get. Secondly, if poorer people are paying less percentage we could say that the tax system is progressive. If lower-income earners pay the less or equal percentage as the richest 10% of the society then we could say that the tax is regressive.

2) I do not understand exactly the question even though i translated it to my mother language. I do not understang preciecly this part ¨ If there are no eligibility restrictions, is this policy likely to be progressive or regressive? What might justify this policy?¨. However answering this questiong i would like to say that if students who got scholarship get a good education abroad and then return bqck with good knowledge and will transfer this knowledge to other citizens (for example being teacher or professor researchers) or even politicians or economists then in a long-run situation in a country could prosper.

My question
What is your opinion? Do you agree with my opinion? Or you maybe can say something in contrary?


texts: Why would a rise in the discount rate stop foreign gold drain and make banks fail?

texts:
I am reading "Capitalism and Freedom" by Milton Friedman. In Chapter 3, "The control of Money", Dr. Friedman explains how the Fed exacerbated the Great Depression of the 1930s. In particular:

  In September 1931, Britain went off the gold standard. This act was
  preceded and followed by gold withdrawals from the United States.
  Although gold had been flowing into the United States in the prior two
  years, and the U.S. gold stock and the Federal Reserve gold reserve
  ratio were at an all time high, the Reserve System reacted vigorously
  and promptly to the external drain as it had not to the previous
  internal drain. It did so in a manner that was certain to intensify
  the internal financial difficulties. After more than two years of
  severe economic contraction, the System raised the discount rate—the
  rate of interest at which it stood ready to lend to member banks—more
  sharply than it has within so brief a period in its whole history
  before or since. The measure arrested the gold drain. It was also
  accompanied by a spectacular increase in bank failures and runs on
  banks. In the six months from August 1931 through January 1932, roughly one out of ten banks in existence suspended operations and total deposits in commercial banks fell by 15 per cent.

My questions are:

Why would an increase in the discount rate arrest gold withdrawal by foreign individuals?
Why would an increase in the discount rate decrease the amount of bank deposits made by commercial banks?
Why would an increase in the discount rate make commercial banks fail?


texts: How much do real-estate prices correlate with apartment rental prices?

texts: I've been trying to find sources that mention this, and have tried to find graphs of data so I can compare myself, but I haven't been able to. Do real-estate sale prices correlate positively, negatively, or not at all with apartment rental prices? A more nuanced answer than that is also appreciated.


texts:
I have the following maximization function -
$\max_{x \in (0,1)} (((p_1e_1x^2)^{r} + (p_2e_2(1-x)^2)^{r})/2)^{1/r}$
where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered to be given for this maximization problem. Here, $e_1$ and $e_2$ are a function of r
FOC are given as -
$\frac x {1-x}$ = ${(e_2p_2/e_1p_1) }^{r/{2r-1}}$
I have to find value of r for which x=1. But substituting x=1 will remove r from the system. So, my question is - does this mean value of x=1 is not possible?


texts: Have the stocks and flows of hunter-gatherer economies been formally analysed?

texts:
A lot of work in economic anthropology seems to be about allocation mechanisms. This feeds into economic discourses about the institutions governing markets and non-market alternatives, e.g. Douglas North (1977):
Markets and Other Allocation Systems in History: The Challenge of Karl Polanyi

It is reasonable to assume that the forces that lead to the
substitution of firms for markets today may also help us to explain
the variety of forms of economic organisation in past societies.

I wonder if similar work has been done on stocks and flows, i.e. a formal economic analysis of stocks (e.g. rights to access common land, its fruits once harvested, services such as healthcare, tools, artefacts) and flows (e.g. reciprocity mechanisms, both within and between groups).
There is ample qualitative analysis, e.g. in this volume edited by John Gowdy (1997) which includes a contribution by Marshall Sahlins (Stone Age Economics, 1972):
Limited Wants, Unlimited Means: A Reader On Hunter-Gatherer Economics And The Environment
I wonder if there have been attempts to formalise the stocks and flows?


texts: Why are some goods without close substitutes not sold in some countries?

texts:
Especially in consumer electronics, a large number of goods are offered only in some countries. Usually this holds only for products which have some close substitutes available (e.g., screens, where a particularly cheap models are often only sold in the U.S. but not in Europe). Such cases are not too hard to explain via price discrimination.

However, I recently found out that there exist products which do not have close substitutes such as Sony's E-Ink readers but are nonetheless only available in some countries. (Production limitations were my first thought, but the example product is already several years old.) Given that the online retailer market is very efficient and that consumer electronics have large development costs I could not come up with a reason why consumer electronics producers would willingly restrict their own market size.

Since I do not believe that producers make such decisions without good reasons, I would like to know what these reasons are. Note that the example product is not the only case, similar cases can be found earlier in the cell phone and PC markets.


texts: Increase in the price of skateboard wheels cause a decrease/no change in the demand of skateboards? (2 separate markets w/ 2 separate buyers)

texts:
Would an increase in the price of skateboard wheels cause a decrease/no change in the demand of skateboards? (2 separate markets with 2 separate buyers)
Note: I'm going to be mainly focused on the demand curve and its shifting rather than supply curve and markets, etc. Trying to simplify the thing I'm trying to figure out here. I'm asking this question more to double-check, but I could be having a major inconsistency in my basic understanding.
So, let's say there's a skateboard-making company that buys skateboard wheels from another company in order to make its product (skateboards). Let's say that other company selling skateboard wheels to the skateboard-making company increases the price of its skateboard wheels. This would cause a movement along the demand curve where the skateboard-making company would decrease the quantity it demands of skateboard wheels. ( Here skateboard wheels are an intermediate good and this is a B2B market (Business to Business) by the way. So no regular consumers involved here! )
This would basically mean the skateboard-making company would have fewer skateboard wheels in its inventory, etc. Now onto the market for skateboards: this would not shift the demand curve to the left/inwards, right? Rather, the demand curve would be unchanged (not shifted left or right). Obviously, there would be a shortage of skateboard, but I'm not so focused on that. I'm just double-checking that for the first market I mentioned, the skateboard-making company was the buyer and due to a change in price there was a movement along the curve. In the second market I mentioned, we have regular people who buy skateboards as the buyers and other than there being a shortage in the number of skateboards being produced the demand curve wouldn't have shifted since they weren't directly affected by the change in the price of skateboard wheels. They still love buying skateboards and continue to do so (only they will be a bit disappointed to know there is a shortage of skateboards because of the skateboard wheel probably explicitly affected the skateboard-making company's quantity demanded)
Yes, I am aware the quantity demanded and demand (market/indiv. demand curve) is different. I've tried to be explicit in which one I am referring to above in my question.


texts: Roy's identities for Stone-Geary utility functions

texts:
I'm having trouble showing Roy's identity for the following Stone-Geary utility function:

$$U(x)=\prod_{i=1}^n\left(x_i-\gamma_i\right)^{\beta_i}$$

where $\sum \beta_i=1$ and $\gamma_i$ is the minimal consumption of $x_i$.

I showed that the Marshallian demand (which I confirmed using multiple sources) is

$$x_i=\gamma_i+\frac{\beta_i\left(I-\sum_{j=1}^np_j\gamma_j\right)}{p_i}$$

Therefore, the indirect utility function is

$$V(x)=\prod_{i=1}^n\left(\frac{\beta_i \left(I-\sum_{j=1}^np_j\gamma_j \right)}{p_i} \right)^{\beta_i}$$

I applied a monotone transformation to simplify the indirect utility function:

$$W(x)=\sum_{i=1}^n\beta_i\left(\left(\ln(\beta_i)+\ln \left(I-\sum_{j=1}^np_j\gamma_j \right)\right)-\ln(p_i)\right)$$

Therefore,

$$\frac{\delta W}{\delta p_i}=\frac{-\beta_i\gamma_i}{I-\sum_{j=1}^np_j\gamma_j}-\frac{\beta_i}{p_i}$$

$$\frac{\delta W}{\delta I}=\frac{\beta_i}{I-\sum_{j=1}^np_j\gamma_j}$$

$$-\frac{\delta W / \delta p_i}{\delta W / \delta I}=\gamma_i+\frac{I-\sum_{j=1}^np_j\gamma_j}{p_i}$$

Basically, as you can see, something doesn't add up: the $\beta_i$ is missing from the numerator. Thus, Roy's inequality is not verified. Where did I mess up?

(Note: I've also tried without the transformation. This is a much more tedious process but it yielded the same answer; the $\beta_i$ was still missing)


texts: How to model best combination of resources

texts:
I don't have an economics background, I come from CS. I am sorry if this question seems weird.

We want to model the combination of a set of resources to either answer the cost of the model, minimize the cost of the model, or find the cheapest combination of resources.

Precisely, we have a network of computers, with some producing data, and some consuming data, organised in stages of Producers and Consumers: P -> C -> P -> C ... but the network is more like a graph with cycles on the data. We already have the model of this communication paradigm from a CS point of view, we are interested on the Economics side since we have to scale, redesign, and build the system in the future.

What are the existing approaches to model such questions?


texts: Should I use panel or cross-sectional weights for survey data when running OLS regression with command "reg"?

texts: if I have a unbalanced panel survey data of four years, I wondered if I still needed to apply panel weights when run "reg", as pool ols regressions on it? Or should I apply cross-sectional weights for "reg" command? There are repeated time values within panel, but the same personal IDs for each year. There might be repeated values for personal IDs. Thank you.


texts: Understanding the Components of Optimization

texts:
What are policy function, objective function, constraint function, choice variables and parameters within the context of a utility maximization problem?

I don't understand which each of these are and I was not able to find out from resources online. Your help will be much appreciated.


texts: What is the latest thinking on the economic calculation problem?

texts:
Eric Posner and Glen Weyl write in the epilogue of Radical Markets (2018) that they “remain confident that for at least a few generations markets – Radical Markets, that is – will remain the best method of large-scale social organization”.

Are there indications that alternative calculation methods may challenge this thesis?

--
CLARIFICATION:

Typically an alternative calculation method, more efficient than markets, is considered to be possible through technology: parallel processing and more recently artificial intelligence:

  The market process … may be considered as a computing device of the pre-electronic age.

Oskar Lange (1967): The Computer and the Market

I wondered what the current discourse was on the topic beyond what is available on Wikipedia.


texts: How can we know how PPF of our country looks like?

texts:
PPF of our country is based on potential the most efficient use of our resources, NOT their actual use. The problem is, it's unclear for me how to estimate said potential. How to know where potentiality ends and impossibility begins? Not necessarily with clean-cut distinction, a rule of thumb can be good enough too.

Examples:

(An increase of productivity needs a cultural shift) Maybe we would be able to increase production by increasing participation of women in the workforce, but our culture CURRENTLY dictates that married women should NOT work.
So would our PPF include increased production caused by by cultural shift? Or would we experience an increase of PPF?
(An increase of productivity needs a political shift) Maybe our production would increase if we used these sweet new technologies. But alas, we can't have them due to sanctions and it would require radical change in our current political regime in order to have possibility for sanctions being lifted. If sanctions were lifted after revolution would it mean that our PPF increased or that we got closer to it?
Maybe our production would increase if we used industrial espionage to get new technologies, but such secret operations have very high possibility of a complete failrue. Would success mean that we increased our PPF?
Maybe our production would increase if there was industrialization in our society. But our society have never been industrialized in the first place. And it would take many years and lots of efforts to industrialize it.


texts:
If a risk averse person is given the option of a certain amount of 2000 or playing a lottery game giving him 10000 with 25% probability, and 500 with 75%, then what would he do ?.

The bet here is not a fair one, so wouldn't his choice depend on the degree of his risk aversion ?. Can somebody please help me out.


texts: Who exactly suffered more in the US-China trade war?

texts:
The US and China signed a trade deal recently that made the news.

Shortly afterwards, Nobel-prize winning economist Paul Krugman claimed that the US lost the trade war. His argument is that US importers have to pay the tariffs to import Chinese goods. China's exporters could drop prices to remain competitive, but they haven't, so it's the US importers and consumers who wind up paying the price. Meanwhile, China's importers have had more success finding replacements for US exports, and because of the tariffs, US farmers suffered hard (which is why the government was forced to bail them out).

Meanwhile, Axios published an article saying that although the US suffered, China suffered more. China's total exports fell for the 12th straight month, the US-China trade deficit narrowed to its lowest point in over two years, and China's trade surplus fell by $8 billion more than expected. Accordingly, S&P analysts wrote that the economic pressure is "working", and there's little reason for the US to back away from the tariffs.

I don't get how to reconcile these two seemingly at-odds positions. Paul Krugman's argument seems logical, but then Axios' statistics also seems impeccable. I imagine one could think "both sides lost", but if China lost harder than the US then Paul Krugman's arguments seem bombastic if not outright misleading. Besides, his statistics seem to claim that the US lost harder than China.

How do I make sense of this? I know little about economics and this is an example of how I can't understand economic arguments when they show up in the media, so I'd appreciate an elementary explanation.


texts:
For what values $x$, $y$ the profile $(D,L)$ is Pareto optimal?

\begin{array}{c|ccc}
& L  & R \\ \hline
U & x,5 & x+2,y  \\
D& 1,-1 & x,0 \\
\end{array}

Is correct $x<1$ ?

I suppose this because $D$ should not be weakly dominated.

And $y<5$ for the same argument.

Is these values enough to answer that $(D,L)$ is Pareto optimal?

Thanks!


texts:
What was the reason for a boom on Wallstreet in 1938?

Our reporter in N.Y. said today that this 1. week of April 2020 was the best since 1938.

What was the reason for this rebound in 1938?


texts: Why are some economists remarkably productive?

texts: I'm a first year PhD student and I randomly go to different professors' websites to admire their works. Usually an economist has around 20 published papers when he/she reaches professorship. But there are a few outliers, like Andrew Lo, Darrell Duffie, Kenneth Singleton and Paul Samuelson, who have like a few hundred of papers published. Are they simply more productive than others? Is the number of publications (of course above a certain standard of quality) a good indicator of the economist's ability?


texts: Why hasn't Quantitative Easing surged inflation, or caused hyperinflation?

texts:
Quantitative Easing (QE) is the buying of bonds and other financial assets by the Central Bank with high-powered money, or money created by the CB for this purpose.

Isn't this ad-hoc creation of money  the main ingredient for hyperinflation?
Why hasn't there been a surge in inflation?


texts: How can I prove $U(x) = [_1_1^+_2_2^]^{(1/)}$ is equal to Cobb-douglas Utility function when $\rightarrow0$

texts:
This is the question, I have problem with part b, I don't know what function should I use to reach the result
thanks in forward


texts: Government Spending vs. Investment Spending

texts: What is the difference between government spending on physical capital and investment spending by government on physical capital?


texts: What is the implicaiton of agent risk neutrality in moral hazard?

texts:
I heard that risk-neutrality of agent in moral hazard imply that the action associated with first-best and the one associated with second-best will be the same. Is it true and why is it so?

Are there other implication of agent risk neutrality?


texts: Is the convexity of production sets necessary for the welfare theorems?

texts:
I have read that the convexity of production sets (for instance non-increasing returns to scale) is not a necessary assumption for the first welfare theorem but it is for the second welfare theorem. Maybe I got things wrong and what the author actually tried to say is that convexity is not necessary for the efficiency of the competitive equilibrium but rather for the existence of the competitive equilibrium.

Could you please elaborate where the assumption of convex production sets is needed in the first and second welfare theorem?


texts: How do I test if a given policy was successful?

texts:
I have some data for medical R&D and sales, my professor has asked me to check if a policy implemented in 2016 has made any effects on R&D and R&D/Sales data.
I tried to plot growth rates over years, but he says we don't need growth rates, and it has to be solved just by mean R&D expenditures each year. (Mean over multiple companies). How do I go about significance testing of policy change?


texts: Best econometric models to fit when there is no control group?

texts:
I am trying to study the effects of a program, where everyone gets treated. I have 50% of the population in t and the rest of the 50% in t+1 period. I understand this gives me a slight opportunity of creating a control group for just one time period and run something like DID. Or I can run a Segmented TS analysis.

I was wondering if there is any better way?


texts: Help with Monopolistic Competition Proof, Prove Love for Variety

texts:
I need some help with a proof.

  Assume η = 2 and there are just two goods.  Verify that the following utility function exhibits Love for Variety tastes, show that:

  u(λa + [1 − λ]b, λb + [1 − λ]a) > u(a, b) for 1 > λ > 0

  Additionally, I am given the utility function:
  $$
\\u(q_1,q_2, ...q_n) = \sum_1^N \sqrt[η]{q_i}\,
$$

In the lead up to the question, I am given a different problem to prove that should help me solve the above one.

It uses the same utility function, and I have to prove that the consumer wants a variety of two firms, rather than just one firm, I think I figured it out but I don't know how to apply what I did in the above proof, I have to prove that sqrt(x) + sqrt(y) > sqrt(x + y):

$$
\sqrt{x} + \sqrt{y} > \sqrt{x+y},
$$
$$
(\sqrt{x} + \sqrt{y})^2 > (\sqrt{x + y})^2
$$
$$
2\sqrt{xy} + x + y > x + y
$$
$$
2\sqrt{xy} > 0
$$

Any help is sincerely appreciated.


texts: Most models I have seen use expected values. Why is this a better economic model than uncertainty and economic agents thus having to make 'best guesses', with the result of 'animal spirits' playing a large role. For example, it seems like no one knows where bitcoin would head for sure, hence the rife animal spirits-eqsue speculation involved and variable price.


texts: What would it mean for a parameter region to be E-stable but undeterminate?

texts:
What would it mean for a parameter region for a dynamic system to be E-stable, but indeterminate?
E-stable: it's stable under learning... so this means, once in equilibrium, you stay there? Or does it mean you always get there under learning?
undeterminate: super sensitive to parameter changes, tipping points may occur easily, there are multiple equilibria, etc etc?
The two seem to rather contradict, however, this combination is put forward in Figure 3 of Bullard and Mitra's (2002) paper for their adaptive learning New Keynesian model for monetary policy rules.
The other combination, Determinate and E-unstable or stable, either way, seems easier to grasp.
reference
Bullard, J., & Mitra, K. (2002). Learning about monetary policy rules. Journal of Monetary Economics, 49(6), 1105–1129. https://doi.org/10.1016/S0304-3932(02)00144-7


texts: Sunk cost fallacy- is it a bug or a feature?

texts:
I was having a conversation with a colleague regarding sunk costs, and discussion came up that the appeal of falling for the sunk cost fallacy might be a feature rather than a flaw, as it is behavior that appears to be very common and very persistent across generations. I'd argue, just looking at the world as I see it, most individuals fall for the sunk cost fallacy, and it doesn't seem to give a serious disadvantage over time

I'm aware of the literature regarding sunk costs and memory. I'm curious about any thoughts you all may have.

Thank you!


texts: Rationalizable strategies and Weak Dominance

texts: Can I find the rationalizable strategies for a game where none of the players has strict dominance but only weak dominance?


texts: The Fed Lowered Interest Rates, Are they going to buy Bonds?

texts:
I originally asked this question on personal finance/money because I didn't know that this exchange site existed. link to same question at person finance/money.  Someone on that site mentioned that it might be off topic, so I thought I would try here.

The Fed just lowered interest rates yesterday by 0.25%. I haven't heard anyone mentioning a resurgence of quantitative easing (QE).

Is the Fed going to start buying bonds in order to influence the interest rate? If so, where can we find the dollar amount of bonds they are buying and over what time frame?


texts: Do across-the-board tax breaks increase wealth if wealth is relative?

texts:
So, as I understand it, the value of one's money is in its purchasing power, and its purchasing power is related to its amount relative to others.  That is to say:  Earning 25k a year in a country where the mean income is 10k makes you very rich, whereas earning 25k in a country where the mean income is 50k means your 25k does not go nearly as far.

So my question is this:  Does this mean that an across-the-board percentage income tax cut does not increase anyone's wealth?  If everyone has x% more money, isn't their purchasing power still identical?  Obviously, the second it happens, prices and wages are the same, so in that moment they have more, but don't prices and wages catch up?  Or does the definition of purchasing power shift.. one could buy more of certain goods, but the prices of things like housing rise to reflect the increased amount of money people have to bid on them?

Confounding factors I can think of: Global prices, capital shift between public and private sector


texts: With OPEC driving the prices of oil down, can American producers simply store oil produced at higher cost to sell later?

texts:
I have been wondering. With OPEC driving down the price of oil in order to stifle the growth of the American oil industry, what can we do about it?

More specifically, why don't these oil producers simply store the oil that is produced for more than the current per barrel selling rate and then sell the stored oil later when the price inevitably rises once more?

I understand that many companies have to keep pumping the oil to retain land rights. But I don't see why we can't get around that by pumping it and then storing it somewhere. Preferably on land and in facilities that are already owned. Then when the price goes into the profitable zone you reduce the volume you are pumping out of the ground and replace the output with the stored oil.

Also, I read that Saudi Arabia is cutting oil production. But that OPEC has taken actions to drive down the cost of oil. Yet I would think that overwhelming the market with supply would be how they drive down prices. So I am confused as to how the production cutting is working.

Any thoughts or information?


texts:
I know expected inflation plays a key role in both the Phillips curve equation and the Fisher equation, but does it also play a key role in Taylor's Monetary Policy Rule?

I'm asking this as I have an assignment question which requires me to derive the DAD curve, with a different expected inflation, and I am unsure if I have to change the expected inflation in the monetary policy rule as well.


texts: New Keynesian Model Output Gap and Calibration

texts:
I am trying to solve following problem regarding the New Keynesian Model:

So, I have calculated following equations by using the Taylor Rule, Phillips Curve and IS Curve:
$$\pi=\frac{\kappa\phi_y}{(1-\beta)\phi_y+\kappa(\phi_\pi-1)}(y^*-y^n)\qquad(1)$$

where $y^*$ denotes the efficient level of output and  $y^n$ the natural level of output.

Also
$$y=y^n+\frac{1-\beta}{\kappa}\frac{\kappa\phi_y}{{1-\beta}\phi_y+\kappa(\phi_\pi-1)}(y^*-y^n).\qquad(2)$$

The parameters were calibrated as follows: $\kappa=0.34,\nu=6,\beta=0.99,\sigma=1,\gamma=1,A_t=1,\phi_y=0.125,\phi_\pi=1.5$ and $$y^*_t-y_t^n=\frac {Y_t^*}{Y}-\frac{Y_t^n}{Y}$$,since $Y=Y^n$ (*).

I tried to solve for $(y^*_t-y_t^n)$ and with (*) and $$w=\frac{\nu-1}{\nu}A_t$$, $$w_t=C^\sigma_tL_t^{\gamma-1}$$, $$C_t=Y_t=A_tL_t$$ I get: $$y_t^*-y_t^n=\frac{1}{(\frac{\nu-1}{\nu})^{\frac{1}{\sigma+\gamma-1}}}-1\qquad(3)$$.

Now, I have a problem solving for (1) and (2).
First, the sample solution is $\pi=0.0249$, but if I insert the parameters into (1) I get $\pi=\frac{34}{137}*0.2$ and in order to get the same solution as in the sample solution it should be $\pi=\frac{34}{137}*0.1$. So, did I do something wrong in (3)?
Secondly, it seems strange to me that if ( * ) holds, shouldn't (2) equal 0?
Also, could someone give me an intuitive explanation for ( * )?

Thank you!


texts:
Hello in the moment I am working with the book "Introduction to the Economics and Mathematics of Financial Markets" by Jakˇsa Cvitani ́c and Fernando Zapatero, which can be accessed at the link.

However, at the moment I am struggling with the third chapter "Models and Securities Prices in Financial Markets". Right in the beginning at page 56 there is an introduction of a formula, which I do not understand completely.

X(1) should display the worth of all the assets (securities,stocks, bonds etc.). Therefore B=Bonds, S=Securities or Stocks. The numbers 0 and 1 illustrate the time. So 1 for the end and 0 for the beginning.

But what is the this sign "δ". Actually it is a delta isn't it? And it actually illustrates a changing process. However, here it is described as follows "Denote by δi , i = 1, . . . , N the number of security i shares that Taf holds between time zero and time one. We denote by δ0 the amount invested in the bank account at time zero, “the number of shares” of the bank account." (page 55, at the same book). My problem is that I really do not understand the meaning of this sign. Also the Sentence, which is illustrated in the picture talks about a vector. I completely do not understand the word vector in this relationship.

I hope I can get some insight to this topic through your help. Overall it should be an introduction to the two periods binomial models.


texts: Hello I want to find a instrument variable for airline "bankruptcy" but that instrument should not affect ticket prices? can any one help me out? I have already tried out the cash flows, current assets and liabilities.


texts: Why lower the deposit rate if it is already negative?

texts:
The European Central Bank (ECB) has been lowering the interest rate on its deposit facility, first to -0.1% in June 2014, then to -0.2% in September and eventually to -0.3% in December 2015.

But what difference does it make whether it is -0.1% or -0.3%, as long as it is negative? I would expect anyone to withdraw all their money immediately as soon as the interest rate gets negative, for you would always be better off just keeping it for yourself, even if the interest rate is just -0.0001%.

I do understand the intention of the ECB, but I do not understand why lowering the already negative interest rate further should make it more effective.


texts: Can anyone help me derive saving from the OLG model? (Just check to see if my start is okay please)

texts:
Question assumptions:
Consider the effect of a capital tax on the OLG model. The government imposes a capital tax rate at the rate $\tau\in[0,1)$ and pays all the tax revenues back to the old in a lump sum T. Assuming log utility, the maximization problem for a household born at the beginning of t is:
$\max lnc_{1t}+\beta lnc_{2t+1}$ s.t. $c_{1t}=w_t-a_{t+1}$ and $c_{2t+1}=(1-\tau)(1+r_{t+1})a_{t+1}+T_{t+1}$
(a) derive the savings of a young consumer of generation t for a given $w_t$, $r_{t+1}$, and $T_{t+1}$.
My solution attempt:
We know that the utility of consumers born at the beginning of t is:
$u(c_{1t},c_{2t+1})=u(c_{1t})+\beta u(c_{2t+1})$ (1)
Where $\beta\in(0,1)$ is the discount factor, c is consumption when young (1t) and old (2t+1)
Our budget constraint is:
$c_{1t}= w_t-a_{t+1}$ (2)
$c_{2t+1}= (1+r_{t+1})a_{t+1}$ (3)
Eliminating $a_{t+1}$ we arrive at our lifetime budget constrain which is:
$c_{1t}+\frac{c_{2t+1}}{1+r_{t+1}}=w_t$ (4)
$(w_t-a_{t+1})+\frac{[(1-\tau)(1+r_{t+1})a_{t+1}+T_{t+1}}{1+r_{t+1}}$
Our log utility function is:
$\frac{1}{c_t}=\beta (1+r_{t+1})\frac{1}{c_{2t+1}}$
with the FOC being:
$c_{2t+1}=\beta (1+r_{t+1})c_{1t}$
Comment: I am unsure if this is the appropriate budget constraint and utility function based on my problem set. Furthermore, when they ask me to derive the savings do they mean the law of motion of savings? Any help would be appreciated.
Notice: the problem is unfinished as I am still working out the solution, and I am just unsure if the basic materials needed to derive the solution are correct. Thank you to anyone who provides a solution.


texts: How do I choose an appropriate Instrument to solve the endogeneity issue?

texts: I have a quadratic regression model and one of the variables is endogenous. How do I choose an instrument to deal with this issue?


texts: Validity condition for Instrumental Variables

texts:
My professor states the validity condition in the following way:
$W$ (the matrix of instrumental variables) must be such that
$ \text{plim} \, \frac{W'u}{N}=0$, where $u$ is the error term.
Intuitively, I can see that in some way, this relates to the covariance between $W$ and $u$, but am not entirely convinced.
Moreover, why do we look at this condition in an asymptotic setting? Why not impose mean independence, i.e., $E(u|W)=E(u)$?


texts: What is the difference between two stage least squares and instrumental variable regression?

texts:
I'm doing independent study and I am having trouble understanding the difference between these two estimators.

I get that 2SLS is predicting the endogenous variable, and that instrumental variables are similar to proxy variables, but I don't get how one differs from the other.


texts:
Let's assume I have a dataset consisting of fiscal/monetary policy responses and non-pharmaceutical interventions to the COVID-19 crisis in tens of countries.

How would I go about analyzing their effectiveness in terms of, e.g., GDP growth (other variables also possible), in short term? What would be suitable methodologies? Let's say I would have quarterly GDP growth data up until Q2 2021. Any interesting papers that focus on similar methodologies?


texts: Can an irrational function be a utility function?

texts:
Given some irrational preferences, that can be represented by a function. If the function does not satisfy rationality (transitivity, completeness), does this imply it is not a utility function.
I know rationality over $\preccurlyeq$ does not imply a utility function. But rationality and continuity over $\preccurlyeq$ implies a utility function. But what about the reverse direction?
For example, $u(x) = sin(x) + 1$, is not rational, but is continuous, is it a utility function?
In my books I see a lot about the requirements needed to make a utility function, but given a function, what are the requirements for it to be a valid utility function?
My Answer A utility function is the representation of a preference relation $\preccurlyeq$. All preference relations are by assumption (or definition), rational. Given a function, if there does not exist any rational preference relation, then it must not be a utilty function.


texts:
In my econometrics and economics classes, the term autocorrelation has come up this quarter. I have read the Wikipedia pages about it and tried to understand them, but they are a bit beyond me. They use too much math from signal analysis that I don't have time to study at the moment. But I would still like to understand the general idea.

Can someone provide a brief explanation of what autocorrelation is and how this concept is used to understand price and analyze price trends?


texts: Strictly increasing but not convex preferences

texts:
Is it possible to have preferences that is strictly increasing but not convex?
Will perfect substitutes indifference curves show strictly increasing but not convex preferences? I am confused, as won't perfect substitutes be considered as convex?


texts: What are the current economic theories of product advertising?

texts:
Are there any well known economic theory references about advertising? It seems you could think of advertising as imposing a negative externality on other producers or on consumers in that it takes up bandwidth, or a positive one instead in that its a way of subsidizing programming or generating public information...

Should we put Pigouvian taxes on advertising or instead subsidize the necessary infrastructure?

This post is about advertising , but does not have any references:


texts: Unusual perfect complements utility function min{ax+y, x+2y}

texts:
What's the graph for this utility function? How can it be represented graphically?

Is this function perfect complements? I do not fully understand that in the question attached in the picture, the slope cannot be a fractionnary number since the goods are perfect complements.


texts:
The state of Minnesota is considering building a highway through undeveloped wilderness. The construction will take 1 year and the construction costs are estimated at 10 million. The annual routine maintenance costs are expected to be 1 million per year. The relevant interest rate is 5%. The expected estimated annual benefits to the public and environment are $2 million per year. Assume an infinite project life.
 is my attempt on the first 3, feel free to correct me if I am wrong.*
I do not understand the parts d and e if anyone could shed some light on it.

PV = Present Value

a. Find the PV of the Costs of this project.

  10,000,000 + 1/0.05 = 30000000

b. The PV of the benefits of this project.

  2,000,000/0.05 = 40000000

c. The PV of the Benefits – PV of the Costs.

  Subtract the above we get 10000000

d. Find the annual value of benefits which generates a zero net present value.

e. Assuming an infinite project life, find the increase in annual routine maintenance costs that make the NPV = 0.


texts: Does National Savings equal zero in a closed economy? Please give an economic intuition

texts:
Context:

$Y -(C+I+G) = X - M$

In a closed economy, $(X-M) = 0$

Notations

Y --> Income/Output

C,I,G --> Consumption, Investment and Government expenditure respectively.

X --> Exports

M --> Imports

I want an economic intuition how is it possible that aggregate of all savings in a closed economy equals 0.


texts: Alpha interpretation in Solow growth model

texts:
Consider the Solow model (without technology):
$Y = F(K, L) = K^\alpha L^{(1-\alpha)}$
What's the economic interpretation of $\alpha$? Prove and argue the result.

I see it as a share that goes into capital and $1-\alpha$ is the share that goes into labour, but how do I prove this mathematically?


texts: Throw-away paradox with independent goods

texts:
The throw-away paradox is a situation in which a trader can gain by throwing away some of his initial endowment.

The specific example, brought by Aumann and Peleg in 1974, concerns an economy with two commodities and two traders:

In one situation, the initial endowments are (20,0) and (0,10). In competitive equilibrium, the bundle of trader A is (4,2).
In the second situation, trader A throws away 10 units of commodity x, so the initial endowment is now (10,0) and (0,10). In equilibrium, the bundle of trader A is (5,5) - more of ''every'' commodity than in the first situation!

In their example, both traders have the same utility function, which has the following characteristics:

It is homothetic;
The slope of the indifference curves at (y,y) is -1;
The slope of the indifference curves at (2y,y) is -1/8.

One such function is $$u(x,y)=\frac{1}{(x+ay)^{-3}+(ax+y)^{-3}}$$

But, in this example, the products are dependent.

MY QUESTION IS: Is there an example of such a "throw away paradox", when the products are independent?

NOTE: both products are goods (have non-negative utility).


texts: Proof of Choice Coherence in Kreps (2013)

texts:
In the first chapter of Kreps (2013), there is a proof that the choice function satisfies choice coherence. Kreps writes:

I do not understand how the third sentence of (b) logically follows from the previous two sentences. How do we necessarily know that there is a third commodity, z, in A? There might just be two commodities. Furthermore, how do we necessarily know that u(z) > u(y)? Why can't the consumer possibly be indifferent between z and y?


texts:
According to the Fischer hypothesis, nominal interest rates increase with inflation, so that the underlying real interest rate is preserved.

One might then expect that if a nation A has a higher interest rate than another nation B, then the expected inflation for nation A will be higher than that of nation B. (Assuming the real rate of interest is the same accross nations as in the international Fischer hypothesis)

However, if a nation sets its interest rates by controlling money supply, then the nation can raise their interest rates by decreasing the supply of money. Wouldn't the decrease supply of money then lead to decreased inflation, rather than the increased inflation described in the Fischer hypothesis?


texts: What's a "relative pair trade" for currencies?

texts:
Is the U.S. Dollar About to Crash? – Pairagraph

The way I see currencies is that they are a relative pair trade. Against gold, with its stability characteristics, I don't like the US dollar. But despite all the warts, pimples, and scars on the greenback, I think most other countries have far deeper problems.

I'm not Rosenberg, but he appears upright.

From 2002 to 2009, he was Chief North American Economist at Merrill Lynch in New York, during which he was consistently ranked in the Institutional Investor All-Star analyst rankings. Prior thereto, he was Chief Economist and Strategist for Merrill Lynch Canada, based out of Toronto, where he and his team placed first in the Brendan Woods survey of Canadian economists for ten years in a row.
Mr. Rosenberg received both a Bachelor of Arts and Masters of Arts degree in Economics from the University of Toronto.


texts: Why does the Fed not fiddle with the reserve ratio?

texts:
We often hear in the news of the Fed changing the interest rate. Why do they not commonly alter the reserve ratio?

Won't either be capable of expanding or contracting the money supply?


texts:
Let $q(p) = \frac{1}{p}$ denote the demand function and $p^*$ some equilibrium price. Consumer surplus is defined as
\begin{align}
CS = \int_{p^*}^\infty\frac{1}{p} dp= \ln(\infty) - \ln(p^*) = \infty
\end{align}
which is quite unsatisfactory. What's the convention here?

Edit: Since I wanna compare welfare under price and quantity competition I found a workaround. Let $n$ the number of firms in the market, $\bar \pi^j$, equilibrium profits of the firm, $\bar p^j$ equilibrium prices and $j \in \{b,c\}$ is the index for the compeition type.
Now we may calculate the welfare difference as
\begin{align}
\Delta W := W^c - W^b &= n(\bar \pi^c - \bar \pi^b) + \int_{\bar p^c}^\infty\frac{1}{p}dp - \int_{\bar p^b}^\infty\frac{1}{p}dp\\
& = n(\bar \pi^c - \bar \pi^b) + \ln(\bar p^b) - \ln(\bar p^c)
\end{align}

Suppose we get the following relationship
\begin{align}
\Delta W = \frac{(n-1)(\sigma-1)^2}{\sigma n^2(\sigma(n-1)+1)} + \ln\left(\frac{\sigma(n-1)+1}{n \sigma}\right)
\end{align}
with $n \geq 2$ and $\sigma \in [0,\infty)$ is a parameter.
Clearly $\Delta W = 0$ for $\sigma = 1$ and for all $n$.
I wanna further show that $\Delta W > 0$ for $\sigma < 1$ and $\Delta W < 0$ for $\sigma > 1$. Any ideas how to proceed?


texts: Objections to total surplus as tool for welfare measurement

texts:
I think people would agree that the most common tool for welfare measurements in economics is the notion of total surplus.

Throughout it's history, total surplus has been criticized several times and on different grounds. This post aims at being a repository of all those critiques.

Which are the critiques of total surplus which seem the most relevant to you?

Note : this is not meant to be a "total surplus bashing" repository. I believe some of the best critique of a concept like total surplus are rarely the one attempting to destroy the concept, and more often those which help us understand when it is best to use it, and when it might be better not to use it.


texts: Shapley value with large number of players

texts:
I'm a complete statistics rookie but I'm looking for some general advice on workarounds if I'm trying to calculate the Shapley Value in games featuring many players.

i.e. If I have 20 players, I need to run all combinations (n!) which is 2,432,902,008,176,640,000.

Is there a solid method of solving the problem by taking a sample of the combinations?  What do I need to look out for in order to make the results of using a sample as accurate as possible?


texts:
In the standard discrete time economies with a finite number of states, $n$, a complete markets economy is simply an economy with $n$ independent assets (Think Ljunqvist and Sargent Chapter 8).  This is because $n$ independent assets is sufficient to span the set of states tomorrow.

I had a discussion with a professor last week in which he stated that one of the conveniences of continuous time when thinking about asset pricing is that within a continuous time economy one can get complete markets simply with a risk-free bond and a risky asset (independent) for each Brownian motion in the economy.

He explained it as we talked, so I think I mostly understand it, but was wondering if someone would mind writing down the details?

I will probably spend a day or two this week on it (depends on some of the properties of the differential calculus), so if no one else answers the question then hopefully I can provide a satisfactory answer.


texts: Economic effects of a Commons Capital Depository

texts:
Yanis Varoufakis (Ιωάννης Βαρουφάκης) proposes to fund a universal basic income (UBI) using dividends from a commons capital depository, essentially  channeling a percentage of shares issued at an initial public offering (IPO) into a depository.  He argues that taxing robots is difficult in practice, that funding UBI through income tax is untenable, and taxing capital/wealth is difficult in practice.  Rather, he proposes (see full article for context; emphasis mine):

So how should society be compensated? Taxation is the wrong answer. Corporations pay taxes in exchange for services the state provides them, not for capital injections that must yield dividends. There is thus a strong case that the commons have a right to a share of the capital stock, and associated dividends, reflecting society’s investment in corporations’ capital. And, because it is impossible to calculate the size of state and social capital crystalized in any firm, we can decide how much of its capital stock the public should own only by means of a political mechanism.
A simple policy would be to enact legislation requiring that a percentage of capital stock (shares) from every initial public offering (IPO) be channeled into a Commons Capital Depository, with the associated dividends funding a universal basic dividend (UBD). This UBD should, and can be, entirely independent of welfare payments, unemployment insurance, and so forth, thus ameliorating the concern that it would replace the welfare state, which embodies the concept of reciprocity between waged workers and the unemployed.

Has anything like his proposed commons capital depository ever been tried in practice?  Although he proposes it in the context of UBI, as a form of/alternative for taxation it could be introduced independently.
Is there any historical precedent for such a model?  Are there any economic studies into what the effects would be to shift government revenue from one based on income or capital gains tax, to one such as proposed by Varoufakis?


texts:
The convexity of an indifference curve results from the fact that the absolute value of its (negative) derivative, which is the marginal rate of substitution is decreasing. But why do we say that it's convex to the origin?

What is an implicit function that is convex and concave to the origin?


texts:
Banks need to maintain certain minimum capital as per Basel norms but where does this money lie. If it lies in a bank account, what would happen if that bank goes bankrupt?

Say, SBI keeps its Tier1 capital in HDFC, what would happen if HDFC goes bankrupt? Or if RBI keeps it with itself, can it loan it out as per fractional reserve system?