Utility function is given as $U = \sqrt{XY}$ find Matthew has a utility function $U = \sqrt{XY}$ where X represents hot dogs and Y represents apples. He has an income of $20.

Hot dogs cost \$1.00 and apples cost \$1.25

Part (i) asks: Matthew's utility fucntion implies that the marginal utility of apples is $0.5 \sqrt{\frac{X}{Y}}$ and the marginal utility of hotdogs is $0.5 \sqrt{\frac{Y}{X}}$. How many apples will he buy? How many hot dogs will he buy?

Part (ii) asks: This year, the price of hot dogs rise to \$3 each while Mathew’s income is unchanged. Mathew’s father decides to help him by giving him a gift of \$20. Consider an indifference curve-budget line diagram with hot dogs on the x-axis and apples on the y-axis. After Mathew gets the \$20 gift, will his new budget line lie above, lie below, or pass through his initial optimum? Justify your choice. Will Mathew be better or worse off than he was last year?

What have I done?

I'm pretty stuck on this. There aren't really any similar examples from me to draw upon from our course literature.

Perhaps the formulas $\dfrac{MU_x}{MU_y} = \dfrac{P_x}{P_y}$ and $I = P_x \cdot x + P_y \cdot y$ might help.

Rather than write a complete answer, I am going to post a couple of hints that will hopefully get you underway.

For part (i), note that

You have two equations: $\dfrac{MU_x}{MU_y} = \dfrac{P_x}{P_y}$ and $I = P_x \cdot x + P_y \cdot y$.
Since we know $MU_x$, $MU_y$, $P_x$, $P_y$, and $I$, these two equations contain two unknowns.
Usually, so long as we have at least as many equations as there are unknown variables, we can find the value of those variables by simultaneously solving the equations.
the $x$ in $I = P_x \cdot x + P_y \cdot y$ is the quantity of hot dogs that you are asked to compute in part (i), so ultimately you are going to have to solve for the value of this variable.
my suggestion would therefore be that you try substituting into your two equations all of the things whose value you know and then try solving for $x$.

Since a budget line is a straight line, it is characterised by an intercept, $c$, and a slope, $m$.

If you think about drawing this line geometrically then you should recognise that

the intercept is the amount of $y$ you could afford if you didn't buy any $x$ and spent all of your available money on $y$.
the slope is the number of units of $y$ you would have to give up to save enough money to afford one more unit of $x$.

Once you know the slope and the intercept, you can write down the equation for your budget line, $y=mx+c$, and answering part (ii) is then just a matter of algebra.


Interest Rate vs. Borrowing Rate - Difference I have never studied economics so the question might be very basic one and would need understandable answer: I would like to know the difference between Interest Rate term and Borrowing Rate term? As far as I understand the Borrowing Rate means when some company borrows money from the bank to pay for some internal staff needed to do their work (e.g. manufactury to buy some materials to produce their own products). Then company returns the money to the bank but with little additional fee and this additional fee is Borrowing Rate in % unit. Please confirm if this is correct. Even if it is, I still don't know the DIFFERENCE between Borrowing Rate and Interest Rate.

The Interest Rate is a more general term, and can cover all shorts of financial transactions where one expects by a contractual clause to get their money back plus "a little something" (I am not referring to the expected profit from an investment, where the "little something" is not a contractual obligation).

So you can talk about "the interest rate of a loan" but also of the "interest rate of a deposit in the bank".

The Borrowing Rate specifically refers to the Interest Rate that the entity under consideration (a business, a public sector, or an individual) has to accept to pay as this extra little something if they want to borrow funds.

So the "borrowing rate" is an "interest rate" - one among many kinds of interest rates.


What is the Relationship between expected return and risk of corporate bonds? So from my past studies i know that if the interest rate is expected to decrease, then the expected return will increase and the demand for long term bonds shifts to the right.

If investors believe that interest rates will decrease in the future, then investors will buy more bonds now. If you believe interest rates will fall, then bond prices will increase. You will buy bonds now, because you will be  buying bonds for a cheaper price (high IR) and resell bonds in the future for a higher price, when market IR decrease.

As a conclusion , if IR decrease in the future, it will make people expect higher return on long term bonds today , since there is more risk. There is a negative relationship between IRs and and expected returns.

Then why , all of a sudden , my text book says :

'If the possibility of a default increases because a corporation begins to suffer large losses, the default risk on corporate bonds will increase, and the expected return on these bonds will decrease'.

SO now all of a sudden expected return decreases when there is more default risk ? Shouldn't expected return increase when there is more default risk?

What am i missing?

If interest rates decrease, people have less alternatives to lend at higher rates. Thus people are willing to accept lower yields. Hence, bonds prices go up (and yields go down).

If the default risk increases, people want higher yields to make up for that risk. Hence, bonds prices go down (and yields go up).


Do new treasuries stop being issued during a debt suspension period? Apparently the United States has been in a "debt suspension period" for the last 175 days, or almost 6 months.

Does that mean for the last 6 months no new US Treasury Notes and Bills have been issued?

If so, doesn't that create a problem for the Wall Street desks that broker such debt (participate in debt auctions), the so-called "primary dealers"?

No, it does not mean that no new debt is issued. All it means is that the value of new debt issuances cannot exceed the value of debt that reaches maturity and is paid off.

Here's a list of recent Treasury debt auctions. You'll note that many T-bills have maturities as short as 4 weeks— a hint that the debt is actively managed.  Simplifying somewhat, when receipts do not exceed outlays by an amount greater than currently-maturing debt, new debt must be issued to generate enough cash to retire the maturing issues.


Question regarding demand schedule and equilibrium consumption Please refer to the two images posted at this link: http://imgur.com/a/si3ko

Referring to Page 2, I'm not quite sure what the author is trying to say regarding the two bracketed portions. Considering the first bracketed portion, when the author says "purchased less than Q0", is the author still referring to a point on the demand schedule line? Also referring to the first bracketed portion, how do we know the consumer "value additional consumption more than its cost to her", and thus purchase more? How do I represent all these graphically?

Yes, he is referring to a movement along the demand line. If the individual purchases less than $Q_0$, than the demand line would be higher than the price for quantities for $Q_0$, this means that the individual values consumption more than its cost (its price). Graphically, you just need to show that for a quantity less than $Q_0$, the demand line is higher than the price, i.e. the individual values consumption more than its cost.


Taking time derivative, growth equations Can anyone please help with taking the derivative of the following equation with respect to time?

$ln(\frac{\gamma_t+(n+\delta)}{sA}) = (\beta - 1)ln{k_t}+(\alpha+\beta-1)ln{N_t}$

This is not a homework question, just reading a text on economic growth and not sure how the author arrived at the final expression.

Thanks

I'll give a try, perhaps it is just this first derivative giving you trouble:

$$ \frac{d}{dt} ln \left( \frac{ \gamma_t + (n+\delta)}{sA} \right) = \frac{sA}{\gamma_t + (n+\delta)} \frac{d}{dt} \left( \frac{ \gamma_t + (n+\delta)}{sA} \right) $$

$$ = \frac{sA}{\gamma_t + (n+\delta)} \frac{\dot{\gamma}_t + 0}{sA} = \frac{\dot{\gamma}_t}{\gamma_t + (n+g)} $$

And the rest are simply the time derivative of a log equals its growth rate $ \left( \frac{d}{dt} ln X = \frac{\dot{X}}{X} \right) $:

$$ \frac{d}{dt} \bigg[ (\beta-1) ln k_t + (\alpha + \beta - 1) ln N_t \bigg] = (\beta-1) \frac{\dot{k}_t}{k_t} + (\alpha + \beta - 1) \frac{\dot{N}_t}{N_t} $$

Hence concluding the time derivative is:

$$ \frac{\dot{\gamma}_t}{\gamma_t + (n+g)} = (\beta-1) \frac{\dot{k}_t}{k_t} + (\alpha + \beta - 1) \frac{\dot{N}_t}{N_t} $$


Why is the equilibrium network size can be less than the socially optimal size in networks w/ positive externalities for single system? For Context, I am reading http://web.mit.edu/rpindyck/www/Courses/NetEx19.pdf. The chapter talks about network externalities in single system like fax machine, email, vaccinations for measles. Paraphrasing from the book "In each of these cases, the
marginal social benefit of one more person joining the “network” is greater than the marginal
private benefit. Hence, the equilibrium network size can be less than the socially optimal
size, so that the competitive market will not be efficient".

Why is equilibrium network size less than socially  optimal?

The equilibrium network is smaller than that chosen by a social planner because agents do not internalize network externalities.

Vaccination against a contagious disease is a standard such example.
Someone who is not vaccinated exposes others to potential infection and prevents others from, say, using public facilities. This is a negative externality for which he pays no cost. A social planner would therefore impose vaccination when an individual agent might choose not to.


In Smith's theory, what is the difference between the "nominal price" vs. "market price" and "real price" vs. "natural price"? In Adam's Fallacy, Foley writes:

"Smith distinguishes what he calls the nominal price of a commodity (the amount of money for which it exchanges) from the real price of the commodity, the amount of labor required to produce it." (p. 12)

Later he writes:

"The market price is just the amount of money for which the commodity changes hands at any particular moment; it rises and falls because of shortages and gluts, changes of taste and supply, and speculation. But Smith believes there are important forces that tend to push the market price back toward a certain level, which he calls the natural price of the commodity. Since there are always disruptions in any market, he does not expect the market price to converge smoothly to the natural price and then stay there, but instead believes it will fluctuate or (adopting an image from Newtonian planetary physics) “gravitate” around the natural price." (p. 13 et. seq.)

Is there a difference between the nominal price and the market price, and between the real price and the natural price? Because to me, the two pairs of terms seem to match up.

Adam Smith in his writing defines the nominal as the price of something at a given time counting prices out of market equilibrium. He refers to it as the price at what something is exchanged between two individuals not taking into account general market conditions or particular affairs at given time.

It's just the price in monetary terms at what something it's exchanged and can or cannot represent the fair trade for one or both parties at a given period.

Market price for Adam Smith is the price at what something is generally traded in the market at given time. It is different than the nominal price and sometimes it's rare when they are the same but nominal price should tend to market price if certains conditions are met in a most free and untroubled markets.
Adam Smith also writes about free market irregularities, monopoly in labor , capital or land markets.

He also makes an extended analysis and compares a market price for gold and silver and how it is different in terms of time periods or given countries due to; coin making fees, coin metal compound, weighting devices and standards, easyness of purity verification or just shortage and abundance of metal resource among others.

The real price he writes is what something costs to produce purely by it's labor value required to obtain it, via exchange or by producing it. I quote "The real price of everything is what anything costs for the person whom wants to posses it, the effort and the fatigue that his adquisition requires."

The natural price for Adam Smith is the price that justly covers the average cost rates of, land leasing, labor wages and capital gains destined to produced it and sell it on the market, and nothing more. Then he writes we could say something is exchanged by it's natural price when that price represents the minimum or cero gains for the factors required to produce it.

I make the observation that those are the 3 main factors that make posible the exchange of a product or service in terms of the classical economic view established by Adam Smith and his contemporary collegues.


A question about intertemporal price discrimination Usually intertemporal price discrimination worked like this :
Releasing something at higher price, then lower the price later.
But did this work in reverse too?
I've seen some example on video games where the publisher charge lower prices for in-game cosmetics at release and increasing the price later(Giving Discount at release).
Is this type of pricing strategy more effective than the usual intertemporal price discrimination?
edit :
To give you some context :  In-Game Cosmetics or Skins changes your characters appearance. which means they share some properties with Fashion in real life. They both can give prestige to their consumer("you're rich when you buy X skin").
which means if the publisher applying the usual price discrimination, when you buy a skin at release, you actually get more utility (You can use your skin more, and some additional prestige in the time where the price not yet lowered).
and usually skins are leaked before release, so the hype/publicity usually already there before the skin was released
The Problem is why there's some publisher that actually giving release discount on their skins? While charging higher at release can potentially raise their revenue and profit?
And BTW, Skins Has Effectively 0 Marginal cost, since what they do when a consumer purchase it, it just changing/editing some data on player account details on their server.

Airline seats are often priced lower when first released and the price can rise, especially as you get closer to flight time.
The effectiveness will depend on the market, pent-up demand, and thus substitution effects. There are not many substitutes for a given video game while for a flight there are many substitutes such as flying earlier or using another carrier. The intertemporal aspect comes in since people buying later were not able to plan ahead and so pay a premium versus people who did plan ahead or are able to fly later.
For something unique, a low price early on might be justifiable as generating publicity; however, I doubt extending that low price to all early buyers would be optimal.


Why shutdown the banks (Greece)? What benefit is there to shutting down the banks in Greece? It seems that this would do more harm than good. Won't this impede economic growth by not allowing companies and startups access to capital? This, I believe, would cause the crisis to last longer or get worse.

The deposits that people have in the banks is a lot more than the money that the banks actually have.  This is due to fractional reserve banking.

As a consequence, if everybody tries to take out their money, the banks will run out of cash: the banks themselves will be unable to meet their financial obligations, and go bankrupt.

When the bank goes bankrupt, people lose their deposits.  Normally the government guarantees the deposits, but in the case of Greece the government is running out of money as well, so it will not be able to meet this guarantee.  Usually a government can print money to meet the demand anyway, but Greece is in the Eurozone so it cannot do this (and the European Central Bank is unwilling).

That's why there are closed banks and capital controls (i.e. at most €60/day withdrawal and other limits).  It's intended to be temporary.  Right now there is a lot of unclarity what will happen.  When there is more clarity the banks will surely open again.


Adjusting a ratio variable to constant 2000 dollars using a deflator index Using Deflation index to create constant 2000 dollars, if I am finding a variable that is a ratio of that variable to GDP (say, income tax revenues), how do I go about this? Should I first divide my GDP variable for each year by the respective index value, then do the same for the income tax revenue variable, and then take the ratio of these newly adjusted variables? Or should I first find the ratio variable, income tax revenue/GDP, then divide this by the deflation index to form a constant dollar variable?

Typically if you have ratio variable then you don't need to deflate the series. This is because for example tax revenues are nominal and gdp is nominal in the ratio the respective price series would cancel out (assuming they are from the same year).

So if nominal tax revenues are RN=RP and nominal GDP is GDPN=GDPP  (where P is the price) then the ratio is RN/GDPN=R/GDP. That way if you choose the first option you suggested then you will get the exact same value as the original ratio (try it if you want).

I hope this helps.


Who is Butler in Marx' footnote in Das Kapital? In footnote [7] of Marx's Capital, T.I, Ch. 1, Sec 1, after ...contradictio in adjecto, there are these quotes: «Nothing can have an intrinsick value.» (N. Barbon, t. c., p. 6); or as Butler says - «The value of a thing is just as much as it will bring.».

Does somebody knows who is this Butler and where is that quote?

I googled "The value of a thing is just as much as it will bring." in quotes, and got several hits that show Marx referred to Samuel Butler, the author of Hudibras.

Here is one.

Here is a another, see Inscription.


What would the indifference curve of min{√x,y} looks like? The locus of kinks would follow x=y^2 but what would the arms look like?


Testing if one regressor is a proxy for another I'm reading Guiso, Sapienza and Zingales: "Trusting the Stock Market" The Journal of Finance, Vol. 63, No. 6, 2008 and have a question about how they test whether trust is a proxy for risk aversion.

I'm looking at pg. 2584 where they talk about the Poisson count model estimate where the dependent variable is the number of stocks invested in (measure for diversification). Their mathematical model implies (in section I) that both risk aversion and trust increase diversification--I think I understand that part. My problem is with the regression they run (results shown in Panel A of Table VIII).

The authors claim that because the coefficient on trust is positive and significant it tells us that trust is not a proxy for risk aversion. I understand that this result is consistent with the model, but since
(i) risk aversion should (theoretically, based on their model) also predict diversification, but
(ii) the regression doesn't give a significant coefficient on risk aversion, and
(iii) their measure of risk aversion is "noisy", i.e. has measurement error, and finally
(iv) risk aversion and trust are correlated--albeit weakly as shown in Table III Panel C,
couldn't they trust still be a proxy for risk aversion and with the coefficient estimate for trust being biased??

I might be missing something basic here...

For the benefit of readers I note that, as the authors write at the bottom of p.2557

  "We define trust as the subjective probability individuals attribute to the possibility of being cheated."

So they actually measure "lack of trust" (the higher the value of the variable, the lower the trust), in order to see whether it co-varies positively with risk aversion, and so whether it can be considered a proxy for it.

But the correlation shown between "Trust" and Absolute Risk Aversion in the table you mention is $0.017$ which is not just "weak" -it is essentially non-existent, since with a finite number of (observational) data points, correlation even between random variables that are in reality uncorrelated, will not be exactly equal to zero (even with a sample size of $n=1,444$ as theirs).

This alone suffices for the argument that "Trust" cannot be considered a proxy for Risk Aversion, since in order for this to be a valid argument, we need the correlation between the two to be high.

The fact that Risk Aversion appears "statistically insignificant" means that Risk Aversion has no explanatory power on Diversification, but this cannot be attributed to the presence of Trust, since their correlation is so small.


What is the interpration of results if adding or subtracting a control variable effects the significance of explanotary variables? I am conducting some regressions on economic growth determinants and I am disillusioned. Essentially by choosing what groups of variable to regress I can get the desired significance. What does this tell about whether the explanatory variables influence economic growth?

When you run a regression you are making the assumptions of the Gauss Markov Theorem, one of which is that the error is uncorrelated with all of the independent variables (exogeneity).

If you remove from your regression a variable that is correlated with other explanatory variables then the error term and those explanatory variables will be correlated and the Gauss-Markov Theorem will then be violated. The consequence of this is that the estimates produced by the model will be biased. This particular form of bias is known as Omitted Variable Bias.

A consequence of omitted variable bias is that spurious variables can often be made significant be deleting important variables from the model. In these instances, the fact that they become statistically significant doesn't signify that they suddenly became important, it just means that you are estimating a mis-specified model that violates your own assumptions. So we can't just blindly interpret the hypothesis tests associated with a regression model, we must pay attention to whether the model is well-specified—including the question of whether all of the relevant variables are included.

Last point: your question is "What does this tell about whether the explanatory variables influence economic growth?" The answer is nothing because a regression in itself will not tell you anything about causality, only whether your variables are correlated. To make a causal connection between variables you have to think about how to build causal identification into your empirical strategy from the beginning.


Axiom: More is Better; But when is more better? I'm taking an introductory microeconomics course and have been introduced to the 3 axioms of economic preferences. These include

Completeness
Transitivity
Non-satiation

My understanding of non-satiation is incomplete. This is because of how the lecturer has described it. I am told that non-satiation means

More is better
Indifference curves further from the origin are better

From some research on the internet I find that non-satiation is also known as the Axiom of Dominance, described as:

  If any combination A has more of one or of both the goods than B, then
  it is said A dominates B. This axiom states that if A dominates B,
  then the consumer will prefer A to B. This axiom is also known as the
  axiom of non-satiation or of monotonicity.

Given this, my understanding is that given 2 bundles $A(x,y)$ and $B(a,b)$, $A > B$ if $x > a$ and $y > b$.

My questions:

Q1) Is my understanding correct?
Q2) What if $x<a$ but $y>b$? Is the agent indifferent? He will have to be, otherwise completeness will be violated?

Thanks for your help.

You seem to be talking about (strong) monotonicity rather than non-satiation (which is closely related to but different from monotonicity).
(Strong) monotonicity says that we prefer one bundle to another if the first bundle has strictly more of at least one good and no less of any good. A bit more precisely and in a two-good setting,

Let $B_1=(x_1,y_1)$ and $B_2=(x_2,y_2)$ be two bundles. Suppose the preference $\succsim$ satisfies (strong) monotonicity. Then $(x_1,y_1)\succ(x_2,y_2)$ if either of the following is true:

$x_1>x_2$ and $y_1\geq y_2$
$x_1\geq x_2$ and $y_1>y_2$

So, to your Q2: If $x_1>x_2$ but $y_1 < y_2$, then (strong) monotonicity says nothing about which bundle is preferred. (This is not to say that the preference does not have any ordering over the two bundles, but merely that strong monotonicity alone won't tell us anything about this ordering.)


Demand function estimation The model specification is:

$$D_{ij} = A + aP_{ij} + bY_{ij} + cN_{ij} + e_{ij}$$

where:

$i, j$ = $i$-th year, $j$-th month,
$D$= demand (outgoing minutes)
$P$ = average price of call,
$Y$ = average income per capita,
$N$ = number of base stations.

During the 5-year period under examination, a tax has been levied on telecom gross revenues for two years. Is it reasonable to include instrumental variable such as amount of revenue/profit which could have direct effect on price? If not, perhaps you have any other suggestions.

Any guidelines would be very appreciated.

It appears that you suspect that the regressor "price" is endogenous, i.e. correlated with the error term, and that you consider what kind of instrument to use in order to tackle endogeneity.

You think a possible instrument could be revenues or profits, because they are correlated with the price. Say, Revenues, denoted by $R$. But

$$R_{ij} = P_{ij}\cdot D_{ij} = P_{ij}\cdot(A + aP_{ij} + bY_{ij} + cN_{ij} + e_{ij})$$

and so Revenues are a function of the error term, therefore they will certainly be correlated with it, and same goes for profits (and this should be obvious since both depend on quantity and therefore on the error term).

In order to find an admissible instrument, you must first conclude about what are the variables that may be included in the error term, and are correlate with price. This will help you to search for admissible instruments.

PS: I cannot see the connection of the tax mentioned with the issue of instrumental variables estimation.


Equilibrium in a labour market and price floors I'm (very) new to economics, taking it as an introductory subject at the moment. I had a quick question regarding labour markets and minimum wages imposed as a form of government intervention.

Is it generally true that for most countries, the free market equilibrium outcome would result in a price below the price floor (hence there is a minimum wage?)

Sorry if this is a stupid question, but I just wanted to make sure.
Thanks!

As VCG stated, no government would impose a minimum wage below what is the countervailing equilibrium wage. To do so would be pointless.

Do remember that undergraduate discussions on minimum wages using the comparative statics (lines on graphs basically) model are erroneous because labour markets do not clear.


Why is there a structural deficit/surplus? I'm going through Fiscal Policy and I'm reading about Structural Budget and Cyclical Budget. To my understanding, Cyclical Budget is what occurs when automatic fiscal policy is in use. So G and T are equal at full employment, if the economy falls into a recession, the automatic fiscal policy will trigger a cyclical deficit.

What I don't understand is the point of Structural Budget. Why is it run if the economy will return to full employment in the long run automatically? I understand that it gives an extra push but why don't we just let it handle it automatically?

In terms of rule's logic, they are the same. The logic of structural budget is to provide stability and long-term planning to government spending. This is implemented by first finding the "long-run" revenue levels. Long run here means the economy in its potential. Additionally, for countries which rely a lot on some particular industries like natural resources (e.g. Copper in Chile), an estimation of the "long-run" price of such resources is required. These estimates are usually conducted by an independent, non-partisan, expert-based body, not affiliated with the government.

Once these revenues are defined, then a rule is chosen. It could be a balanced budget (all long-run revenues are spent), which is what you are calling Cyclical Budget, or a deficit/surplus, defined as % of total revenues, which is what you seem to refer to as Structural budget deficit/surplus. Either of these methods provide stability to spending, as the committee evaluating the long-term revenues of the government does this for several years in advance.

Why to chose a structural deficit/surplus? A structural surplus can be chosen to accumulate savings over time, and have a cushion in time of a crisis. In the case of Chile, the aim was to build a cushion in case the long-run price of Copper fell sharply, and long-term government revenues shrank considerably. Others might chose a deficit in order to provide a constant stimulus to the economy. Naturally, the size of the public debt is something to have in consideration regarding which rule to choose.

You can read a bit more about this rule, for the case of Chile, here or here.


How to prove dynamic inefficiency in the Solow model? I know that if capital is below the golden rule level in the Solow model, then we are dynamically efficient, and vice versa.

How is that proven?

I give the intuitive explanation in words first, then below is the proof.

Define a Pareto improvement to be where consumption is no lower in every period and higher in at least one period. We're said to be dynamically efficient if there's no possible Pareto improvement and dynamically efficient if there's a possible Pareto improvement.

Assume we start off already in steady state.

Proposition 1. If the savings rate is below the golden-rule level (or equivalently, the steady-state capital stock is below the golden-rule level), then we're dynamically efficient.

Proof. If we switch to a lower savings rate, the new steady-state level of consumption will be lower, and so this cannot be a Pareto improvement.

Conversely, if we switch to a higher savings rate, then consumption in the initial period of the switch will be lower, so that again this cannot be a Pareto improvement.∎

Proposition 2. If the savings rate is above the golden-rule level (or equivalently, the steady-state capital stock is above the golden-rule level), then we're dynamically inefficient.

Proof. We claim that switching to the golden-rule savings rate is a Pareto improvement.

First, note that by switching, the new steady-state level of consumption will be higher.

Next, note that in the initial period (after we've switched), consumption is higher than before, because we've lowered our savings rate.

In fact, in the initial period, consumption will be higher than the new steady state. Consumption will then fall monotonically towards the new steady state level (which is higher than old steady state).

Altogether then, by switching to this lower savings rate, consumption in each period is higher than the old steady-state level (or in other words, than it would've been had we not made the switch). This is thus a Pareto improvement.∎


Why is elasticity not constant on a straight line graph? There are different zones of elasticity on a graph, but if we are to imagine a negatively sloped, straight line on a price v quantity graph, we find that elasticity differs based on where we look on the graph. Why is this the case, rather then elasticity being constant?

Theoretically, the responsiveness of quantity demanded is different at different prices. Take the equation for the elasticity of demand:
$$\epsilon_{D}=\frac{\Delta{Q}}{\Delta{P}}\frac{P}{Q}$$
The equation itself is non-constant as it depends on P and Q. Lets assume a linear demand curve with the simple form: $P(Q)=6-Q$. If we take an equal change in price, say $\Delta{P}=1$, and since the demand curve is linear in this case, we see it has a slope = $-1$ and thus the $\Delta{Q}=1$. If we have two situations where $P=5$ and $P=4$, then, to keep in accordance with our slope, lets say $Q=1$ and $Q=2$, respectively.
The two elasticities of demand for these two prices would be $\epsilon_{D}=5$ and $\epsilon_{D}=2$ for the higher and lower price respectively.

In short, the elasticity of demand is a function of the responsiveness of quantity demanded to changes in prices that depends on the current price/quantity combination.
At a higher point up the demand curve, the elasticity is higher, or demand more elastic, than at lower points.


Estimated betas and optimal portfolio I ran a regression on 20 assets to estimate their beta with different methods. I would like to see the differences of these estimation differences in terms of mean-variance optimal portfolio. How can I do that?

The problem is that I do not see clearly the role that the estimated beta plays in portfolio optimization empirically. A mean-variance optimization with N assets should be something like

$min_{\textbf{w}}$ $\textbf{w}^{'}\textbf{V}\textbf{w}$

subject to

$\textbf{w}^{'}E(R)=\bar{R}$,$\textbf{w}^{'}\textbf{I}=1$

Where w are the weights of the N assets, our choice variable. $\textbf{V}$ is the covariance matrix of the returns, $\bar{R}$ is the target return, $\textbf{I}$ is just a vector of ones and $E(R)$ is the vector of expected returns of our assets.

The "unknowns" are V and E(R), should I use historical returns to replace them? If yes, then what is the use of the betas in portfolio optimization? none? or maybe should I use the betas to get the values of E(R) and V?

I do not understand, could someone provide a mini-guide to get from betas to the optimizing portfolio?

Let me begin with noting that models such as the CAPM have been extensively falsified, beginning with Mandelbrot in 1963 and ending with the Fama-MacBeth testing in 1973.  Other falsifications followed, but really, it has been a zombie theory since the early seventies.  The difficulty is that the falsification has been like the Michaelson-Morley experiments in the 1880s.  Once they were done, classical physics was falsified, but Plank and Einstein were not around yet.

I have a paper in peer review proposing a new stochastic calculus for options pricing and portfolio construction, but there is nothing resembling a consensus on a replacement.  The math is very different.

The core of your problem can understood in two equations.  The first is $x_{t+1}=\mu{x}_t+\epsilon_{t+1}$.  The second is $r_t=\frac{p_{t+1}q_{t+1}}{p_tq_t}-1$.

For the first equation, for someone to be willing to invest, $\mu>1$.  It was proven in 1958 that this problem has no meaningful solution in Frequentist statistics.  The CAPM is a Frequentist model.  For the CAPM, this means that $\tilde{w}=R\bar{w}+\varepsilon$ only has a solution when $R$ is known, which is an assumption of the math underlying the model.  In other words, models such as the CAPM and Black-Scholes depend on it being true that people know the true values of the parameters.  If they do not, it is known that these models cannot be solved.  The argument has been that the market behaves as if it knew the parameters.  A Bayesian derivation of the CAPM results in a Cauchy likelihood not a normal one.

The second equation makes returns a function of data rather than a known parameter.  As such, it must be derived.  I have a paper deriving the distribution of returns.  The distribution is the product of the ratio of prices and the ratio of volumes if dividends are ignored.  Dividends create their own complications.

However, from auction theory, it can be determined that the dominant element of the resulting mixture distribution is the truncated Cauchy distribution.  It has no first moment, so $\beta$ cannot exist as described in the CAPM.  That is different from saying that it cannot be found.  Such a thing implies the non-existence of the population parameter as the model describes it.

I left out the logarithmic models for two reasons.  First, the CAPM has additive errors.  Second, the distribution created by taking the log of Cauchy distributed variables is the hyperbolic secant distribution. It has no covariance structure in the multivariate form, so the CAPM is defeated anyway.

A short proof that the CAPM cannot function would be to note that if $q_t=q_{t+1}$ which rules out mergers and bankruptcies and $\delta_t=0,\forall{t}$ and there are no dividends, then return is $\frac{p_{t+1}}{p_1}$.  Because stocks are sold in a double auction, there is no winner’s curse.  The rational behavior is to bid your expectation.  Using the assumption of many buyers and sellers from the CAPM, the limiting distribution of the limit book must be normal.

If you center the distribution of prices around the equilibrium prices and assume the market is approximately in equilibrium, ruling out things such as a liquidity crisis, then you end up with a bivariate normal distribution.  The equilibrium return $r^*=\frac{p_{t+1}^*}{p_t^*}$.  Errors could be thought of as excess return, plus or minus.

Noting that the slope is the same as the tangent of the angle, you quickly get very close to the Cauchy distribution by observing that $$\theta=\tan^{-1}(r).$$  The arctangent is the kernel of the cumulative density function of the Cauchy distribution.  The angle is, minimally, a transform of returns via the Cauchy distribution.

Solving for the ratio of two normal distributions by integrating around the equilibrium rather than (0,0), in other words treating the equilibrium as the location of no error, or conceptually by operating in the error space rather than the price space, give you a Cauchy distribution.  It is well known in statistics that the ratio of two normal distributions centered around zero is a Cauchy.  By treating the equilibrium as zero, it still comes out a Cauchy distribution truncated at -100%.  If there exists just one stock that didn't pay a dividend, then the CAPM is intrinsically falsified.

So the answer to your question is, there isn’t a solution.

If you want to optimize a portfolio, use the Kelly bet instead.

Visually, I took the returns for Carnival Cruises, I didn't subtract one, I just took the ratio.  I performed a kernel density estimate having removed the return from dividends to make it consistent with the above.  I then mapped the truncated Cauchy distribution from the maximum likelihood estimator.  As you can see, even if everything I wrote above is false, there cannot be a $\beta$ as described in the CAPM.

There are actually three ways to improve the fit, but I used the method most quants would use instead.


Examples of non-differentiable problems in economics As a research project, we're investigating various algorithms developed for non-differentiable, convex (or concave, if you're into economics) optimization. I'd like to find some good examples of real problem formulations that arise in different fields, especially economics.

Any example is welcome, as long as it is non-smooth in some sense, either in the objective function or the feasible set. Ideally I'd like examples of both strictly concave and not strictly concave functions. Both problems that are separably concave and problems that aren't are of interest.

Here are four I could think of:

Leontief and Lexicographic functions, used in preferences or
production functions are non-differentiable.
Labor models often employ a discrete labor supply (work or don't
work, sometimes alongside the decision of how much or how hard to
work).
Housing models often employ a non-convex adjustment cost to ensure
that there is a discontinuity in the cost function for the choice of
housing.
Kinked objective functions, where at one or more points the
left-hand and right-hand limits  differ, are also common in
economics (e.g. optimal option exercise at maturity)


Consumer preference and price in the Cobb-Douglas function I believe I’m using the most basic version of Cobb-Douglas: $U(x,y)=x^\beta * y ^{(1-\beta)}$.  The question I have is: in this example would a consumer’s preference ($\beta$) change if the price of either X or Y changes?

I.e., when presented with several options of a  good at different prices the budget line will change for each.  Given this change the indifference curve will at least shift, if the entire function doesn’t change altogether (different total Utility due to a different basket of goods).

This question is came up when solving for beta and utility using actual data where 1 good is X and the other is all goods not X (income less spend on X).

Got started solving for beta after seeing how they solved for the total derivative here.

No, preferences are stable. That is not to say that the quantity demanded or marginal utility obtained at the new price level is the same though.

If we'd allow the exponent of the utility function to vary for different price levels we'd let utility depend on prices, which it does not. Of course the actual utility that can be obtained depends on prices, but not the utility itself.

Back to your problem. You probably obtained a $\beta$ by observing one price and X quantity, with Y the remaining budget, filled that in in the formula:

$\frac{dY}{dX}=-\frac{\beta Y}{(1-\beta) X}$

and solved for $\beta$, and then did that again for a different price and found a different $\beta$. Given that you use real world data, that in itself is not surprising.

Unfortunately, the real world does not always match our models, so you would have to estimate $\beta$ using econometrics. Given that in CD models expenditures are fixed proportions of the budget you should be able to simply estimate:

$\beta=\frac{p_x X}{M} + \epsilon$

That is $\beta$ is the average proportion of the budget spent on X.


Equations of "rational mechanics" and general equilibrium Vilfredo Pareto, referring to the equations that determine equilibrium, wrote:

  These equations do not seem new to me, they are old friends. They are
  the equations of rational mechanics.

This quotation appears in the paper On the Economic Phenomenon: A Reply to Benedetto Croce he doesn't make clear what specific equations he's referring to. As someone with a physics background I am curious if anyone knows/could guess what he is referring to.

Pareto believed economics could be studied with the same mathematical rigor as physics, so it's quite possible he was speaking to the similarities between mathematical economics and classical mechanics (the latter of which was just coming into its own in the early 1900s).  I'm a physicist by training too, and those similarities helped me rapidly cover a great deal of ground my colleagues in economics had to learn fresh, so your intuition makes sense to me.


Why is the Social Security tax split midway between employer and employee? On page 99 of Hidden Order, David Friedman writes:

Social Security taxes are paid half by the employer and half by the worker. How would the effect of the tax change if it
were collected entirely from the worker or entirely from the
employer? Why do you think Social Security is set up this
way?

Earlier in the book, Friedman proved that who actually pays a tax - that is, whether the money comes out of the profits of the producers or is paid by the consumers in the form of higher prices - is not determined by who hands over the money to the government, but whose supply/demand curve is more elastic. That is to say, asking the producer to pay some tax per widget sold is equivalent to asking a consumer to pay the same tax per widget bought. If the demand for the widget is inelastic, much of the tax burden would fall on the consumer and not if the widget has a fairly elastic demand curve.
In light of this fact, it shouldn't matter which way the tax burden of Social Security is split. If the employer had to pay the entirety of the tax, she would pay a proportionately lower salary to the employee; if the tax burden fell solely on the employee, his salary would be higher.
One possible explanation of the present setup of Social Security is that voters don't understand economics. Although this answer works remarkably well as a justification for other inefficient government practices like trade barriers and rent controls, it flies in the face of the "don't attribute to incompetence what can be explained by rationality" principle that Friedman has adhered to throughout the book.
I am not from the US so I could be missing something obvious here, but given what I know I can come up with no better explanation. Any help would be appreciated.

It is actually a little bit more complex because there are special cases where there might be no tax burden shifting (see discussion in Mankiw Principles of Economics ch 12) although, generally speaking the statement of D. Friedman would be correct.
As to why government does that, besides incompetence that should not be too casually dismissed, there might be completely rational reasons.
If people do not understand economics, and if people do not understand that they are still being taxed, they might be more likely to vote to candidates that they believe are not taxing them (regardless of whether they are actually being taxed or not). This is fully consistent with those voters being rational mind you since rationality only requires people to act consistently with their beliefs and  makes no assumptions on what peoples beliefs are (see more discussion of rationality in Tadelis Game Theory: An Introduction). Consequently it might be rational for politicians to do this to maximize their votes.
For example, consider analogy with food producers. Some food producers put on their food labels reading "no chemicals". This is prima facie absurd statement as anything made from ordinary matter even plain water is by definition made from chemicals. To have food without any chemicals the food would have to be made out of plasma  or dark matter. Even interpreted generously as meaning there are no synthetic chemicals, there is no real difference between synthetically made atoms and molecules and the same atoms and molecules being produced by nature.
Yet customers who are illiterate when it comes to physics and chemistry might still prefer such products 'without added chemicals' making it rational for profit seeking companies to produce such products.


Basic New Keynesian model with flexible price I would like to know what would be the response of variables in the Basic New Keynesian model but with flexible prices (ie not with Calvo pricing). For example I have troubles to see how having flexible prices will matter for a productivity shockk or for a decrease in interest rate of the central bank.

I think what you are looking for is a standard RBC-model. Because the main step, going from RBC to New Keynesian, is to include Calvo pricing among other things. This is covered in many textbooks like Gali's, where he first introduces the RBC model and then moves on to the New Keynesian setup.


Marginal cost given (Cobb-Douglas) production My function is $y=x_1^\alpha x_2^\beta$ with $\beta={1-\alpha}$.
I found: the minimization problem for demand to be
$x_1^{*}(w_1,w_2,y)=\left ( \frac{w_2}{w_1}\frac{\alpha}{\beta} \right )^{\frac{\beta}{\alpha +\beta}}y^\frac{1}{{\alpha +\beta}} \; \wedge \; x_2^{*}(w_1,w_2,y)=\left ( \frac{w_1}{w_2}\frac{\beta}{\alpha} \right )^{\frac{\alpha}{\alpha +\beta}}y^\frac{1}{{\alpha +\beta}}$
and the cost function to be
$C=w_1^{\frac{\alpha}{\alpha+\beta}}w_2^{\frac{\beta}{\alpha+\beta}}y^{\frac{1}{\alpha+\beta}}\left ( \left ( \frac{\alpha}{\beta} \right )^\frac{\beta}{\alpha+\beta}+ \left ( \frac{\alpha}{\beta} \right )^\frac{-\alpha}{\alpha+\beta} \right )$.
Now, how would I find Marginal cost (MC)? Why does it not depend on $y$ and only $w_1,w_2$?

The Cobb Douglas production function with constants returns to scale
$$y = \prod_i x_i^{\alpha_i} = A \prod_i \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i} ,$$
where $A:= \prod_i \alpha_i^{\alpha_i}$ annoying constant.
Cost minimization with perfect competition
$$\min_x \ \ p^\top x\  \lvert \ y = \prod \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i},$$
implies FOC
$$p_j - \lambda \left[A\prod_i \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i}\right] \left(\frac{x_j}{\alpha_j}\right)^{-1}=0 \Leftrightarrow
\frac{\lambda y}{p_j} =\frac{x_j}{\alpha_j},$$
insert in production function to get
$$y = A\prod_i \left( \frac{\lambda y}{p_i}\right)^{\alpha_i} \Leftrightarrow \lambda = \frac{\bar p}{A},$$
where $\bar p := \prod_i p_i^{\alpha_i}$ which is a price index for production factors. Reinsert in FOC to get
$$p_j - \frac{\bar p}{A}\left[A\prod_i \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i}\right] \left(\frac{x_j}{\alpha_j}\right)^{-1}=p_j - \frac{\bar p}{A}y \left(\frac{x_j}{\alpha_j}\right)^{-1}=0,$$
from which you find
$$(1) \ \ \ p_j x_j = \frac{\alpha_j \bar p}{A} \cdot y,$$
using this formula several implications follow. First take sum over $j$ and use $\sum_j \alpha_j = 1$ to get cost function
$$(2) \ \ C(p,y)= \frac{\bar p}{A} y.$$
Set $y=1$ to get unit cost, diffrentiate with $y$ to get marginal cost, divide with y to get average cost and it follows that
$$(3) \ \ C(p,1) = \frac{\partial C(p,y)}{\partial y} = \frac{C(p,y)}{y} = \frac{\bar p}{A}.$$
Finally from (1) divide with $x_j$ to get
$$(4) \ \ x_j^\star(p,y) = \frac{\alpha_j C(p,y)}{p_j} = \frac{\alpha_j}{p_j} \frac{\bar p}{A} y,$$
stating that the share $\alpha_j$ of the costs are used on production factor $x_j$ and under perfect competition there is zero profit so revenue equals costs, hence $\alpha_j$ of the revenue must be used (price of $y$ must be unit cost, marginal cost, average cost = $C(p,1)$).
With only two production factors the cost function can be written as
$$C(p,y) = C(p_1,p_2,y) = \frac{\bar p}{A} y = \frac{p_1^{\alpha} p_2^{1-\alpha}}{\alpha^\alpha (1-\alpha)^{(1-\alpha)}} y,$$
hence marginal cost are easily seen to be
$$\frac{\partial C(p,y)}{\partial y} = \frac{p_1^{\alpha} p_2^{1-\alpha}}{\alpha^\alpha (1-\alpha)^{(1-\alpha)}}.$$


Usage of natural gas in 1970 (where was the demand elasticity?) The following historical graph of US Marketable Natural Gas volume has me puzzled:

How was the gas used in 1970 (a peak production period), given that we would seem to be using a lot more gas now? Normally, I think of natural gas as having relatively inelastic demand because it relies on fixed distribution networks which are time-consuming and expensive to build.

In 2010, the graph shows less gas being produced than in 1970, but considering the huge increase in the retail use of natural gas for heating in recent decades, how can this be? Apparently there was some huge, elastic demand in 1970, which I presume was some industrial process. What would that have been? Before you say "power generation" look at this graph:

So, we are using a LOT more natural gas now compared to 1970 both in homes and for power generation. So, what is this huge extra use of natural gas in 1970? Where was it going?

tl;dr: it's basic engineering: efficiencies improved between 1970 and 2010. Additionally, net USA imports increased from 0.75 trillion cubic feet in 1970 to 3.8 trillion cubic feet in 2007

I think there may be some misunderstandings. Firstly: the first chart shows domestic gas production. "Domestic" doesn't refer to residential-only use - it just means natural gas produced within country, rather than imported by pipeline or on ship. Secondly: the second graph does not show the amount of gas uesd to generate electricity. It shows the amount of electricity generated by gas. There's a huge difference. The latter is the former multiplied by the volume-weighted efficiency of the generation fleet. And thirdly, you discuss the lack of responsiveness because of the need for gas infrastructure, but the period under consideration is 40 years, which is the long run: that's sufficient time for replacement of capital; pretty much all costs are variable over 40 years in gas.

Just because there may have been an increase in demand for gas-fuelled energy services, does not mean there has been a big increase in demand for gas, for example, when part of the increase in demand is stimulated by improvements in energy efficiency.

The USA has two sources of natural gas: domestic production, and imports. One of the ways you get a disconnect between local production and local consumption is a change in net imports, which is what happened:  net USA imports increased from 0.75 trillion cubic feet in 1970 to a peak of 3.8 trillion cubic feet in 2007.

Natural gas gets used directly for heating, including in industrial processes; it also gets used for electricity generation. The latter also had a local peak around 1970. The amount of electricity generated by gas turbines very closely tracks domestic gas production until about 1990.

What's happened over the last 40 years is that energy efficiency has improved. There has been fuel-switching, so that some processes that were done using gas now use coal or electricity; and some processes that did use coal now use gas. There have been net efficiency gains over time, just as you'd expect. Some of this was outside the residential sector, and some is within it.

Some energy efficiency improvements have come about through improvements in boiler technology such as the mainstream appearance of condensing gas boilers; as well as a better understanding of maintenance. And improvements in building heat tightness, from enforced tighter building controls, better materials, better construction techniques. In the UK, we've also seen the replacement of open gas fires with central heating systems, which tends to be more efficient too, and that may have played a role in the USA over the last 40 years.

And particularly, from 1990, the upward trend in electricity generated from gas (the second graph) is stronger than the domestic increase in gas production. Around 1990, there was the introduction of a new type of process, the combined cycle gas turbine (CCGT), which increased the gas-to-electricity efficiencies from around 30% to around 55% - i.e. almost doubling. By 2007, CCGTs had displaced pretty much all the old open-cycle turbines, resulting in almost twice the electricity generated from the same amount of gas.


Erik Reinert's conclusions and experiments in economics I have just read Erik Reinert's, "How Rich Countries Got Rich… and Why Poor Countries Stay Poor". Can anybody advise me some further reading on this topic? I wonder, in particular,

if there were investigations on the influence of the international specialization of labour on the migration processes?
if there were experiments in this field?

Thank you.

It's been too long since I read those, so I don't exactly remember  whether they answer your two specific questions, but if you are interested in the topic you should definitely have a look at:

https://en.wikipedia.org/wiki/The_Bottom_Billion
https://en.wikipedia.org/wiki/The_New_Bottom_Billion

and the corresponding TED talk at

http://www.ted.com/talks/paul_collier_shares_4_ways_to_help_the_bottom_billion?language=en


Checking incentive compatibility of a mechanism I was thrilled at seeing an interesting bidding system in an academic institutions. This bidding is for registration of courses.
Each student is allocated some points based on her grade point(GPA). So, a student with higher GPA gets more points.
Each course has a maximum strength of 60 students and a set of say 15 courses is offered.
A student bids higher for the courses that she wants and feels will be oversubscribed.

According to the literature in this subject, I know that this is not an incentive compatible mechanism as the students' bids are considered equivalent to their preferences but a student may bid more for a subject with less utility but which is has higher number of subscribers.
Also, I feel that this is a kind of first price auction. Whatever bid I propose, it is consumed if I cross the minimum bid at which the subscription closes.

Courses are different and students have different preferences. Each student would bid for any number of courses that she prefers and expects to go oversubscribed. Students' preferences over courses are on academic basis i.e. courses that are popular or taken by some famous faculty. So, student's objective is to get her favorite course.

EDIT : In first round, the students give a list of 5 courses they wish to enroll in.
In second round, bidding happens for the oversubscribed courses. So, if I entered course A in round 1 and it got oversubscribed, then in round 2 I will have to bid for it.
After round 2, if I get the courses that I wanted then it's fine else I will have to choose some other course (for which seats are not completely filled) so that I have 5 courses.

I am not being able to understand in intuitive terms how a student can behave wrong and hide her true preferences while bidding in such a mechanism.
Please help point out some intuitive examples which violate the incentive compatibility. Thanks in advance.

An example:
Student type $t_1$ has 10 points to bid based on her GPA. Her favourite courses are A,B,C,D,E.
Student type $t_2$ has 0 points to bid based on his GPA. His favourite courses are F,G,H,I,J.
Student type $t_3$ has 1 point to bid based on her GPA. She ranks the courses alphabetically, A being best, Z being worst. (Or if there are only fifteen courses then O, as that is the 15th letter.)

Assume sixty $t_1$ type, sixty $t_2$ type and one $t_3$ type students. If all types were to subscribe to their favourite kind of courses, then A,B,C,D,E would have sixtyone applicants and hence they would be oversubsribed. F,G,H,I,J would have sixty applicants and would be full. $t_3$ may lose the bidding war in a reasonable equilibrium of round 2: If all type $t_1$ students bid 2 points on each course they will all get their favourite picks while $t_3$ type, who can only bid 1 point will lose out on all picks. Now she can only pick K,L,M,N,O, as F,G,H,I,J are already full. She would have been better off if she had picked F,G,H,I,J in round one, as there she would have one the bidding for at least one of the courses. Thus the 'truth-telling' strategy is not an equilibrium and hence the mechanism is not incentive compatible.


Low oil price and impact Today I read  an artcicle about the falling oil price (maybe it'll go under 30$ per barel the next days). Why is this a bad news? Lower oil price can give an advantage for a higher productivity.

It is not necessarily bad news.

Simply put, if you're willing to buy product x (bread, car, house, ect.) then falling prices are good news for buyers, but bad news for the sellers. The same logic applies for oil. If you are a buyer, you are optimistic about falling prices, however being a seller would make you loose money and/or postpone new investments.


The term "Most Favoured Nation" is misleading to me. Please explain My understanding

If Country A extends MFN status to Country B with reduced tariffs for a product, then it must treat all other nations in the same way. By this WTO encourages multilateral concessions rather than trade-distorting bilateral concessions.

Question

What is the point of granting Country B, the MFN status if it's going to be the same for all countries? Also, the term 'Most Favoured Nation' is completely misleading here. Country A could have announced that it's going to reduce tariffs for that specific product to all WTO members rather than bringing Country B into the whole picture.

Please explain what's the point of a country granting another MFN status, and why does it apply to all WTO members if only two countries are involved here.

You seem to have it the wrong way around.

The act of country A extending Most Favoured Nation status to country B only affects the import tariffs on country B's products, not those on other countries' products. MFN status means that the tariffs on the Most Favoured Nation's products cannot be higher than the lowest import tariff on similar products from other countries to country A. (Hence the name 'most favoured', as it will have the lowest tariff.) Similar products from other countries without MFN status from country A may have higher tariffs than those imposed on country B's products.

There are some caveats. E.g. if country A is in a free trade zone with countries X and Y and charges no tariffs at all on their products then even if country A grants country B Most Favoured Nation status, it does not mean it cannot impose any tariffs against country B's products. Basically country B has to get the lowest tariff, but free trade zones are not regarded as having 0 tariffs, rather as being exempt from tariffs.


How do you find marginal revenue if you don't have a production function? I was given a word problem. No formulas. So I set up the following equations:

Demand Function
\begin{equation}
D(p) = a - p
\end{equation}
Cost Function:
\begin{equation}
c(q) = 9 + 10q
\end{equation}
Marginal Cost
\begin{equation}
MC = 10
\end{equation}

I am supposed to find how much the man in the problem would produce for any value of $a$. But, without a production function, I am unsure how to determine how much he will produce.

Specifically, suppose I write

\begin{equation}
R = pD(p)
\end{equation}

I can't then differentiate R by q to find marginal revenue.

So how do I know how much he would produce?

Here are some hints. Either solve the profit function in terms of $p$, substituting out all references to $q$ (recall that $D(p) = q$), or solve the profit function in terms of $q$, substituting out all references to $p$. Then you'll find that the profit function is concave and the differentiated with respect to $p$ in the first case or $q$ in the second case will give you the profit maximizing solution.

EDIT: Yeah, $a = 2q + 10$ looks correct. Just solve the equation for $q$ and the interpretation is clear. That is, the quantity produced is $q = (a - 10)/2$. If you want to know the price, then just substitute $q$ in for $D(p)$ like so: $a - p = D(p) = q = (a - 10)/2$.


Optimal Price and Quantity of Externality I am trying to solve the following question:
Let $h \geq 0$ represent a negative externality of a firm's production on one (representative) consumer. The consumer has a quasi-linear utility function and attaches a utility of $\phi(h) = -2h^2$ to the externality. The firm's profit function is $\pi(h)=120-2(h-10)^2 $. Suppose the consumer has the property right concerning $h$ and can sell the right to produce a quantity $h$ at some price $P$. The consumer's utility function from some combination $(h,P)$ is $u(h,P)= \phi(h) + P$. The firm's profit function is $\Pi(h,P)=\pi(h)-P$.

Suppose the firm can make the consumer a take-it-or-leave-it offer for an externality level $h$ at price $P$. If the consumer rejects the firm's offer the firm does not produce so the consumer's utility is 0. Compute the firm's optimal offer $(h_p^f,P^f)$ to the consumer.
Suppose the consumer can make the firm a take-it-or-leave-it offer for an externality level $h$ at price $P$. If the firm rejects the offer it cannot produce so the firm's profit is 0. Compute the consumer's optimal offer $(h_p^c,P^c)$ to the firm.

Edit: Approach using the hint from Herr K.

The consumer can reject the offer giving him a guaranteed utility of 0. Maximize the firm's profit subject to this constraint, $u(h,P)= \phi(h) + P = 0$. Solve this using Lagrangian method.
$$ Lagrangian = objective function + constraint  $$
$$\mathcal{L}(h,P,\lambda) = \Pi(h,P) + \lambda(\phi(h)+P)$$
$$\mathcal{L}(h,P,\lambda) = \pi(h) - P + \lambda(-2h^2+P)$$
$$\mathcal{L}(h,P,\lambda) = 120-2(h-10)^2 - P + \lambda(-2h^2+P)$$
$$\frac{\partial\mathcal{L}}{\partial h} = -4(h-10)-4h\lambda = 0 \rightarrow \lambda = \frac{-4h+40}{4h}$$
$$\frac{\partial\mathcal{L}}{\partial P} = -1 + \lambda = 0 \rightarrow \lambda = 1$$
$$\frac{\partial\mathcal{L}}{\partial \lambda} = -2h^2+P = 0$$

When we set both $\lambda$ equal to each other we get $1=\frac{-4h+40}{4h} \rightarrow h=5$. Plugging this into $\frac{\partial\mathcal{L}}{\partial \lambda}$ we get $-2(5)^2+P=0 \rightarrow 50=P$
Thus $h_p^f = 5$ and $P^f= 50$

We do the same thing but this time the objective function is the consumer's utility function $u(h,P)= \phi(h) + P$ and the constraint is the firm's profit function $\Pi(h,P)=\pi(h)-P$ = 0.

$$ Lagrangian = objective function + constraint  $$
$$\mathcal{L}(h,P,\lambda) = \phi(h)+P + \lambda(\Pi(h,P))$$
$$\mathcal{L}(h,P,\lambda) = -2h^2+P + \lambda(\pi(h) - P)$$
$$\mathcal{L}(h,P,\lambda) = -2h^2+P + \lambda(120-2(h-10)^2 - P)$$
$$\frac{\partial\mathcal{L}}{\partial h} = -4h -4\lambda(h-10) = 0 \rightarrow \lambda = -\frac{h}{h-10}$$
$$\frac{\partial\mathcal{L}}{\partial P} = 1 -\lambda = 0 \rightarrow \lambda = 1$$
$$\frac{\partial\mathcal{L}}{\partial \lambda} = 120-2(h-10)^2 - P = 0$$
When we set both $\lambda$ equal to each other we get $1=\frac{h}{h-10} \rightarrow 2h=5$. Plugging this into $\frac{\partial\mathcal{L}}{\partial \lambda}$ we get $120-2((5)-10)^2 - P=0 \rightarrow 70=P$
Thus $h_p^c = 5$ and $P^c= 70$

Your steps look correct. There is one small typo in the first $\frac{\partial \mathcal L}{\partial h}$: the term $-4h(h-10)$ should have been $-4(h-10)$.
The results also look reasonable: Regardless of who makes the offer, the Pareto optimal level of $h$ is produced. Given how the bargaining procedures are structured, whoever gets to make the offer gets to keep the surplus of $20$.

P.S. There is an issue in part 2 of the question. It says: "If the firm rejects the offer it cannot produce so the firm's profit is 0." This statement is a contradiction. If the firm cannot produce ($h=0$), then profit would be $-80<0$; if its profit is $0$, then it must produce some positive amount of $h$. But this lack of rigor is on whoever wrote the question, not you.


How to auction shared item with a roommate? My roommate and I split the cost of a game console a year ago (~$400) but he is now moving out.

We were wondering how to fairly auction the console given the situation:

We both paid an equal price of $200+
Right now half the market price of the console is \$175
We both would prefer having the console than being paid for it
He will be splitting the price with his new roommate whereas I will be paying by myself

With regular bidding, as my roommate representing both him and his next roommate and me myself, is he at an advantage because he has double the market power? If yes, how can we fix that problem?

Outcome:

Thank you for your answers. While the chosen answer seemed the best way to do this, we both felt it involved too much strategy and would have resulted in envy from one of us. We instead went with the Divide and Choose method, which worked out fairly for both of us.

If you think that the distribution of your value and your roommate's value are the same then I would suggest that you consider the following bidding protocol:

each bidder submits a sealed bid, $b_i$.
the highest bidder, $i$, received the console and makes a payment of $\frac{b_i+b_j}{2}$ to the loser, where $b_j$ is the loser's bid.

Cramton, Gibbons, and Klemperer (Econometrica, 1987; Section 4) show that this is an efficient way to dissolve a partnership with joint ownership stakes in an asset.

If you think that the two of you have differing value distributions (e.g. because your roommate has a new friend) then Cramton et al. show in Theorem 2 how to adjust the pricing rule to restore efficiency.

I highly recommend taking a look at the Cramton et al. paper. It's surprisingly readable for an Econometrica.

Let us know how you get on if you decide to try it out!


How to value market size? Where can I learn about market value of specific sector? What keywords should I be looking to being understand which reserch facilities publish relevant reports?

I'll put it simple: I'm building a startup, and I need to answer how much my market is worth. Where do I being this research? I believe this is a question every aspiring entrepreneur has to deal with, and I'm sure answers by knowledgeable people on this forum will become invaluable resource to the general community.

In my specific case, I'm looking at the b2d market where companies such as Twilio, Stripe, Github, Zencoder and StatHat operate.

You might want to check out Fermi estimation. XKCD did a very accessible example of Fermi estimation being used to estimate paint production. This method can be quite good at providing estimates within an order of magnitude of the correct answer.


Understanding Gorman Polar Form I've been reviewing my microeconomics notes and have found a point that I still don't quite understand. this being Gorman Polar Form

Gorman form of the indirect utility function is  as defined by Varian is:

$$v(p,m)=a_i(p)+b(p)m$$

where $a_i(p)$ differs from each consumer and $b(p)m$ is the same for every consumer.

How does one estimate $b(p)m$?

After doing some reading on the topic, it appears we would estimate this equation as we would with any other demand estimation.

the reason why the term $b(p)m$ is written this way is due to the assumption of homothetic preferences (or homogeneous of degree 1, this dosen't matter in demand analysis). Since Gorman polar form is a homothetic form this implies that:

$$v(p,m)=a_i(p)+b(p)m \equiv a_i(p)+b(p,m)$$

more specifically $$b(p,m) \Rightarrow b(p)m$$

if preferences are homothetic or homogeneous of degree 1.


What is the average percent of value an employee makes which he gets on salary (called)? I'm looking for any statistics showing the average percent of money employees get from the monetary value they create, primarily from the US or EU. Is there a term for this ratio?

You are most likely looking for labor or wage share defined as the ratio of labor costs to nominal GDP. It basically expresses how much share of nominal GDP gets captured by labor.

You can find the data for the labor share in the US here, under that bit of text (for some reason I could not find direct link to pure dataset). The data are from the US bureau of labor statistics.


Terms definition in Balance of Payment I have problems in distinguishing among terms in the Balance of Payment / the international balance sheet of a nation.

As far as I know, on Assets and Liabilities sides of BPM, there are Portfolio Equity, Portfolio Debt, FDI, Other Debts.

What is the difference between Portfolio Equity and Portfolio Debt? Is it true that Portfolio Equity is about stocks/shares, whereas Portfolio Debt is about Bonds?

Many thanks for your help.

Your statement "Portfolio Equity is about stocks/shares, whereas Portfolio Debt is about bonds" is essentially correct, with the associated income being dividends and coupons respectively

Direct investment (FDI) has the associated income of profits, while other debts may have the associated income of interest (if any)

Chapter 6 and other chapters of the IMF Balance of Payments Manual discuss these issues


Marshallian demand with Leontif preferences Consider a utility function on the form $u(q_{1},q_{2},q_{3}) = min\{\alpha ln(q_{1}) + (1 - \alpha) ln(q_{2}), ln(q_{3})\}$

I know that optimal behaviour requires $\alpha ln (q_{1}) + (1 - \alpha) ln(q_{2}) = ln(q_{3})$

I tried substituting this into the budget constraint (after raising both sides to the power of $e$)

$p_{1}q_{1} + p_{2}q_{2} = y$

But I am unsure how to proceed in finding the Marshallian demand, since I have two variables $(q_{1}, q_{2})$ and only one equation. I have tried different transformations but my main problem is that it feels like I'm missing an equation.

Any help is greatly appreciated.

EDIT: I just re-read the question and I misspecified the budget constraint! The consumer only spends on $q_{1}$ and $q_{2}$.

So, I have not really worked out the maths behind solving this. I prefer to take a shortcut and just compute it numerically. Here is what I have.

These are the contour surfaces and the budget constraint. Notice how the solution will be at the "kinked" curve in the middle of each surface.

The levels 1 and 2 are only for example. The third level, u = 3.92762 is related to the next part of my answer. Also, BC is the budget curve with income = 300. I have chosen $\alpha = 0.5$ and $P_1 = 2, P_2=3, P_3=1$.

Now, using the parameters mentioned in the last paragraph, the maximum is found to be at $q_1 = 65.8896, q_2 = 39.1448, q_3 = 50.7863$ and the maximized utility is $u = 3.92762$. I assumed that all goods are strictly consumed at positive amounts.

I am attaching my Mathematica code below, so that you can replicate and modify these results as you want

  u = Min[a*Log[q1] + ((1 - a)*Log[q2]), Log[q3]]

  BC = p1*q1 + p2*q2 + p3*q3
    a = 0.5; p1 = 2; p2 = 3; p3 = 1;

  ContourPlot3D[{u == 1, u == 2, u == 3.92762, BC == 300}, {q1, 0,
  100}, {q2, 0, 100} , {q3, 0, 100}, AxesLabel -> Automatic,
  ContourStyle -> {Opacity[0.5], Opacity[0.5], Opacity[0.5],     Opacity
  [1]}, Mesh -> None, PlotLegends -> "Expressions"]

  NMaximize[{u, BC <= 300, q1 > 0, q2 > 0, q3 > 0}, {q1, q2, q3}, Reals]


When the Fed increases the money supply, does any of the additional supply go directly to the government? When a central bank increases the money supply, how much of it goes directly into the government purse? Say for example:

The money supply is $150
The populace has $100
The government has $50.

If the Fed decided to increase the money supply to \$200, does any of the extra $50 go into directly into the government purse? Does it vary?

The answer to this question is maybe (but most likely not).

The most common method central banks use to increase money supply (assuming they control their own monetary policy) is through open market operations. Open market operations is when the central bank purchases or sells treasuries in the secondary market (typically). The answer to your question depends on where the central bank buys the treasuries.

If the central bank uses an open market purchase of treasuries in the secondary market, then the money goes to the entities which sold them the treasuries, so none of the money would go directly to the government. However, hypothetically in some countries where corruption is prominent, there may be a situation where the government forces the central bank to purchase treasuries in the primary market (directly from the government). In this situation, all of the money that is being pumped into the economy would go directly to the government.


In what country outside of the EU is the public sector the highest percentage of GDP? The article Railway strikes test Macron’s reforms - French strikes states that "Mr Macron’s reform of SNCF is only part of a bigger effort to reshape the welfare state in a country where the public sector consumes 56% of GDP, the highest in the EU."

What country outside of the EU has the highest percentage of GDP in the public sector?

The answer seems to be Kiribati, with a whooping 92%.

https://en.wikipedia.org/wiki/Government_spending#As_a_Percentage_of_GDP


Deficit: can be seen as a return? Suppose I have a series of debt as % of GDP.

By computing returns on this serie e.g.

debt as % of GDP in year 1 is 50% in year 2 is 60%

I compute $(60\%-50\%)/50\%$ can I interpret this measure as a sort of deficit for year 1-2? Hence, deficit for this period is 20%. Or shall it rather be the difference $10\%$?


Sunk cost fallacy- is it a bug or a feature? 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!

Very interesting question.
To answer the direct question in the title, I'd say I'd have to break the sunk cost fallacy into two arenas. In the first I'd say it is a feature not a bug, but in the second, vice versa.

As a means to keep a business from dying before it's been given opportunity to profit.

I think that the sunk cost fallacy is still a double edged sword, I think that it may serve to keep businesses alive longer than they should, but I also believe that it at times keeps businesses alive long enough to see a return. Most small business owners I know, successful or not, have fallen victim to the underlying logic- for good or bad. In that way I do not consider it bad or good, I just see it as a feature of the economy, especially local economies.

As a flaw in the human psyche taken advantage of by MLM schemes, Casinos, numbers games and similar enterprises.

I believe that in these cases, it becomes a bug, not a feature. A terrible flaw that extracts great amounts of wealth from those of us who are vulnerable, intoxicated (not necessarily by narcotics, but by grand promises to we who are not in a secure position), and caught off guard. That's not to take responsibility away from our choices. I just think that most people, after being had as a result of falling into the trap of this logic, feel angry at themselves not in the way that Bismark might have felt after making a strategic error (which is what I have seen from business owners), but closer to the way that Heracles felt after murdering his own children. I stayed at the Cosmopolitan in Vegas recently, and noted that my room was one of the few with balconies that I could see anywhere on the strip. W Therefew balcony rooms in Vegas for a reason. Just my raw thoughts on the subject and are mostly anecdotal, this is the first time I've considered the sunken cost fallacy in this light.


Utility function of habit formation model In the habit formation RBC model, the utility can be given as follows:

$U(c_{t},n_{t}) = \ln(c_{t}) - \frac{\theta}{1+\upsilon} \bigg(\frac{n_{t}}{n_{t-1}^{\phi}}\bigg)^{1+\upsilon}$

When I do FOC wrt $n_t$, I'm confused about how to treat the variable $n_{t-1}$. Is it exogenous or should I try to find $\frac{\partial n_{t-1}}{\partial n_t}$?

Many thanks.

I believe $n_{t-1}$ is a quantity from the past, so you should be able to treat it as an exogenous variable


Tendency of the rate of profit to fall https://en.wikipedia.org/wiki/Tendency_of_the_rate_of_profit_to_fall

The tendency of the rate of profit to fall (TRPF) is a hypothesis in economics and political economy, most famously expounded by Karl Marx in chapter 13 of Capital, Volume III.[1] Economists as diverse as Adam Smith,[2] John Stuart Mill,[3] David Ricardo[4] and Stanley Jevons[5] referred explicitly to the TRPF as an empirical phenomenon that demanded further theoretical explanation, yet they each differed as to the reasons why the TRPF should necessarily occur.[6]

Now, I have some years trained as an economist; but, find the whole fuss around the TRPF somewhat strange. Marx lived in a time of a non-fiat economy. The inherent value of one kopiejek or what have you was based on how much bread it could exchange. Nowadays money is defined to be a unit of account maintained by trust in the FED. Hence, inflation targeting.

So, did Marx really miss the memo about credit? Can someone help me better understand where am I getting this concept wrong as so many think this is the cornerstone of Marxian economics.

I'm not sure what the "fuss" is.  Is TRPF really so heavily disputed?  In a sense, profits are just a kind of arbitrage, and so the reasoning behind TRPF is similar to the reasoning around zero-arbitrage assumptions (profit-maxing agents under perfect competition with free entry/exit and full information will drive supply up and prices down until the profit gap closes).

Obviously, these assumptions make for boring problems; the real world is far from boring, so profits happen and can be sustained for a really long time in some cases.  I think the diversity of viewpoints you're seeing are more explanations for the varying degrees of failure of TRPF in real markets, than they are explanations of empirical evidence of TRPF.


Why is the opportunity cost 0 in this case? My book says that the opportunity cost of purchase of a specialized equipment that has no alternative use is zero and hence such an expenditure is a sunk cost. However, while calculating the user cost of capital, it takes into account how much interest one could have got had one not purchased the capital and invested the money somewhere else. So, why the same treatment has not been applied on the specialized equipment. Rather than buying it for $ \$20000$ (say), I could have invested the money somewhere else and earned a return of $ \$2000$ (say). So, shouldn't my opportunity cost amount to $\$22000$ rather than 0

I think the point that the author was trying to make was that opportunity cost refers to the "best alternative use" of something. The measure is used to understand marginal decision making. Suppose you have just purchased an Oven which can either bake cakes or bake bread. Now if you decide to bake cakes, your opportunity cost is the number of loaves of bread that you could have baked at the same time. However, all this analysis is done keeping in mind that - "once the oven is purchased".

The machine in your example has no alternative use and hence has zero opportunity cost. Your analysis about the interest is regarding the money using which the machine was purchased. Sure that money could have been put to some other use - like buying a Netflix suscription or putting into bank deposit and hence will have an opportunity cost. Bust as far as the machine is concerned " once it is purchased", on the margins, it has no alternative use hence no opporunity cost.


How does an increase in USD money supply affect inflation? Say an average american household is bringing in $50,000 a year.
Between ongoing quantitative easing and the drastic stimulus packages passed in February-May 2020, the USD Money Supply increased by 25% or 16% depending on if you look at M1 or M2, respectively. (I assume M2 is more directly related to inflation, but would love if anyone can provide clarity there)
Assuming 0 change in real output (not likely, but for simplicity) would the last 3 months actions to increase the money supply equate to a direct equivalent loss of value per USD?
Would this average American family's \$50,000/yr income in February become equivalent to a \$42,000/yr salary(in Feb \$'s) by May?
Or are there other factors in play? (outside increasing real output)
Adding this question and its answers as they're relevant here.

Yes there are other factors at play. Inflation is change in a price level. The price level, according to classic textbook monetary equation, is determined as follows:
$$P = \frac{MV}{Y}$$
Where $M$ is the money supply, $V$ velocity of money (how much is one dollar used in the economy) and $Y$ is the real output.
So beside money supply and real output inflation depends also on velocity of money. Furthermore, the inflation also depends on peoples expectations of these quantities. That is on what people expect the money supply, real output and velocity will be (although this is not shown in the simplified textbook model above).

Would this average American family's \$50,000/yr income in February equivalent to a \$42,000/yr salary in May?

Not likely. According to the International Monetary Fund the the annual inflation forecast for USA for 2020 and 2021 is $0.6\%$ and $2.2\%$ respectively. These are mean forecasts so of course the actual realized values will not be exactly the same, but I would be surprised if even $99\%$ confidence interval would even include double digit inflation. The assumption that output does not change is currently also not realistic. USA lost $6\%$ of GDP just in 2020Q1 according to the Bureau of Economic Analysis and the fall for Q2 is projected to be even worse.


Demand curve deriviation My fundamental concern is whether in real life when applying to microeconomic theory, we derive the demand curve using utility and indifference curves approach, or we simply may get data on quantity demanded of the consumer for different prices and using linear regression derive the demand curve?

If I understand your question properly, it is correct that we do more ordinary statistical analyses such as linear regression to determine relationships between economic variables (e.g. price and demand.)  Utility is a tool which gives us a model of consumer behaviour based on very loose assumptions about how consumers behave (convexity of preferences, monotonicity, etc.)  While the demand curve can be derived from utility if we somehow knew the full preferences of all consumers, it can also be approximated from data by observing the real-world relationship between price and demand.  It is very difficult/impossible to measure utility in the real world, so using regular statistical techniques like linear regression to estimate the relationship is the logical thing to do.

Of course, the real-world demand curve may not be linear, so a simple linear regression on observed data in the form $p = \beta_0 + \beta_1 q$ may not accurately the demand curve.  Here, theory may help you decide on what nonlinear terms you should include in your model, but you would still need to do the regression analysis on real-world data to actually find the parameters.


Why is it relevant for a company to use dividends to incentivize shareholders to maintain ownership of the company's stocks? I was reading the definition of "Bottom Line" on Investopedia  and one of the reasons companies increase their bottom-line is to issue payments (dividends) to stockholders as an incentive to maintain ownership
However, I'm a bit confused about why maintaining ownership is a reason for companies paying dividends to shareholders.  Particularly because if a stockholder did decide to sell his shares (for whatever reason which could be that there were no dividends/not enough dividends), since its a secondary market, it would just go to another buyer who really wanted those shares. I understand at the start in the primary market a company would want to incentivize buyers to buy their shares, but once we get into the secondary market it's not like the stocks are going to disappear, so it doesn't matter who it goes to as long as someone is holding it. Essentially, a share cannot be sold without a buyer, so regardless of whether ownership is maintained there will always be a new owner to pay for and hold that share.
I know there are other reasons why a dividend's existence is important, but specifically, Investopedia's reasoning on maintaining ownership doesn't make much sense to me/seems irrelevant.
I know I'm wrong, so hopefully, I can figure out soon why... Thank you so much for all your time!

As I say in the comments, I would speculate share prices must be maintained because shareholders are collectively the owners of the company, and they want to maximise rent extraction from the operation, including maintaining or improving the resale price of the shares.
If the existing management do not cooperate to that end, they can be fired and replaced by those who will, or the entire business may be sold for scrap and the capital proceeds invested elsewhere.
I agree though that the linked article is not at all clear about why "maintaining ownership" is important.


How is software treated in Gross Domestic Product calculations? Is there a concise explanation of how software is treated in GDP calculations? It seems a bit complicated. I can only figure out part of the story:

For consumer purchases, I think all software spending shows up as final consumption, whether it's purchased shrinkwrapped software or whether it's access to a software-as-a-service (SaaS) website like TurboTax.
Business purchases confuse me more. In the US anyway, software is now counted as part of Private Fixed Investment. But I don't fully understand all the jargon, e.g. about "originals"/"copies"/"own-account"/etc.. Some of the main cases that need to be addressed seem to be: 1) software written purely for internal use, 2) software written by one company and sold to others, and 3) software-as-a-service (SaaS) tools like Salesforce.

Another wrinkle is open source software, or other types of software that are given away at no cost. Does that always count as $0 in GDP? Does the answer change depending on whether the open source project has a corporate sponsor or two that pay for much of the development work?

And what about updates to software -- Major releases? Minor releases? Bug fixes?

The National Income and Product Accounts (NIPA) are used to calculate GDP. The Bureau of Economic Analysis (BEA) prepares methodology papers discussing how they calculate various contributions to the NIPA. They happen to have one on software for business software and this paper should be of use:

  This section describes the methodologies used to prepare (1) annual
  estimates of business and government purchases of software
  (prepackaged and custom), (2) annual estimates of own-account
  production of software, and (3) price indexes that are needed to
  prepare the real estimates of capitalized software. The description is
  limited to the period beginning with 1992.

Estimation of Software in the U.S. National Accounts: New Developments (Moylan (2003))

The methodology for household consumption of software is in the personal consumption expenditures document.

Open-source software is a non-market transaction and not in GDP directly though it may boost the value of goods (like computers) and services (like consulting):

  But by the 1950s, critics of GDP as a metric were emerging, critics
  such as the economist Moses Abramovitz. Indeed, Kuznets himself had
  written that ‘the welfare of a nation can scarcely he inferred from a
  measure of national income. One criticism of the use of GDP focuses on
  the effectiveness of GDP as an economic measure per se. As a number of
  critics have pointed out, GDP can he considered flawed. It does not,
  for example, measure volunteer or non-market transactions. These types
  of transactions are both numerous and wide ranging and can cover
  anything from the care of sick relatives to the creation of
  open-source software. Furthermore, GDP is either a sum total or per
  capita measure. As such, it does not reveal the distributions of
  wealth behind the per capita figure. Indeed, the GOP per capita
  figures may hide important and potentially divisive wealth
  inequalities within a country.

Government for a new age: The transformation agenda by Khoury and Abouchakra (p. 190)


Dollar Value And Commodity Prices How does stronger dollar drive down prices of commodities and/or materials like oil?

There are two reasons I can think of for this effect.

The more economic reason is that commodity prices are usually pro-cyclical. In economic booms those commodity producing countries and their currencies do quite well (their currency goes up and hence USD goes down). And vice versa, in uncertain economic times, there is not as much demand for commodities, and hence less demand for currencies of commodity producing countries (USD goes up and price of commodity declines).
Another reason is more due to unit of account. Many of these commodities are traded in dollars even though the end users are global. If USD went up 1% against all currencies, however the main suppliers and end users of a commodity (say copper) are mostly in Chile and China respectively, then conceivably the cost of copper denominated in Chilean Peso might not have changed at all. This could happen because the Chilean supplier would be willing to sell their copper at 1% lower in USD terms and still get the same profit in Chilean Pesos terms. Therefore, in certain cases it is just a matter of perspective.


In April 2019 our economy created 263000 new jobs, however, total employment went down from March to April by103000 jobs. Why this difference? https://tradingeconomics.com/united-states/employed-persons

This link shows that total employment declined from March to April even though we added 263000 new jobs. Can someone explain why?

The main difference comes from the source of the data. While both figures can be found in the latest BLS report, the +263K comes from their establishment survey, which includes only non-farm jobs as reported by employers.

  Total nonfarm payroll employment increased by 263,000 in April, compared with an average monthly
  gain of 213,000 over the prior 12 months. In April, notable jobs gains occurred in professional and
  business services, construction, health care, and social assistance. (See table B-1.)

On the other hand, the -103K figure comes from the household survey and reflects a shrinkage on the workforce (due to a decrease in labor force participation).

  The household survey includes agricultural
  workers, self-employed workers whose businesses
  are unincorporated, unpaid family workers, and
  private household workers among the employed.
  These groups are excluded from the establishment
  survey

Furthermore, in the latter (household) survey the number of the unemployed decreased even more by 387K. The difference between 387K and 103K is about 284K which is a good enough approximation for the 263K from the establishment survey given the different methodologies.


Corner solution-consumer theory $$U(q_1,q_2)=4{q_1}^{0.5}+q_2$$ $$P_1=1$$ and $$P_2=2$$ Initially $$Income=40$$ Then the question asks :how do I know what income I can get a corner solution?

Anyone can help me with this?

Thank you

The corner solutions are where $q_1=0$ or $q_2=0$. So just take the first-order conditions, plug in zero for the value, and solve for income. For incomes less than that amount, the quantity demanded is zero.


Social choice theory Is it possible for a social choice rule to simultaneously violate the condition of non dictatorship and weak pareto property?
Non dictatorship is when there is no individual such that if he prefers x over y, then so does the society irrespective of what the society feels.
And Pareto property is that if all individuals prefer x over y, then so should the society. It is about how society preserves total agreement.

I don't think it's possible because of the following reason.
Now, if we have dictatorship and rest all also agree with him, then society is essentially preserving that opinion (so Pareto property satisfied).
On the other hand, if Pareto property is not satisfied, ie total agreement of x preferred over y by each individual doesn't not lead to society choosing x over y, this means there is no individual such that if he prefers x over y, then society prefers x over y. So non dictatorship is satisfied.
Please see if this line of thought is correct.

You are correct that it is not possible to violate Weak Pareto and Nondictatorship at the same time.  But your explanation (second paragraph) is a bit muddled.  Here is how I would put it.

To prove, "it is not possible to violate Weak Pareto and Nondictatorship at the same time", it suffices to prove:  "Any Dictatorship satisfies Weak Pareto."  To prove this, suppose F is a social choice rule in which voter i is a dictator.  So for any alternatives a and b, if i prefers a over b, then so does the output of rule F.  To see that F satisfies weak Pareto, let a and b be social alternatives, and suppose that everyone prefers a over b.  Then in particular, i does.  Thus, the output of F prefers a over b (because i is a dictator in F).  Therefore, F satisfies Weak Pareto.


Composition of EEX energy prices I am working currently on EEX energy price data from Germany and so far I couldn't find out, if the prices already include taxes and the German Renewable Energy Act feed-in tarif (EEG-Umlage).

I would appreciate help.

They don't include anything. It is the pure price for 1 MWh.

Edit.

The producers have been paid the tariffs, which lowers their short run marginal costs quite a lot. There has not been added any taxes to the consumers at this point, however.