Is foreign-financed Basic Income Guarantee inflationary? The question came up on comments in Politics.SE:

Situation:

A government of a country sets up an unconditional Basic Income Guarantee (defined as monthly payments to EVERY resident, unconditionally, of a certain sum).

The sum can be  roughly estimated as "only enough for a person to survive on" as per Wiki definition.
The financing of the program is 100% entirely set up from external, foreign sources - charity donation, or no-strings-attached aid from another government.

Is it a certainty that such an arrangement would be highly inflationary for recipient country, assuming that BIG total financing is a non-trivial compared to recieving country's GDP?

All Wikipedia says on the topic is:

  A common concern with Basic Income among the general public is the risk of inflation raising prices and thus undoing its effect. Economists Ed Dolan and Karl Wilderquist say that since the funding for basic income would come from reductions in public spending and/or taxation, there would be no inflationary effect.[citation needed]

... which seems to NOT address foreign-financed BIG at all.

Assume that a big country decides that, from here on, it will distribute for free 1 Kgr of bread to every citizen of a neighbor small country. The bread will be made, transported and distributed with big country resources (raw materials, labor, equipment, wheels, etc). Moreover, big country's representatives will sit around while local citizens eat it.

Will this create inflation? It doesn't seem so.

Now assume that instead, the big country gives for free to the local government electronic funds which the local government transfers to its citizens which in turn transfer it to the bakeries of the big country in order to buy bread and have it delivered (and being watched at, while they eat it). Will this create inflation? It doesn't seem so.

But assume now that the funds are given, always for free and always from the big country, and the citizens of the small country are free to do what they want with them. Will everybody buy bread from abroad? Hmmm, not likely. They may want to go cut their hair with that money. Lots of them. So they rush to all the barber shops and beauty parlors in the country, whose owners start to live this dreadful paradise of every supplier, to be drowning in demand and not have the capacity to fulfill it. And the barbers may think, "hey these people are dying to have their hair cut now. I have two hands and 16 hours a day -They're not enough for all these customers... what if I ask for a little more money per haircut in exchange, say, for a reservation?"

The moral here is that injecting resources into a country may result in excessive demand in local sectors where the productive capacity is not enough to cover the demand, leading to inflation. This is why the ever-sung mantra is "productive investments" rather than "consumption transfers".

If one extends the horizon of course, excessive demand will signal "hey! you, productive resources over there! Come over here! There is more demand than anyone can cover!" -but relocating productive resources takes time, more time than it takes for prices to rise.

(I apologize for the fairy-tale approach, it just came out and for once, I thought "let MathJax lie in peace". But it is perfectly valid scientifically.)


Modified core for cooperative games In the core of cooperative games, the total cost of forming a coalition is shared by all members in a coalition (efficiency). However for my problem I only require that all members are individually rational in the coalition - that is, if the utility of at least one member of the coalition is less than the utility he would gain by being alone, then he will break away from the coalition.

In other words, what is the solution concept that only requires stability and does not carry the notion of efficiency?

If I understand the question correctly, I believe the neatest way to put it is to simply call you solution concept "individual rationality".

Individual rationality can easily be seen as a cooperative game theory solution concept in its own right. I am not aware of any other name for a solution concept consisting only of an individual rationality requirement.


Why isn't PPP given due importance? A unit of money in Country X may buy far more goods in Country Y than in the former. But Country X prides in calling itself a larger economy and a more prosperous entity.
As money is just a social construct created as a substitute to represent the value of goods and thus is useless by itself : How can mere money, such as GDP be given more importance and atfention than its PPP counterpart ?

Nominal GDP is often more quoted in media and in politics than the GDP in PPP, but that doesn't make it be less important. In fact, as stated by 1muflon1 on the comments, economists typically like to measure differences between comparable things, so when comparing GDPs there are usual corrections done on purchasing power parity, as well as inflation.

The PPP indicator has been present in literature for a long time, mentioned in the early 1500's, and translated to modern terms since 1918. It's regularly calculated by international bodies (such as the UN under it's International Comparison Programme).

The GDP PPP is also regularly used in real life by institutions such as the OECD, IMF and World Bank to make recommendations on economic policy, and by traders to better assess when stocks and currencies might be under- or over-valued. This article on investopedia provides a concise overview.


Why are we using exp(.) as the functional form in the household maximization problem inside the RCK model? Currently I'm studying the RCK model at my Advanced Macroeconomics I classes.
A question arose almost immediately when I saw the utility function of a household in this model.

The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so.
Thank you really much in advance for your kind responses.

I guess you already know that $\exp(-\rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor

$$\exp(-\rho t)=\lim_{m \to \infty} \left(1+ \frac{\rho}{m}\right)^{mt}$$


Newly issued shares are sold on the stock market? When a company issues new shares in order to raise it's capital, can it sell those shares on the stock market? Or they have to be sold outside of the stock market?

I mean in general, rules can differ from one country to another.

A company will typically employ an investment bank to act as an underwriter when it wishes to issue new stock. The investment bank essentially agrees to buy the issued stocks from the issuing company and its job is then to sell them to investors.

Investment banks employ a sales force who try to persuade large investors (such as pension funds) to commit to buy the stocks before the date of issue. If the investment bank does a good job then all of the issued stocks will be allocated to a buyer in advance. If the investment bank fails to fails to find enough buyers then it is stuck with the unsold stock and must try to sell them to the public in the stock market.


If a GDP deflator is continually greater than 100%, does that mean inflation is still occuring? If a GDP deflator is continually greater than 100%, does that mean inflation is still occuring?

If the difference in deflators from year to year is continually greater than 1%, does that mean inflation is occuring at a greater and greater rate?

No, a deflator greater than 100 means that the price level is higher than in the base year. It doesn't mean that inflation is still occurring. In fact, you could be experiencing deflation after a period of inflation and if prices today are still higher than the base year, have the deflator be above 100. A growing deflator is an indication of inflation. To detect inflation acceleration you'd need to see changes in the log(deflator) growing over time.


Effect of money supply on price level Consider a macroeconomy defined by following equations:
$$M = kPy + L(r)$$
$$S(r) = I(r)$$
$$y = m $$
 Where $M$ is money supply, $P$ is price level, $y$ is output, $r$ is interest rate, while $k,m$ are constants. $S(r)$ is saving function with $S'(r) >0$, $I(r)$ is investment function with $I'(r) <0$,  and $L(r)$ is speculative money demand function with $L'(r) <0$.

Now how an increase in M affects P? Does P decrease or increase more than proportionately or less than proportionately or proportionately?

I am more interested in approach than in solution. I am not able to understand how to approach this problem.

You can make $P$ the subject of the equation:
$$P=\frac{M-L} {ky} $$ then find the derivative $$\frac{\mathrm d P} {\mathrm d M} = \frac 1{ky}>0$$ to show there is a positive relationship (when $M$ increases, $P$ increases). The elasticity answers your question about proportionality: \begin{align*}
\frac{\mathrm d P} {\mathrm d M} \cdot \frac MP &= \frac 1{ky}\left( \frac {kPy} P + \frac {L \cdot ky} {M-L} \right) \\
&= 1 + \frac L{M-L} \end{align*} shows that $P$ increases more than proportionally (because the elasticity is greater than 1).


Is M&A valuation a good proxy for company fair value? I'm building a model for estimating a fair value of a company. Naturally I'd like to see if model's predicative capabilities are any good.
Would using a value of a friendly M&A deal be a good proxy for company fair value?
One could argue that in a hostile M&A, buyer usually overpays, but in a friendly M&A both parties agree on the deal valuation having insider knowledge not only of the current status of both companies but also of their future projects, R&D, etc. which would allow them to arrive to a more precise valuation than for any external observer.

The thing to always remember is that the valuation of any asset always comes back to the price that someone is willing to pay for it (i.e. if you can’t hope to sell it for that price, it’s not worth that much).
When you describe using the “value of a friendly M&A deal” as a proxy for fair value, I assume you mean price paid for the very company you are trying to value. (Analysts valuing a potential acquisition target won’t know ex-ante what the ultimate deal price will be so they instead will look at precedent transactions for comparable companies to get a range for what type of multiples buyers are paying).
Assuming you know the price paid in the friendly M&A deal, yes that is a very strong data point for what that business is worth. That being said, there are some caveats. For instance, say the buyer was a “strategic” (meaning an often bigger company in a similar industry as opposed to a financial buyer like a private equity firm). There may be some synergies only available to that buyer that raise the price they are willing to pay for it. For instance, say the buyer can close plants, eliminate duplicative sales roles by moving the acquired company’s products onto their sales platform, etc. Those cost savings only available to the strategic buyer make it a more valuable acquisition target than a pure financial player.
Alternatively, the context of the acquisition matters. Say the acquirer bought the business in 2008 (during the financial market collapse) vs in a booming period or in a low vs high interest rate environment. Make sure the M&A transaction you are comparing to is recent because the market (and the company itself of course) can change over time.
Lastly, was the acquisition “market tested”, meaning there were multiple bidders? A friendly transaction where the acquirer was an insider can sometimes result in shady below-market prices paid. Check out lawsuits relating to Delaware shareholder appraisal rights.
The price paid in a friendly M&A deal for the company you are trying to value is an incredibly strong data point, but I would caution against saying it’s better than a hostile price. The acquirer, context, timing and whether the acquisition was market-tested are all important factors in assessing the fair value (or intrinsic value) of a business.
And of course, when looking at any single acquisition, the acquirer might just have been wrong and overpaid—and you could never reasonably expect another buyer to pay that much going forward.


I cannot find for this Simple shared effort level game Each player can contribute to the project with non-negative effort.

Player 1's utility is $u_1=e_1(1+e_2-s\cdot e_1)$ where $s\in [0,1]$.

Player 2's utility is $u_2=e_2(1+e_1-e_2)$

For case 1, each player contributes to the project simultaneously.

For case 2, player 1 moves first then play 2 moves next

I cannot find a Nash equilibria (SPNE for case 2) if $s$ is less than  $1/4$.

If I draw best a response diagram, the two best response functions do not intersect. But I don't think that $e_1=0$, $e_2=0$ is a Nash equilibrium, since they have would have an incentive to exert more than $0$ effort.

Can $e_1=\infty$, $e_2=\infty$ be a nash equilibrium?

You are right, there is no equilibrium for $s\leq \frac{1}{4}$. Note that Nash's theorem only guarantees the existence of an equilibrium in finite games (which this game is not). (Also note that $0$ is not in the best-response set of any of the two players, so we know that, if there were an equilibrium, it would not contain zero effort by any player.)

To get an intuition of what is going on, consider the plot below, which shows the best response functions for the two players, with  $s=\frac{1}{4}$. As you point out, the lines do not intersect. Suppose we start at point $(0,0)$, and let each player revise their action in turn, holding the other player's action constant (dashed line). Player 1 will update their action to $e_1=2$, the best response to $e_2=0$. But then, player 2 will update their action to $e_2=\frac{3}{2}$. This goes on ad infinitum, never reaching an equilibrium.


How is AVC(Average Variable Cost) ‘U’ shaped because of the principle of variable Proportions? How is AVC(Average Variable Cost) ‘U’ shaped because of the principle of variable Proportions?
How are average variable cost(AVC) and marginal product(MP) related?

I obtained the definition of the principle of variable proportion from this site
It states:

... means that upto the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing.

The following is a technical derivation. See the picture at the end for an illustration of the various results.
Denote by $X$ the variable input and by  $Q = {\cal Q}(X)$ the output produced by the amount $X$. The marginal product can be expressed using the first derivative $MP(X) = {\cal Q}'(X)$. The increase or decrease of the marginal product then says something about the second order derivative $MP'(X) = {\cal Q}''(X)$.
The principle of variable proportions then states that $MP'(X)$ is first positive and then negative.

period
change
sign of $MP(X) = {\cal Q}'(X)$
sign of $MP'(X) = {\cal Q}''(X)$

1
marginal product increases
$>0$
$> 0$

2
marginal product decreases
$> 0$
$< 0$

Given that ${\cal Q}'(X) > 0$ we can invert ${\cal Q}(X)$ to obtain  $X = {\cal X}(Q)$ which gives the amount of variable input that produces $Q$ Then as the following identity holds for all $X$:
$$
{\cal X}(Q(X)) = X,
$$
We can take the derivative on both sides and obtain:
$$
{\cal X}'({\cal Q}(X))\,\, {\cal Q}'(X) = 1 \iff {\cal X}'(Q) = \frac{1}{{\cal Q}'(X)}.
$$
and taking derivatives once more gives:
$$
{\cal X}''({\cal Q}(X)) \,\,({\cal Q}'(X))^2 + {\cal X}'({\cal Q}(X))\,\,{\cal Q}''(X) = 0 \iff {\cal X}''(Q) = -\frac{{\cal X}'({\cal Q}(X))\,\, {\cal Q}''(X)}{({\cal Q}'(X))^2}.
$$
This allows us to complete the table:

period
change in $Q$
sign of ${\cal Q}'(X)$
sign of ${\cal Q}''(X)$
sign of ${\cal X}'(Q)$
sign of ${\cal X}''(Q)$

1
marginal product increases
$>0$
$> 0$
$> 0$
$<0$

2
marginal product decreases
$> 0$
$< 0$
$> 0$
$>0$

Now, let's have a look at the variable cost. If $w$ is the unit price of an input $X$,  then total variable costs is:
$$
VC(Q) = w {\cal X}(Q).
$$
Marginal costs is the derivative of the variable costs:
$$
MC(Q) = VC'(Q) = w {\cal X}'(Q)
$$
Th Marginal costs are first decreasing and then increasing.

proof: follows from the previous table as ${\cal X}''(Q)$ is first negative and then positive.

Average variable cost is variable costs divided by output:
$$
AVC(Q) = \frac{w {\cal X}(Q)}{Q}.
$$
Now let's have a look at how the  $AVC(Q)$ varies with $Q$ (which can be expressed using the derivative $AVC'(Q)$). We have:
$$
AVC'(Q) = \frac{(w {\cal X}'(Q))Q  - (w{\cal X}(Q))}{Q
^2} = \frac{MC(X) - AVC(Q)}{Q},\\
$$
Th $AVC(Q)$ is decreasing if  $MC(Q) < AVC(Q)$ and increasing if $MC(Q) > AVC(Q)$. If $AVC(Q)$ is at a minimum (or maximum) then $MC(Q) = AVC(Q)$.

proof: follows from the equation above as the sign of $AVC'$ depends on the sign of $MC - AVC$.

The following shows that for $Q = 0$, average and marginal costs are identical.
Th If $MC(0)$ exists, then $MC(0) = AVC(0)$.

proof: We have that $AVC(Q) = w {\cal X}(Q)/Q$. Using l'Hospital, when taking the limit of $Q \to 0$, gives  $AVC(0) = w {\cal X}'(0) = MC(0)$.

The following shows that initiall, for low values of $Q$, the $AVC$ will be decreasing.
Th for $Q$ small enough, $MC < AVC$, and therefore $AVC$ is decreasing.

proof, Assume not, then $MC > AVC$ in some neighbourhood $]0, Q[$ which means that $AVC$ is increasing. Also, we know that $MC$ is initially decreasing. As $MC(0) = AVC(0)$, this means that $AVC > MC$ in $]0,Q[$, a contradiction.

The following shows that the $MC$-curves cuts the $AVC$-curve from below.
Th let $Q^\ast$ be the first point where $MC(Q^\ast) = AVC(Q^\ast)$, then $MC'(Q^\ast) > 0$ , so the $MC$-curve cuts the $AVC$-curve from below.

proof: From the previous result, we know that slightly before $Q^\ast$, $MC < AVC$  and at $Q^\ast$, $MC = AVQ$ so $(MC - AVQ)' > 0$ at $Q^\ast$.  Working out this derivative, shows that $MC' - \frac{MC - AVC}{Q} > 0$. As $MC = AVC$ at $Q^\ast$, we have $MC'(Q^\ast) > 0$.

The following shows that the $MC$-curve cuts the $AVC$-curve at most once.
Th let $Q^\ast$ be the first point where $MC(Q^\ast) = AVC(Q^\ast)$ and let $Q > Q^\ast$  then $MC(Q) > AVC(Q)$ and therefore $AVC$ is increasing. As such, there is at most one point where the $MC$ is equal to the $AVC$.

proof: As at $Q^\ast$ , $MC$ is in its increasing part, we have (from the table above) that $MC(Q) > 0$ for all $Q \ge Q^\ast$,  Also, as  $AVC(Q^\ast) = MC(Q^\ast)$ and $MC'(Q^\ast) > 0$ and $AVC'(Q^\ast) = 0$, we have for $Q > Q^\ast$ close enough to $Q^\ast$ that $MC(Q) > AVC(Q)$. So $AVC(Q)$ is increasing for all $Q> Q^\ast$ close enought to $Q$.
Next, for such $Q$,  $(MC(Q) - AVC(Q))' = MC'(Q) + (MC(Q) - AVC(Q))/Q > 0$, so the distance between $MC(Q)$ and $AVC(Q)$ is increasing. this means that the distance between $MC(Q)$ and $AVC(Q)$ will grow bigger and bigger. As such, the two curves will never again be equal so $MC(Q) > AVC(Q)$ for all $Q > Q^\ast$.

The final situation can be seen in the picture below. The $MC$ curve is first decreasing and then increasing. At $Q = 0$ the two are the same. First the $MC$ curve obtains its minimum. Then in its increasing part, it cuts the $AVC$ curve at the point where the $AVC$ curve is at its minimum. After this point the distance between the $MC$ and $AVC$ curve grows bigger and bigger, so the two curves never intersect again, and both courves keep increasing.


In this scenario, which coin is more valuable? There are two coins, Coin A and Coin B. You can transfer Coin A for Coin B or Coin B for Coin A only in the two following ways:

Give 100 Coin A for 10 Coin B

Or

Give 10 Coin B for 50 Coin A

In this situation, which of the coins is worth a higher value? A friend of mine presented this problem and we were unable to find a solution. Any thought?

The word 'valuable' is not well defined in this question.

If I am willing to buy an apple from you for \$1 and but I am only willing to sell an apple to you for \$4 which is more valuable: An apple or \$2? You cannot tell because neither option is sufficient to get the other option by trade.

You are faced with the same dilemma in your problem. There are different prices at which to sell and buy so neither one of the options is clearly more valuable.

EDIT:
As @Adam Bailey points out in his excellent answer in this situation even though the exact value ratio is ill defined, it is clear that coin B is more valuable than coin A, because you can exchange one coin B for five coin A, thus you can get more by chosing coin B.


Can the coming recession - or any recession - be avoided? I keep reading about all these warning signs of a coming recession, and I have a very silly question: If we can see it coming, why can't we do something about it now, instead of after we are deep in it and fighting about stimulus packages like last time?

Now, I said it was a silly question, so I know the reason we don't is because of a lack of political will as well as a lack of political and economic consensus as to what that action should be. But I never hear anyone talking about what can be done to prevent a recession before it hits when all the signs tell you it is coming. Why not? Thanks.

(p.s.- Wow, you don't even have a tag for recession? What a bunch of optimists! LOL)

So here is the unpleasant truth about recessions.
"The economy" as a whole consists is a broad term that in all forms, will always be comprised of so many moving parts, so many transactions, that it is hard to not only describe what is happening to it, but why those things are happening. In order to answer your question on why we "can't/don't" do anything about recessions, you have to understand that recessions are harder to predict that whatever the news makes it out to be. We can maybe see the signs that they are just about to come, when the whole snowball is already rolling down the hill, but trying to predict recessions from the long term is basically impossible.
That said, there are two points I'd like put into focus.

We do have some tools for trying to blunt the force of recessions, and we do try to use them!

The warning signs you are reading about, what I imagine most notably being the yield curve inverting, is only a warning sign for certain reasons that don't necessarily have to hold in our current economy.

To the first point, I say "blunt" because trying to completely avoid recessions would probably mean making some big systematic changes, but also probably getting rid of a lot of uncertainty in the world. And our world is unfortunately full of it. We can argue over what causes boom and bust cycles and whether we would prefer to live in a world where growth is slow, but we can consumption smooth and prevent all dips in economic activity. Those are separate issues.
What tools do we have to blunt recessions? There is fiscal policy and monetary policy. With fiscal policy, you can change taxes to try to encourage economic activity (for consumers, business, depends on where you cut the taxes), and with monetary policy you can lower the federal funds interest rate to encourage more lending and thus more investment. But of course these tools may not work as directly as we'd like. Cutting taxes may have to come with cutting spending on government programs that also encourage economic activity. During the 2008 recession, the federal funds late got floored down to 0%, leading the Federal Reserve to have to think of more creative measures of using monetary policy to help boost the economy.

The second point I think is more interesting to talk about. The financial news these days probably talks a lot about the yield curve inverting. What is this exactly?
Imagine you are the government borrowing money through bonds. People value having money as accessible as they can, so a short term bond usually doesn't have a high interest rate. Investors don't get a high rate of return because they are getting compensated with more liquidity. If the government wants to borrow money for a longer time though, then the government will put a higher interest rate on it. This compensates investors who have to sit there and wait for their money longer, money that could have been used to invest in a more lucrative project that could have popped up in the meantime. There is uncertainty in the path of future interest rates, so you take on risk by holding onto a debt contract longer.
So if you were to graph "length of time of a bond or other debt contract" (time to maturity) and "interest rate" (yield), you would normally get an upward sloping curve that tapers off. Why this particular shape? Again, holding shorter term debt is pretty preferred among investors, so there is a steep upwards slope initially. The relative difference between a 3 month contract and a 6 month contract is a lot bigger than the relative difference between a 40 year and 40.25 year contract.
So now we can ask why the yield curve would invert. This usually happens if investors expect a cut in future short term rates. The Federal Reserve is known as the "lender of last resort" and will more or less set the price of liquidity using the federal funds rate. If people expect the Fed to cut it, then the yield curve will invert. And the Fed often only makes big cuts to the federal funds rate to try and prevent or blunt a recession. So that's why the yield curve inverting is usually associated with a nearby recession.
But suppose the yield curve inverts, the Fed cuts the rate and...there is no recession. And maybe the Federal Reserve never anticipated one. This could feasibly be the case too. The idea is that when setting the federal funds interest rate, usually unemployment and inflation tend to be tradeoffs, but they aren't always. Lowering the rate in recent years doesn't seem to have increased inflation expectations very much (a lot of that probably due to the aforementioned 0% bound that was around from the 2008 recession). Since the 1970s reforms to the Federal Reserve, the institution has gotten a reputation for being more committed to fighting inflation in the long run, which also helps with their ability to cut rates and not immediately see inflation boost up. So ultimately it's possible that the Fed may want to cut the rate for other reasons, like simply maintaining a healthy economy.

All that said, you might still be concerned about the yield curve inverting or other indicators that you read in the news. I think it is not unreasonable. But I think the important thing to realize is that people in the news industry frankly do not really understand or even care to explain the nuance behind these signals. They may not understand or explain what is being done about these signals at the policy level. A lot of mainstream news competition is just trying to get people's attention, and honestly who is going to watch a segment on monetary policy. Snore. So the reason you do not see anyone talking about how to respond to a recession is probably just because you don't listen to anyone who really knows much about them.
Really, at the core of your question, you are basically asking why don't economists just predict all the bad stuff that can cause a recession and then stop it. The answer is because we just can't observe all of that, and it's goofy for anyone to think we can. We can only see some things, respond using some limited tools, and give our best policy suggestions. It is wishful thinking to believe we can stop all or even most of hardship in this uncertain world.

If you would like to read more about some recent research on recessions and macroeconomic policy, here are just a small number of papers you could try reading. Even if you don't read beyond the abstract, perhaps it will give you an idea of what sort of research economists are trying to do related to recessions and business cycles.

Aikman, David, Jonathan Bridges, Anil Kashyap, and Caspar Siegert. "Would macroprudential regulation have prevented the last crisis?." Journal of Economic Perspectives 33, no. 1 (2019): 107-30.

Vassolo, Roberto, Javier Garcia-Sanchez, and Luiz Mesquita. "Competitive dynamics and early mover advantages under economic recessions." Revista de Administração de Empresas 57, no. 1 (2017): 22-36.

Martin, Philippe, and Thomas Philippon. "Inspecting the mechanism: Leverage and the great recession in the eurozone." American Economic Review 107, no. 7 (2017): 1904-37.

Koijen, Ralph SJ, Francois Koulischer, Benoit Nguyen, and Motohiro Yogo. Quantitative easing in the euro area: The dynamics of risk exposures and the impact on asset prices. No. 601. 2016.


What does "to be in the double digits to get inflation" mean? Until last year, the Chinese government set 8 percent annual growth as a goal, and the economy frequently delivered several percentage points more than that.
  Then last March, the government pared the goal to 7.5 percent, and actual growth seems likely to be little higher.
  “The potential growth rate of the economy has come down,” Stephen Green, a China economist in the Hong Kong offices of Standard Chartered, said Sunday. “You don’t have to be in the double digits to get inflation.”
  Prices rose faster in December, according to government data released Friday. Consumer prices rose 2.5 percent from the level of a year earlier, their fastest pace since May.
  China Again Is Growing, More Slowly

Hi, I read this article and I do not understand what "be in the double digits" means here.
Could you please help me?
Thank you.

Economists believe that higher growth rates tend to also mean higher inflation rates.

So in this case what Mr. Green means is that

  You don't need a GDP growth rate of over 10% to get inflation. (Even GDP growth of 7.5% or 8% will be enough for the return of high inflation.)


What is the purpose of the Treasury issuing bonds? I have always thought that the US Treasury issues bonds to raise money to allow the US to pay off debts in the short- and long-term. However, recently, I have read in a book on Modern Monetary Theory that that is not the purpose of bond issuance by the Treasury. In fact, the Treasury issuance of bonds serves the purpose of aiding the Fed in conducting monetary policy. May I know if this is the case? If that is the real purpose, then what then does the Treasury do to raise money to pay off US debt?

There are some semantic issues here. A more careful statement of the MMT position is that there is no economic reason for the Treasury to issue bonds. However, there is a self-imposed institutional need to do so: the Treasury has a balance at the Federal Reserve, and the rules it follows appears to imply that the balance cannot go negative. Issuing a Treasury increases that balance, as that is where the borrowed money goes. Note that I believe that some MMT academics have argued that there is no legal need for the balance to remain non-negative - and thus this argument does not apply - but I do not have the legal expertise to judge those arguments. In any event, the Treasury acts as if this requirement exists.
However, the economic purpose of the bonds is that they offer an alternative to holding deposits at the Fed (“reserves”), and bear interest. They create a risk-free yield curve that acts as a benchmark for private sector borrowing. The Fed can set the overnight rate, and influence the rest of the yield curve. This allows it to conduct interest rate policy.
Note that although the phrasing might be disputed, the previous paragraph describes very well all standard models that include a bond market. As such, there’s no debate about the facts, rather the interpretation of the facts.

If that is the real purpose, then what then does the Treasury do to raise money to pay off US debt?

When a Treasury bill/bond expires, it is paid out of the Treasury’s balance at the Fed. This balance comes from tax receipts, and bond/bill issuance. Like corporate borrowers, the stock of Treasury bonds is continuously rolled over.
This mechanism has very little to do with the Fed’s conduct of monetary policy, it’s just the mechanics of bond issuance.


Optimal point and MRS I read that the tangency condition is not sufficient for optimality, and that one other condition is that the MRS must equal the slope of the budget line at an interior optimum. My confusion is that since MRS is the slope of an indifference curve, then wouldn't it automatically be equal to the slope of the budget line of the budget line is tangent to the indifference curve?

The tangency condition itself is the condition that the optimal point, for an interior optimum, is the point where the MRS must equal the slope of the budget line. So the second part of your question is true. It is at the tangent point where MRS equals the slope of the budget line. You've confused yourself with the second (sufficient) condition which, on the other hand, states that the utility function must be strictly quasi-concave in order for an interior optimum to exist.
Hope this clarifies.


Why does BC Hydro want us to use less power? I live in British Columbia, Canada, and we have a hydro electric company called BC hydro that supplies our power. They run ads encouraging us to use less power. I have been wondering why they would do this as money we spend on power is their profit. What is their incentive for us to use less? From an economic perspective, this doesn't make sense to me. Any explanation for the rationale behind this would be appreciated.

BC Hydro is a a public body: that means it can run for the wider public good, rather than purely as a profit-maximiser.

Pretty much everywhere in the world, electricity markets are dysfunctional. They typically have high negative externalities.

Historically, electricity prices haven't included all the costs of the electricity, which means that electricity has been over-consumed, relative to economically-efficient levels.

Energy-efficiency is, typically, the cheapest (when measured as a whole-system cost) way to provide additional energy services.

Furthermore, there is some evidence that energy-efficiency measures have a lower uptake than would be efficient, due to consumers having insufficient information, and due to them having irrationally high discount rates for future energy-bill savings.

So the ads can help to correct these imbalances.


How to distinguish between nominal and real GSP growth? What is the process used to distinguish the change in Gross Domestic Product (GDP) due to an increased output of goods and services from the change due to an increased prices? Why do we make it distinction?

Real GDP (RGDP) is a measure of the value of goods and services produced in an economy over a period of time for a fixed set of prices. Nominal GDP (NGDP) is a measure of the value of goods and services produced in an economy over a period of time for  the prices over that period in time. The way they calculate changes in RGDP is to first measure changes in NGDP, separately measure prices, and then subtract the difference. For NGDP in year $t$ and reference price year for RGDP of $k$ it works like this:

$$NGDP_t = RGDP_{t,k} \cdot \frac{P_t}{P_k}$$
Rearrange:
$$\Rightarrow RGDP_{t,k} = NGDP_t \cdot \frac{P_k}{P_t}$$
Take logs:
$$\Rightarrow \ln(RGDP_{t,k}) = \ln(NGDP_t) +\ln(P_k) - \ln(P_t)$$
Now we can calculate a change ($\Delta X_t = X_t - X_{t-1}$):
$$ \Delta \ln(RGDP_{t,k}) = \Delta \ln(NGDP_t) + \Delta \ln(P_k) - \Delta \ln(P_t)$$
But by definition $\Delta \ln(P_k)=0$ because the reference year prices don't change so:
$$ \Delta \ln(RGDP_{t,k}) = \Delta \ln(NGDP_t) - \Delta \ln(P_t)$$
So as claimed above, the percent change in real GDP ($\ln(RGDP_{t,k})$) equals the percent change in nominal GDP ($\Delta \ln(NGDP_t)$) less the percent change in prices ($\Delta \ln(P_t)$).


What is the difference between the international Fisher effect and uncovered interest rate parity? References:
https://en.wikipedia.org/wiki/International_Fisher_effect
https://en.wikipedia.org/wiki/Interest_rate_parity#Uncovered_interest_rate_parity
As far as I can tell, these two are the same. What is the difference? (Is the former a statement without taking expectation over future exchange rate, and thus, a stronger prediction?)

They are related and have very similar implications but they are not the same. I will try to provide simple explanation here for more nuance you can have look at for example Mogaji (2019) and sources cited therein.
Uncovered interest rate parity (UIP) says that the ratio expected exchange rate $E_t[S_{t+k}]$ to spot exchange rate $S_t$, has to be equal to nominal interest rates between home $i$ and foreign $i_f$ country.
$$   \frac{E_{t}(S_{{t+k}})}{S_{t}} = {\frac  {(1+i)}{(1+i_{f})}} \implies E_t [\Delta S] \approx i - i_f$$
This is based on the idea that there should be no possibility of arbitrage (riskless profit) in the market resulting from different nominal interest rates.
For example, if interest rate in US would be $10\%$ and interest rate in UK would be $5\%$ and if exchange rate would be exactly $1{\\\$}=1£$, anyone who could would stop saving in UK and just transfer all their savings into US. However, to do so they have to go through forex market and by creating new demand for USD they should change exchange rate sufficiently enough to eliminate the arbitrage opportunity.
The UIP simply  posits that due to this possibility the ratio between expected exchange rate and spot exchange rate must be equal to the ratio of interest rates otherwise people would start entering forex market and making trades that would force the above parity hold true.
International Fisher effect (IFE) is based on the idea that ultimately exchange rate must reflect differences in price levels between two countries the expected change in exchange rate must reflect the relative differences in expected inflation rates between two countries ($E_t[\pi]$ and $E[\pi_f]$), since if change in price levels between two countries would not be balanced there would be arbitrages in goods market and violations of the law of one price.  Hence we should have:
$$E_t[\Delta S_t] \approx E_t[\pi] - E_t[\pi_f]$$
Now in turn by Fisher equation the rate of inflation is approximately equal tot he difference between nominal ($i$) and real $(r)$ interest rate $e_t[\pi] \approx i-r$. Furthermore, IFE assumes that due to perfect capital mobility the real interest rate must be everywhere equal $r=r_f$. Well given these assumptions we will find out that change in the exchange rate should be given by change in nominal interest rates since:
$$E_t[\Delta S_t] \approx E_t[\pi] - E_t[\pi_f] \approx  i-r - (i_f-r_f) \approx i - i_f$$
Hence there are subtle differences between these theories as the mechanisms in UIP and IFE are different. UIP is based on an idea of impossibility of arbitrage in money market. IFE is based on the idea that there cannot be arbitrage in goods market.
Sometimes two different theories might predict the same outcome, this is known in science as observational equivalence. Observational equivalence does not necessarily mean there is no difference between two theories as two different mechanisms can sometimes give rise to same outcome.


In a trading economy with many agents, can two agents with the same income envy eachother? In a economy with an arbitrary number of agents whose preferences all satisfy the usual equilibrium conditions and with each starting with a random starting endownment, are there any two agents with the same income at equilibrium who might envy eachother?

Please notice that not all agents have the same income.

Consider a pure exchange economy with $N\geq2$ consumers, each of whom has locally non-satiated preferences. We know from the First Welfare Theorem that any Walrasian equilibrium is Pareto-efficient. We index consumers by superscripts.

Say that consumer $i$ envies consumer $j$'s allocation if $i$ strictly prefers $j$'s allocation to their own:

$$ x^j \succ^i x^i $$

If these preferences have a utility representation, then this is equivalent to

$$ u^i (x^j) > u^i(x^i) $$

It is an easy consequence of the First Welfare Theorem that in any Walrasian equilibrium, no two agents, regardless of income, envy each other's allocations. If they did, this would violate Pareto-efficiency.

Notice, however, that this is not the same as the allocation being envy-free.


Why exactly does a perfectly competitive market depend on consumers having perfect information about a product? My book states that one factor defining a perfectly competitive market is its participants having full information about prices and product characteristics. I can understand how having perfect information about prices promotes price taking behaviour (you can't charge me a higher price for your product if I know I can buy it cheaper from other producers). However, why exactly is having full information about product characteristics important for characterizing perfect competition? Thanks in advance.

Perfect information implies every buyer and every seller knows everything in the market. As soon as a firm brings a new product to the market, other firms start selling the same, identical, product. In practice, say a kebab shop comes up with a secret new ingredient and attracts more custoemrs, but as soon as this happens, other shops copy it. Bottomline: any information-advantage is short-lived in perfect competition. This also leads to the other characterisation, all products are homogeneous.

If the firms/customers do not possess full information about the market/products, then you should characterise the market differently i.e. oligopoly, monopolistic competition or monopoly.


Can a progressive marginal taxation be regressive in terms of average tax rate? Or does progressive marginal taxation imply that it is a progressive average taxation?

Here, I mean that if $T(Y)$ is a tax function of income, marginal tax rate would be $dT/dY$ and average tax rate would be $T(Y)/Y$.

$$
\frac{\partial\frac{T(Y)}{Y}}{\partial Y}= \frac{T'(Y)}{Y} - \frac{T(Y)}{Y^2}
$$

This can only be smaller than 0 if

$$ T'(Y) < \frac{T(Y)}{Y} $$

In other words, the marginal tax rate needs to be smaller than the average tax rate. This can't happen because you start with an average tax rate of zero and a positive marginal tax rate. From then on, in a progressive scheme, the tax due increases faster than taxable income. Progressive taxation is actually characterized by the fact that the marginal tax rate exceeds the average one. See here, p.27.


Is a loan lent with a rate under the inflation rate free money? Suppose we have an inflation in a country with an annual 2% and we get a loan for an annual 1% (real interest). Is the money we receive free?
This is a common practice in some European countries, where the mortgages are around 1% fix rate plus the Euro Interank Offered Rate.
If so, why? Are the banks loosing money by lending in such low rates?

Inflation: 2%
Interest:  1%

This means the real rate is 3%.
So no; not free money.

Free money would be negative interest rates.
Example: Inflation: 0%.
         Interest on loan I get from the bank: -1%.
This would mean they are paying ME 1% to take the loan from the bank.

Negative interest rates are a real practice, with many historical examples that can be researched.

The banks are theoretically losing 1%(+2% inflation) on the loaned amount, however it's important to understand that deals are made among negotiations with central banks in the background that can still produce gains from this.


Can anyone help me understand the Motrtensen-Pissarides model? I am seeking help with the Mortensen-Pissarides model in discrete time? Basically, I was given the following in class example (which we didn’t complete do to time constraints associated with the end of the semester).
Our workers Bellman Equations are as follows:
$V_u=b$$+\frac{aV_e+(1-a)V_u}{1+r}$ and
$V_e=$$w+\frac{\lambda V_u+(1-\lambda)V_e}{1+r}$ respectively
With $V_u$ and $V_e$ are expected utility values for unemployed and employed worker(s). a (∈ (0,1)) is the job-finding rate, b (> 0) is the unemployment benefits, r (> 0) is the real interest rate, w is the wage; and λ (∈ (0, 1)) is the job-destruction rate.
find the law of motion of the unemployment rate, given a and $\lambda$
Suppose that w is set to the reservation wage. Describe the condition that $V_u$ and $V_e$ must satisfy in this case. Then, given the values of b, a, λ, and r, compute the equilibrium values of $V_u$ and $V_e$.
My professor didn’t have time to explain this concept, but said it would be super important if we intend to take the next highest macro course my universities grad school offers. Essentially this is a solve for yourself equation for summer vacation, but I am lost. Can any one show me what to do?

To get things started:
The reservation wage is the wage that makes the worker indifferent between taking a job and getting V_e and not taking a job and getting V_u. To find it, solve for the value of w that makes V_e = V_u.
Solving the entire model is not possible given the info you provided. You need the block that describes the firms.
My sense is that it would be most useful for you to read about the MP model and then post more specific questions based on a complete model. A good reference is Romer's Advanced Macro book.


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

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

Yes, you are wrong. As the quoted part explains,

In this case, economists say there has been an increase in “quantity supplied” but no change in “supply.” Supply refers to the position of the supply curve, whereas the quantity supplied refers to the amount producers wish to sell.

Are you willing to sell your current computer for say \$1 000? What is the lowest price that you are willing to sell for? (Just a ballpark estimate will do.)
If you came up with a number, you did that without knowing anything about the prospective buyers of your computer.
Of course it is very nice to be able to sell for more, if the customers are - for some reason - willing to paying more, but the ability to do this is determined by the equilibrium. The supply curve merely describes the vendors' preferences. What is the lowest price at which they are willing to sell / what quantity are they willing to sell if the price turns out to be X.


Gale-Shapley Follow-up Literature and General Questions The Gale-Shapley Algorithm is a way of matchmaking between two different entities of people. It guarantees that every individual player is matched and that the matches are stable.

What sort of literature has been done building off of this? How does social welfare change when the two entities do not have the same number of individuals in them, so that not everyone can be matched? Are there faster ways to match individuals with each other (lower runtime?). And most importantly, what sort of applications does the Gale-Shapley algorithm have in economics?

It seems like a very weird game theoretic model just because when I read the proof for the validity of the algorithm, it doesn't seem like the problem is "discrete"; that is, optimizing who gets matched with who and finding a Pareto efficient result can't be solved through maximizing a continuous function. (As a side question, is the Gale-Shapley allocation Pareto efficient?)

Edit I meant to say, in the second paragraph, "it seems like the problem IS "discrete". So my apologies there.

How does social welfare change when the two entities do not have the same number of individuals in them, so that not everyone can be matched?

The algorithm works fine in this case. The important assumption is still that the underlying graph is bipartite (and that preferences are transitive). If we allow for members of a given type to propose to each other, then we lose convergence. Suppose we have three players: $A, B, C$. We have $A$'s preferences as $(B, C, A)$; $B$'s preferences as $(C, A, B)$; and $C$'s preferences as $(A, B, C)$. So $A$ proposes to $B$, which accepts. Then $B$ proposes to $C$, which accepts. This unmatches $A$. Next, $C$ proposes to $A$, which accepts. This unmatches $B$. We then repeat.

    Are there faster ways to match individuals with each other (lower runtime?)

Gale-Shapley has a runtime complexity of $\Theta(n^{2})$. In graph theory, most bipartite matching algorithms take $\Omega(|E| \sqrt{|V|})$ time. In the worst case, $|E| = |V|^{2}/4$. So I wouldn't bank on much better.

Additionally, this isn't a problem that lends itself well to a divide and conquer approach. It's really a greedy problem. You might be able to get the expected runtime down by selecting a random ordering for proposing. The analysis would be involved though.

    It seems like a very weird game theoretic model just because when I read the proof for the validity of the algorithm, it doesn't seem like the problem is "discrete"; that is, optimizing who gets matched with who and finding a Pareto efficient result can't be solved through maximizing a continuous function.

Actually, it's a discrete model. In more traditional fields of economics, we have continuous variables. So linear programming makes sense. We could actually formulate an integer-linear program for the stable-marriage problem if we look at it from a graph theoretic perspective. Matching problems can be formulated in the language of flows. And we can write flow problems as LPs. The flow constraints form a convex polytope. If the graph is bipartite, the vertices of the polytope are the matchings. The trick here is that we have to add additional constraints to ensure we end up with the correct matching (since the matching from the Gale-Shapley algorithm is unique, regardless of the order in which the men propose).

Even if we go to the trouble of formulating the linear program, solving an LP for this problem by hand or by a computer is less efficient than using the algorithm.

    (As a side question, is the Gale-Shapley allocation Pareto efficient?)

The matching generated by the Gale-Shapely algorithm is in the core. An imputation belonging to the core satisfies the property that no coalition can collude their initial endowments and improve its members' outcomes. An imputation is Pareto optimal if no set of agents can improve their outcomes without another player's outcome being less favorable. So core allocations are Pareto optimal.

For more on Gale-Shapley, check out my blog: https://michaellevet.wordpress.com/2015/05/22/algorithmic-game-theory-stable-marriage-problem/


Understanding the shape of a Marginal Cost Curve My class IB has just discussed allocative efficiency and hence consumer and producer supply. They explained the concepts with a diagram like this:

It all made perfect sense to me until it was mentioned that the supply curve can also be seen as a marginal cost curve. If this is the case, I don't understand why it is only sloping upwards. I know that marginal cost curves (at least at short-term) look something like...
But the curve in the first diagram is different.

Is is an oversimplification of a real marginal cost diagram, or am I missing something?

You are missing the average cost curve in the same diagram.
Basic algebra gives us the following.

Let's find the minimum of the $AC = C/Q$. We have

$$\frac {\partial AC}{\partial Q} = \frac {MC\cdot Q - C}{Q^2}$$

For this to be equal to zero, we must have $MC \cdot Q = C \implies MC = AC$. So when $AC$ is at its minimum, it equals $MC$. But we also want the second order condition, and we want the second derivative to be positive, evaluated at the critical point.

$$\frac {\partial^2 AC}{\partial Q^2} <0 \implies ...MC'\cdot Q^3-2MC\cdot Q^2 + 2QC >0$$

At the critical point $MC = AC = C/Q$. Inserting this we get the condition

$$MC'\cdot Q^3-2(C/Q)\cdot Q^2 + 2QC >0 \implies MC'>0$$

So at the point where $MC = AC$ we want MC to be rising. But this implies that it will cross the $AC$ curve from below. In turn this implies that for quantities lower than this point, marginal cost curve will be below the average cost curve, which means that if this left part of $MC$ curve was a supply curve the firm would have losses.

Therefore the supply curve is only an upwards-sloping part of the marginal cost curve. You can now superimpose the $AC$ curve that is consistent with all these.


preference relations and monotonic transformations of utillity functions Given a choice set $X$ (NOT assumed to be a commodity set...), and utility functions $u,u'$ on $X$, it is clear that if $u'$ is a strictly monotonic transformation of $u$ then they induce the same preference relation on $X$.

My question is, under what conditions does the opposite hold? What are the least strict conditions we can think of that imply that if $u,u'$ induce the same preference relation on $X$, that $u'$ must then necessarily be a strictly increasing transformation of $u$?

Depending onhow one reads the question, the converse holds either always or basically never. Let $u:X\to\mathbb{R}$ and $v:X\to\mathbb{R}$ be arbitrary functions with ranges $u(X)$ and $v(X)$, respectively. It is not hard to show that $u$ and $v$ represent the same preferences if and only if there exists a strictly increasing function $h:v(X)\to\mathbb{R}$ such that $u=h\circ v$. So this is the "always"-answer.

Now one might require $h$ to be defined and strictly increasing on all of $\mathbb{R}$. In that case, one can basically never guarantee the existence of such an $h$, at least for standard economic applications. Let $X=[0,1]$, $u$ be given by $u(x)=x$ and $v$ be given by $v(x)=x$ for $x\leq 1/2$ and $v(x)=x+1$ for $x>1/2$. Then $v(X)=[0, 1/2]\cup (3/2,2]$. If $h:\mathbb{R}\to\mathbb{R}$ is a nondecreasing function such that $u=h\circ v$, all $r\in(1/2,3/2]$ must be mapped to the same point by $h$, so $h$ cannot be strictly increasing.

Such a problem occurs whenever $X$ is a connected topological space (say, a convex subset of some $\mathbb{R}^n$) and some continuous utility representation exists that is not constant.

The problem can even occur if both $v$ and $u$ are continuous. Let $X=\mathbb{R}$, $u$ be given by $u(x)=x$ and $v$ be given by $v(x)=e^x$. Then $v(X)=\mathbb{R}_{++}$, the set of strictly positive numbers. Suppose there were some strictly increasing function $h:\mathbb{R}\to\mathbb{R}$ such that $u=h\circ v$. Then $h$ would be a strictly increasing extension of the logarithm function to all of $\mathbb{R}$, which is impossible.

Finally, some positive result: If $X$ is a connected topological space, and $u:X\to\mathbb{R}$ and $v:X\to\mathbb{R}$ are continuous functions that represent the same preferences and are either both bounded above or unbounded above and are either both bounded below or unbounded below, then there exists a strictly increasing continuous function $h:\mathbb{R}\to\mathbb{R}$ such that $u=h\circ v$.


Does it matter which is the dependent variable in regression of time series data? I am testing for cointegration between the Real GDP per capita of England and France. I use a Dickey-Fuller test to test for stationarity and concluded that both of my series are non-stationary. So I then ran the regression and did the second Dickey-Fuller test for co-integration on the residual. Here is what I am confused about:

If I ran the regression and had rgdpe of England as a dependent variable I concluded that my regression was spurious. (My residuals were non-stationary).
If I ran the regression and had rgdpe of France as a dependent variable I concluded that the rgdpe are cointegrated (My residuals were stationary).

Can anyone explain the reason for this discrepancy?

Asymptotically, you should be able to interchange the role of $Y_t$ and $X_t$ and estimate lets say $$X_t =\alpha^* + \beta^* Y_t+u^*_t$$ where $\alpha^* = -\alpha/\beta$ and $\beta^*= 1/\beta$ and still get cointegrated relationship.

However, crucial caveat here is that this holds only asymptotically and only for $R^2$ close to unity. In finite samples you can find discrepancy between the two. Moreover, if $R^2$ is not high you will also find discrepancy and in that case you should not even model cointegrated relationship with standard OLS but rather with something like Fully Modified OLS (FMLS) or Canonical OLS. Also, which variable is exogenous and which endogenous will matter if the variables are not integrated of the same order or one of them is stationary. Maybe you just got false negative in one of the previous tests.

All this aside if you believe that there could be a cointegrated relationship that could go both ways it is not really appropriate to use Engle-Granger approach to test for it by two Engle-Granger tests. Rather you should use Johansen cointegration test that tests for it by estimating simultaneous system of these all in one model.


Economics and formulating predictions I was just wondering as a science major, science can be done through inductive reasoning at first by trying to gather examples and information through observation then coming to general conclusion or hypothesis on this observation.

I believe that in Economics, they also have similar tools to come up with various theories which govern how our economy functions. But towards more behavioral economics, how would one test the hypothesis? Unlike natural sciences, we needs to test on human behavior, but how can one formulate predictions and testify the hypothesis if human trials are not available to a large extent?

In other words, how good are human sciences (such as economics) when formulating theories and coming to making predictions unlike the natural sciences?

That's a big one. I'm trying without claiming to be near exhaustive.

The fundamental challenge for social sciences, as you rightly point out, is the absence of carrying out experimental designs on a large scale. Introducing a minimum wage in one half a country and not so in the other half would fail because of e.g. equity concerns (why would you advantage certain workers?) or external effects (firms moving from one region to the other, differential effects on trade).

On a small scale though, you might certainly be able to run experiments which might inform you on the large scale. An example would be random assignment in school to different pedagogical approaches. Tracking students over longer period of time might yield insights on how changing things might turn out on a larger scale.

Having said that, Economics, as widely understood by the public, deals with question on the large scale. The traditional approach to those question is to set up mathematical models which describe the behavior of economic actors. These models are not fundamentally different to what natural sciences refer to as laws (...of motion, of energy conservation).  The difference is that social models do not (and cannot) claim their general validity and their reliability about the mechanism proposed. These models have been (and still are) derived from assumptions on individual (firms, households) or collective behavior (price mechanism). It is these assumptions which can be tested. They often have been tested with macro-scale regression analysis, such as explaining GDP growth by development aid to test effectiveness of those programs. While this is still done, at the research frontier such findings are by and large ignored.

Instead, Economics has undergone a so-called Credibility Revolution. In a nutshell, this entails the development and application of quasi-experimental methods which try to imitate the experimental ideal from natural sciences. If your question at hand is not feasible for a field experiment, you may look for settings where there is exogenous variation in a treatment variable that allows you identify its effect on a outcome variable of interest. There are numerous examples for this, also cited in the linked paper. One of the most famous ones is the comparison of increasing the minimum wage in one of two similar U.S. states. Exogenous variation may be geographic (compare two similar cities across a country border) or over time (a sudden reform that was not anticipated), to name just two. Nowadays, Empirical Economics tries to exploit these kind of variations with large-scale data on the micro level (the firm, the household, the individual) to come up with causal estimates on specific settings. If their findings can be confirmed by other settings, consensus on certain mechanism emerges, which might then be used to inform large scale theories.

To answer your question rightaway: Economists are not nearly as good as natural sciences regarding to the empirical basis of their theories, but they have greatly improved. On a more fundamental note, economic "laws" can never match the universality of natural science laws, as it's human behavior underneath.


Explanation for Mundell-Tobin Effect Apparently, Mundell and Tobin used different methods to explain the Mundell-Tobin effect (which means that in general higher inflation increases the nominal interest rate, but decreases the real interest rate so Fisher's statement about the one-for-one adjustment of the nominal interest rate to the increase in inflation is slightly wrong) and I have two questions regarding their arguments:

According to Mundell, higher inflation reduces demand for money and increases demand for Bonds, decreasing the required return on bonds and decreasing the real interest rate.

Question here: Aren't required return on bonds "nominal"? So I assume here that the decrease in the required return for bonds means a decrease in the "nominal" interest rate. But isn't the Mundell-Tobin effect supposed to result in 'higher' nominal interest rates? This looks likes a contradiction to me but obviously I'm pretty sure I'm misunderstanding something here so I wish to know what I'm missing.

According to Tobin, higher inflation reduces demand for money and increases demand for real capital, decreasing the marginal productivity of capital and decreasing the real interest rate.

Question here: I believe that an increase in the demand for real capital means the same thing as the increase in the demand for loanable funds to acquire capital as investment(in the loanable funds market). In this case the rightward shift of the demand curve for lonable funds actually increases the real interest rate in the loanable funds market, which directly contradicts Tobin's statement (since it is the real interest rate that is associated with the loanable funds market, not the nominal interest rate). So how should I understand this contradiction?

Robert Mundell originally wrote about Mundell-Tobin effect in response to the Fisher effect, which states that "the real interest rate is unaffected by monetary policy and hence unaffected by the expected inflation rate." In other words, nominal interest rates will always adjust such that real interest rates stay at whatever the market rate is. Hence, if inflation rises, then nominal interest rates must rise. Which brings us to the first point of confusion...

  Mundell-Tobin effect supposed to result in 'higher' nominal interest rates

This is the Fisher effect not Mundell-Tobin. Note the Mundell-Tobin effect explains why nominal interest rates will not rise as high as expected by the Fisher effect - it will be less than one-to-one. This is not a contradiction as much as a competing factor.

  I believe that an increase in the demand for real capital means the same thing as the increase in the demand for loanable funds

The reduced demand for money increases the supply of loanable funds, which induces more demand, which is then used to purchase real capital. This in turn reduces the expected rate of return on this capital. If expected rate of return is not as high on capital, real interest rates do not have to be as high to compete in terms of opportunity cost.


TFP estimation in R by using prodest and estprod packages I am writing my Bachelor Thesis and I really need help with the TFP estimation. so far I have a dataset with log values of Value added (va), Labour (l), Capital (k), and Materials (m). The initial dataset is available here:
https://drive.google.com/file/d/1aedWYABus1fQjKWxkOmYOmxv-qSja7hF/view?usp=sharing
So far my code is:
remove(list=ls())

library(plm)
library(dplyr)
library(ggplot2)
library(prodest)
library(estprod)
library(broom)

setwd("C:/Users/vadya/Desktop/baka")

Data <- read.csv("LV.csv", header=TRUE, sep=",")
str(Data)

summary(Data)

DataA <- Data %>%
  filter(NACE == 'A') %>%
  filter(VA > 0, L > 0, K > 0, M > 0) %>%
  mutate(l = log(L),
         va = log(VA),
         k = log(K),
         m = log(M))

wooldridge(data = DataA, va ~ l | k | m, id = "ID", time = "Year", bootstrap = TRUE, gross = FALSE)

levinsohn_petrin(data = DataA, va ~ l | k | m, id = "ID", time = "Year", bootstrap = TRUE, gross = FALSE)

olley_pakes(data = DataA, va ~ l | k | m, id = "ID", time = "Year", bootstrap = TRUE, gross = FALSE)

mod1 = estprod::levinsohn_petrin(data = DataA,
                                 formula = va ~ l | k | m,
                                 id = "ID",
                                 time = "Year",
                                 reps = 20,
                                 gross = FALSE)
mod1

mod2 = prodest::prodestLP(DataA$va,
                      fX = DataA$l,
                          sX = DataA$k,
                      pX = DataA$m,
                          idvar = DataA$ID,
                      timevar = DataA$Year,
                          opt='optim',
                          exit = FALSE,
                          tol = 1e-100)

omega = prodest::omega(mod2)

So far, the problem is the following - with estprod package I get only coefficients estimated for l and k, without m

With prodest package, the problem is the following:

A saw the same discussion in another theme on StackExchange where a guy was asking the same question, but he had provided some part of his data, and everything worked. But in my case the problems are different.
Does anyone faced the same problem, and is it possible to solve these issues, since I only have begun studying TFP in R, so I would really appreciate your help and any impact provided. Thanks in advance!!!

You get the error because your ID is string and the prodestLP function has a problem with that here - leading to incorrectly specifying that replacement matrix in this case.
You can solve this issue with:
 DataA$ID<-as.numeric(as.factor( DataA$ID))

once you declare the ID as numeric the code works:
     mod2 = prodest::prodestLP(DataA$va,
+                            fX = DataA$l,
+                            sX = DataA$k,
+                            pX = DataA$m,
+                            idvar = DataA$ID,
+                            timevar = DataA$Year,
+                            opt='optim',
+                            exit = FALSE,
+                            tol = 1e-100)
>
>  omega = prodest::omega(mod2)

with output:
    summary(mod2)

-------------------------------------------------------------
-               Production Function Estimation              -
-------------------------------------------------------------
                   Method :    LP
-------------------------------------------------------------
                               fX1       sX1
Estimated Parameters      :   0.107     0.458
                             (0.012)   (0.052)
-------------------------------------------------------------
N                         :  4397
-------------------------------------------------------------
Bootstrap repetitions     :  20
1st Stage Parameters      :  0.107     0.249
Optimizer                 :  optim
-------------------------------------------------------------
Elapsed Time              :  0.02 mins

-------------------------------------------------------------

summary(omega)
       V1
 Min.   :-3.452
 1st Qu.: 1.428
 Median : 1.842
 Mean   : 1.778
 3rd Qu.: 2.202
 Max.   : 4.492

Update these are the packages I am running and code before the one shown above (also I am running R  version 4.0.2 (2020-06-22)):
rm(list = ls())

Data <- read.csv("~/R studio/excercises in randomness/tfp2/Gmail/LV.csv")

 View(Data)

 pckg<-c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod")
 #install.packages(c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod"))
 lapply(pckg, require, character.only = TRUE)

 head(Data)

 summary(Data)

 DataA <- Data %>%
         filter(NACE == 'A') %>%
         filter(VA > 0, L > 0, K > 0, M > 0) %>%
         mutate(l = log(L),
                va = log(VA),
                k = log(K),
                m = log(M))


What is the difference between 'actual' and 'potential' interaction between buyers and sellers? In the book "Microeconomics" by Pyndyck and others, the author(s) define a 'market' as a collection of buyers and sellers, who by the actual or potential interaction with each other determine the price of a product or a set of products.

What is the difference between these two terms that the author(s) have taken effort to differentiate?

The traditional representation of a market, with the curves of supply and demand reflects potential transactions: for each price, we can derive the quantity that would be offered or asked. The actual transactions only occur at the market price, but ignoring all other intentions is too restrictive to define a market.

For example, stock exchanges often give the possibility to agents to express their intentions (that is,  the quantity they would offer or buy for a certain price) about a particular security, which will form the bid (supply)  and the ask (demand). Even if the ask and the bid never meet, there is still a market as people are willing to exchange goods, though they cannot find an acceptable compromise.


Does the concept of Nash-equilibrium conflict with the concept of market equilibrium in the lemon market Consider a version of Akerlof's Lemon market with two types of sellers. One type sells Quality cars the other type sells Lemons. Buyers' reservation prices are $r_{B,Q}$ for a Quality car and $r_{B,L}$ for a Lemon. Sellers' reservation prices are $r_{S,Q}$ for a Quality car and $r_{S,L}$ for a Lemon. The buyers cannot differentiate between the types of the sellers but the sellers know their type. Given a market price $p$ sellers decide whether to sell or not by maximizing their surplus $p - r_{S,t}$. (Not selling yields a surplus of zero.) Buyers decide whether to buy or not by maximizing their expected surplus $E(r_{B,t}) - p$. (Not buying yields a surplus of zero.)

Given a number of buyers $n_B$ a number of sellers for both types $n_Q, n_L$ we can reason about the type of equilibrium. Depending on the parameters you can have total market collapse (if no purchase occurs), adverse selection (if only Lemons are bought and sold) and also markets where both types of cars are sold. For some parameter sets you have multiple market equilibria. That is you have a price $p_1$ at which adverse selection occurs and the corresponding demand at $p_1$ is equal to the supply at $p_1$. You also have a price $p_2$ at which adverse selection does not occur and the corresponding demand at $p_2$ is equal to the supply at $p_2$.

If the surplus of a single buyer is larger at $p_2$ and the surplus of sellers is not smaller at $p_2$, can I claim that $p_1$ is an equilibrium? Seems like any buyer would benefit by deviating from $p_1$ and unilateraly setting $p_2$ or $p_2 + \epsilon$. In competitive equilibrium it is assumed that market actors are price takers but if they are sufficiently small (have no bargaining power like a monopoly) then this coincides with their strategic interests. Here even if the buyer is insignificant, this does not hold (probably due to asymmetric information). So is the market in equilibrium with price $p_1$ or not?

Such parameter combinations exist, an example:
$$
n_B = 4, n_Q = 2, n_L = 4
$$
$$
r_{B,Q} = 18, r_{B,L} = 6, r_{S,Q} = 8, r_{S,L} = 5
$$
$$
p_1 = 8, p_2 = 5
$$

So this seems to be a known issue. Quoting from the Wilson article of 1980,
The Nature of Equilibrium in Markets with Adverse Selection:

  Using a variant of Akerlof's model of the used car market, we examine the equlibrium of the model under three distinct conventions: (1) an auctioneer sets the price; (2) buyers set the price; (3) sellers set the price. Only in the case of the auctioneer is the equilibrium necessarily characterized by a single price which equates supply and demand.

Thus the answer to the question is a partial yes. Given some (most) variants of the lemon market the two equilibrium concepts do not result in identical outcomes.


Prove that the set $X = \{x \in R^L_+| u(x) \geq \bar u\}$ is closed Prove that the set $X = \{x \in R^L_+| u(x) \geq \bar u\}$ is closed.

Saw this statement in the textbook but I'm not sure how this is the case when we don't have any restrictions on $u(x)$ such as continuity. I can prove this if it is continuous, but I'm not sure how to do it if  isn't.

The statement does not seem to be true.

Define $u$ as $u(x) = -1$ if $x \leq 0$, $u(x) = 0$ if $x \in (0,1)$ and $u(x) = 1$ if $x \geq 1$. The set of points $x$ for which $u(x) \geq 0$ is $(0,\infty)$, which is not closed.


Graphics card shortage - why don't they just raise prices? See e.g.

Nvidia CEO: GeForce RTX 3080 and 3090 Shortages To Last Until 2021 (Tom's Hardware, 2020-10-05)
The great graphics card shortage of 2020 (and 2021) (BBC, 2021-01-24)

Why don't Nvidia and retailers just raise the prices of these graphics cards (as might be predicted by Econ 101 supply-and-demand theory)?

Actually, just recently (a few days ago; January 2021 - for anyone reading this later), the major retailers of these graphics cards did raise their prices (see example here for EVGA). Or more broadly Forbes reports that at the beginning of this year due to shortages and in addition also due to increased tariffs on China graphics card prices:

are going up anywhere from 7 to 25%.

It’s difficult to know how much of that is due to the China tariff and how much due to shortage, but most sites reporting on this quote the shortage of GPUs due to increased demand from Bitcoin miners as one of the main reasons for price rise.
But the question still can be reformulated in another way. Why did it take them so long to adjust their prices?
I believe the answer to that is sticky prices. Research generally finds that in the EU and the US respectively data on the frequency of price changes (Alvarez, et al., 2006).

imply average price durations close to one year in the euro area and slightly above half a year in the US.

In addition, more recent studies for US show that there is also very large heterogeneity in price stickiness as about 1/5 of prices take more than a year to change (see discussion Klenow & Malin 2010).
The average price durations above are not that far from the time it took graphics card prices to start to rise.
It is very difficult to know exactly what is the reason for price stickiness on a firm level, but research on price stickiness further shows that:

Firms usually don’t want to raise prices ahead of their competitors, hence in data we can observe a great degree of price change coordination among firms in the same industry (see Levy et al. 1998; Klenow & Malin 2010).    This seems to fit the facts of this case as the big price increase followed the tariff news (but as mentioned above, observers seems to agree that tariff could not account for all the price increase), and thus firms likely reasoned that everyone will have to increase prices now, so now is the right time to increase their prices as well.
The above is also further corroborated by Eichenbaum et al. (2011) who show that price changes usually take place when firms costs change but that the change in costs itself is not sufficient to induce the change in price (similar findings were also found by Dias et al. 2011).

Firms will change prices less frequently when ‘menu’ costs are high. Anderson et al (2015) show that menu costs can easily reduce frequency of price changes by over 13 percent which is not trivial. I would not be surprised if it would be expensive to change pricing strategy of big multinational company such as Nvidia or AMD. Possibly some of the prices might be also locked by contracts with retailers.

When manufacturers use reference prices and recommended prices, which is usual strategy for many manufactures that want to ensure uniform pricing, the prices tend to be stickier than retail prices  (Klenow & Malin, 2010 - although not all studies find this result). Indeed, in this case we can clearly see that retailers were rising prices ahead of manufacturers and especially scalpers were already taking advantage of the situation by reselling GPUs with higher prices much earlier (see news article on that here).

Empirical evidence shows that prices tend to be stickier when competition is less intense (Dias et al. 2011). GPU market is for all practical purposes a duopoly of Nvidia and AMD.

Empirical evidence also shows that goods with higher elasticity of demand adjust their prices more slowly, and this holds even in presence of demand shocks  (Dias et al. 2011). However, I could not find any empirical study on the elasticity of demand for GPUs so it is hard to know what role this plays in this case, but a priori I would expect GPU demand to be more price elastic since GPUs are not necessities and especially high-end GPUs could be considered a luxury good, and you can still play games with reasonably good graphics even on less powerful GPUs. Consequently, this could be a reason as well.

the evidence also shows that large firms are slower to adjust their prices (again see Dias et al. 2011). This also seems to fit the observable events. That is, as mentioned previously, scalpers adjusted their prices almost immediately, large retailers and manufacturers took their time.

This being said, as mentioned earlier, it is important to keep in mind that it is very hard to explain the behavior of few firms especially as the events unfold. There might further issues playing some role here. Possibly even a failure to act optimally perhaps due to some agency problems within the firms.


Where do remittances come into play in the formula for GDP? In the classic formula for GDP, i.e., GDP=C+I+G+X-M, where are remittances accounted for? With remittances as high as third of GDP for developing countries, I wonder how they are not explicit in this equation.

Gross domestic product (GDP) is the total value of output in an economy, this can be measured only by Output using this formula.

This method uses GDP = C + I + G + (X-M) where

C: Consumption (Household spending)
I: Investments
G: Government spending
X: Exports from an economy
M: Imports into an economy

The remittances that you mention about are not made against any services.  While remittances can be a source of GDP growth by increasing household consumption, it does not directly add to GDP, it does affect GNP though.

For a clear comparison of these two terms GDP and GNP use this

Alternatively you can use incomes to calculate GDP, however note that even in that method you add only those incomes that are made from the production of goods and services are included and not transfers


How does imposing 100 percent cash margin requirement on imports help to stabilize foreign exchange reserves of a country? My country is facing a critical depreciation of its currency's exchange rate and the central bank has introduced a 100 percent cash margin requirement on a selected set of imports.

My main problem is how this can help to stabilize the currency?
The selected set of imports include some products which my country doesn't manufacture at all. So how can this help stabilize the exchange rate if people still keep consuming the imported goods because they have no other alternative?

Simply because when you want to buy goods from country A, you (generally) first have to buy A's currency, which means selling yours.

And given that selling a currency exerts a downward pressure on its value, the main idea behind a 100 percent cash margin requirement is about counter-balancing the depreciation by exerting an inversely-proportional upward pressure.

That being explained, if importators do so by mobilizing already-owned and in-excess cash, there is no reason for such a policy to work... which is unlikely, say, in the case of Turkey, since domestic liquidity have already been sold, which means buying them back.


Are slacks the same as mix-inefficiency? On the diagram below it is stated that A' has input slacks as it could reduce the amount of $x_2$ and still be on the frontier (by moving to C). However I recall mix-inefficiency having a similar definition. Is there any difference between slacks and mix-inefficiency?

If by "slack" we mean that part of the quantity used from an input does not result in an increase in output, then it is evident that this is an inefficient mix of inputs. It is not even about re-allocating inputs to reduce/minimize costs, we are clearly totally wasting some input quantity.


Is it true that the U.S has to run a chronic trade deficit with the rest of the world as a price to pay for being the world's reserve currency? I have heard of the argument that in order for USD to be reserve currecy, the rest of the world must own enough USD to store it as reserves. In order for the rest of the world to own enough USD, U.S has to buy more goods than U.S sells to the rest of the world. In other words, run a trade deficit.

Is this a sound economic argument? If no, what are some holes in this argument? If yes, wouldn't the trade tariffs that President Trump is imposing on its trade partners all over the world lead to the end of USD as world's reserve currency?

https://qz.com/1266044/why-does-the-us-run-a-trade-deficit-to-maintain-the-dollars-privileged-position/

This is an excellent question and I will do my best to give you a well thought out answer.

Many observers believe the U.S. dollar (USD) will lose its status as the world's reserve currency. In fact, I got pushback from another forum regarding finance about this. These doomsday dollar folks cite agreements between China and Iran on settling trade in their own currencies rather than US dollars as evidence that the end of the dollar as a reserve currency is near.

You can actually find documentation from the IMF on what are some of the worlds currency that are being held in reserve by the planets nations: Currency Composition of Official Foreign Exchange Reservers (COFER)

Back in 2013 the U.S. trade deficit shrank to $34 billion and it was presented as good news. But if we don't run a trade deficit, that would lead to problems for us, in particular, on U.S. corporate profits. The financial media does not talk about this because it does not understand the connection between our trade deficit and our currency being the world's reserve currency which creates a dynamic that was coined in thee 60s, known as Triffins' Paradox, based on the observations of Belgian-American economist, Robert Triffin.

It was Robert Triffin who pointed out that the country whose currency foreign nations wish to hold (the global reserve currency) must be willing to supply the world with an extra supply of its currency to fulfill world demand for this 'reserve' currency (foreign exchange reserves) and thus cause a trade deficit.

So there always has to be a fundamental imbalance in the balance of payments. Depending on the goal at any given period, it may require an overall flow of dollars out of the United States, while at other periods of time, it may require an overall flow of dollars in to the United States, but net currency inflows and outflows cannot both happen at once.

How sound is this? You will have to look at it for yourself as we have been doing this for almost a quarter of a century now. So we have all been living it since the day we were born. A better question would be, how sound is it for the U.S. to maintain its dollar as the world reserve currency and run a trade surplus. That's a new one, that's one we haven't tried.

This leads us to your last question.

Just like we invoked Triffin's Paradox to explain our current situation, for this new one we can invoke Hobson's Choice.

If you run trade surpluses, you cannot supply the global economy with the currency flows it needs for trade, reserves, payment of debt denominated in the reserve currency and credit expansion, so yes it would lead to the end of the USD as a global reserve currency.

If we no longer possess a global reserve currency, we can't print money and have it accepted as payment. (The euro and yen are quasi-reserve currencies based on the size of the European Union and Japanese economies, but neither acts as the primary reserve and as a result both are vulnerable to currency crises, despite the conventional wisdom that both are on the same footing as the U.S. dollar.)

So trade surpluses on our part are impossible as we hold the global reserve currency.


Recession and Net Export When a country's economy is currently in recession (or has entered a recession), will the net export increase or decrease? What will happen to the major trade partner's net export (will it be the reverse, such that the country's net export decreases, the other's increases)? What is the reason behind the phenomenon?

My hypothesis right now is that recession will lead to a decrease of export (less production due to less demand and the high price of labor), which will lead to the rise of net export of its major trade partner (export - import, import reduces). The major argument against this is that the demand for imported goods in the country that undergoes recession will fall, leading to a fall in export of the trade partner country.

Considering that modern economies rarely experience recessions due to supply shocks (such as spiking oil prices), we should look at this from the perspective of a demand shock, a decrease in spending. This should not have too significant of an impact on the supply of exports. The supply for these depends on foreign demand, theoretically unaffected by the recession in this country thus far. Some firms may produce both for export and for domestic demand, and some of these might need to shut down if prices drop below a certain level, but this should not occur on a large scale. The fall in domestic demand may even be largely compensated for by foreign demand, with a slight fall in price. The "high wages" would be no different from before the recession, and they would eventually fall as the economy comes back to potential output.

In contrast, net imports will definitely fall if aggregate demand does. Considering that spending on these is tied to, well, the same factors influencing aggregate demand, anything which might have induced a contraction of spending on domestic goods would similarly decrease demand for imports.

Given an at worst moderately impacted supply of exports and a massively impacted demand for imports, the net export of the recessionary country would certainly fall (though this may be more ambiguous if there is expansionary monetary policy to counteract the recession, but this might work in the same direction). The major trade partner would, of course, see its net export move in the opposite direction, importing at similar levels and exporting less. The key thing here is that the target country's demand for imports would not be modified.


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

Since the dependent variable is log-wage, I presume this is some form of earnings equation that it is estimated.

To the degree that nominal wages may be correlated with the price level (or some appropriate delfator), using the nominal wages as dependent variable, immediately requires that the (log) deflator be included as an explanatory variable in the right hand side of the equation. This some times is useful, because it essentially tests whether the coefficient attached to the deflator is equal to unity. If it appears to be so, then using the nominal wage with log-deflator in the right hand side is statistically equivalent to use the real wage.

If this coefficient does not (statistically) appear to be equal to unity, it means that, in the presence of the other variables, nominal wages do not correct fully for inflation. In such a case, it is perhaps better to use real wages, and estimates the effect of the regressors on them.

Controlling for years is an indirect way to account for inflation, usually used in hedonic price analysis.


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

It depends on whether the other players' strategies in the initial equilibrium are still best responses to the deviator's new strategy. For example, $(T,L)$ is the unique NE in the game below. Player 1 (the row player) can deviate from $T$ to $B$ without hurting his own payoff, but $(B,L)$ is not a NE, since $L$ is not a best response to $B$ in this game.

\begin{array}{|c|c|c|}\hline
&L&R\\\hline
T&1,1&2,0\\\hline
B&1,0&0,1\\\hline
\end{array}

Of course you can easily construct a game where such a unilateral deviation still leads to a NE. As the game below shows, player 1's deviation from $T$ to $B$ is still without loss of profit, but it changes the NE from $(T,L)$ to $(B,L)$. There are also infinitely many other possible deviations for player 1 if you consider deviations in mixed strategies.

\begin{array}{|c|c|c|}\hline
&L&R\\\hline
T&1,1&2,0\\\hline
B&1,2&0,1\\\hline
\end{array}


What would happen if China called in its debt? I was talking with a friend of mine the other day about Trump putting the 35% tax on all overseas manufacturing. Couldn't this hurt those countries that have plants where US manufacturing comes from? I think, and correct me if I'm wrong, the tax is to encourage businesses to bring their manufacturing back to the US?

I'm not sure how accurate this site is but here is the Top 10 of countries the USA owes money to:

China, Mainland, $1244.0 billion dollars
Japan, $1133.2 billion dollars
All Other, $416.0 billion dollars
Cayman Islands, $260.2 billion dollars
Ireland, $259.8 billion dollars
Brazil, $249.5 billion dollars
Switzerland, $228.7 billion dollars
Luxembourg, $221.8 billion dollars
United Kingdom, $216.5 billion dollars
Hong Kong, $192.7 billion dollars

Looking over this link (which is a little old but I couldn't find anything newer), looks like most of oversea manufacturing by US companies is done in China.

What if China said it wants its money back? Is that possible?

You have to understand how international debt works. These are not loans, but bonds. China buys a US bond for, e.g., 98 USD. This bond is a promise by the US Treasury to pay 100 USD one year from now. China owns a lot of this type of bonds. Once the bond hits maturity, China is paid 100 USD and the thing it typically does with these 100 USD is it buys the same type of bond again. If it decides it no longer wants to hold US debt, it can do one of two things:

First, it could decide to sell all its bonds at market prices to someone who's willing to buy them. This would be a terrible idea for the Chinese, since they'll lose a lot of money in this kind of fire sale. Second, it could just stop rolling over the debt and invest its foreign reserves in other kinds of bonds.

In any case what will not happen is that the US suddenly has to pay back all its debt at once. It will become more expensive for the US to refinance its debt, since the demand for treasuries will go down, but this is more of a long run problem. Also, it is not trivial to find an alternative asset market that can absorb an investment of 1200 billion dollars without prices going through the roof.


Supply/Demand of Smuggling I am attempting a (very) basic analysis of smuggling from one economy to the other (Venezuela to Colombia) - arising from price ceilings ceteris paribus. e1 are the equilibria without intervention (price controls), e2 are the equilibria after price ceilings, and e3 show what I assume the markets would look like if Venezuelans supplied Colombia (by smuggling) where the Venezuelans' profit =

[Colombia p-hat - cost of smuggling - Venezuela p-hat]

The supply curve for Colombia becomes the sum of the Venezuelan and Colombian supply curves above the [Venezuelan price ceiling + cost of smuggling], while there is a movement along the Venezuelan supply curve to the point of [Colombian price ceiling - cost of smuggling].

Is this correct?

Thanks!

You can consider a single competitive firm model with quadratic cost function say $c(y) = \frac{y^2}{2}$. This firm is in Venezuela. Let $\hat{p}_c$ and $\hat{p}_v$ be price ceilings in Colombia and Venezuela respectively. Also, $\hat{p}_c > \hat{p}_v$ indicating the opportunity to smuggle. Also, assume demands are sufficiently high so that the ceilings are binding. Consider competitive suppliers' problem without smuggling:

\begin{eqnarray*} \displaystyle\max_{y\geq 0} && p_vy - \frac{y^2}{2}\end{eqnarray*}
Solving it, we get the supply curve as $y = p_v$.

Given that the price in Venezuela is $\hat{p}_v$, equilibrium quantity in this case will be $y^* = \hat{p}_v$.

With an option to smuggle with the additional cost say $c(z) = \frac{z^2}{2}$, the profit maximization problem is:
\begin{eqnarray*} \displaystyle\max_{y\geq 0, z \geq 0} && p_vy + p_cz - \frac{(y + z)^2}{2} - \frac{z^2}{2}\end{eqnarray*}

This gives us the new domestic supply function as:
$y = 2p_v - p_c$

and the quantity smuggled as
$z = p_c - p_v$

So, equilibrium quantity sold in Venezuela has fallen to
$y^{**} = 2\hat{p}_v - \hat{p}_c$ and the quantity smuggled is equal to $z^{**} = \hat{p}_c - \hat{p}_v$.