The beta delta model What is the $\beta$-$\delta$ model? How does it relate to present bias and the present value calculation?

The $\beta$-$\delta$ model, otherwise known as the quasi-hyperbolic discounting model, is introduced as an alternative to the traditional exponential discounting which suffers the problem of being inconsistent with empirical evidence.

Exponential Discounting

Traditionally, economists use exponential discounting to capture the fact that things in the future has less value compared to things at present. Such a model presumes a constant discount factor $\delta$, which is used to weight utilities in different periods. For instance, the present value of one's utility from consumption over the next $T$ periods can be written as
\begin{equation}
u(x_0)+\delta u(x_1)+\delta^2u(x_2)+\cdots+\delta^Tu(x_T)=\sum_{t=0}^T\delta^tu(x_t),
\end{equation}
where $x_t$ is the consumption/investment decision made at time $t$. If we let $u(x_t)$ be the amount of money earned in period $t$, then the above formula is also the usual way to calculate the present value of a stream of income. From a theoretical perspective, the exponential discounting model has the desirable feature that it produces dynamically consistent choices. That is, choices deemed as optimal today will still be considered optimal at arbitrary points in the future.

Issue with Exponential Discounting

Despite the theoretical appeals of exponential discounting, evidence suggests that this model does not measure well against actual human choices. The classic example involves two sets of choices:

Getting \$100 today vs. Getting \$101 tomorrow
Getting \$100 30 days from today vs. Getting \$101 31 days from today

When presented with these two choices, most people would choose to get \$100 today but would choose to wait one more day for the extra dollar. This is a clear violation of exponential discounting. If people are exponential discounters with a constant discount factor $\delta$, then choosing \$100 today implies
\begin{equation}
u(\$100)>\delta u(\$101).\tag{1}
\end{equation}
But choosing \$101 31 days from today implies
\begin{equation}
\delta^{30}u(\$100)<\delta^{31}u(\$101)\quad\Rightarrow\quad u(\$100)<\delta u(\$101).\tag{2}
\end{equation}
The incompatibility between $(1)$ and $(2)$ suggests that exponential discounting is not a very good descriptive model of people's time preference.

Quasi-Hyperbolic Discounting

The above example illustrates that people have a strong "bias" toward current consumption, or receiving a reward today as opposed to any future date. In other words, the values of all future ($t\ge1$) rewards/utility are downplayed relative to the reward/utility of the current period ($t=0$). Therefore, based on the exponential discounting model, the quasi-hyperbolic discounting model introduces an extra parameter $\beta$ that captures this bias towards the present. The mathematical formulation is as follows:
\begin{equation}
u(x_0)+\beta\bigl(\delta u(x_1)+\delta^2u(x_2)+\cdots+\delta^Tu(x_T)\bigr)=u(x_0)+\beta\sum_{t=1}^T\delta^tu(x_t).
\end{equation}
The parameter $\beta$ is the present bias parameter, as it measure the extent to which future outcomes are weighed relative to the current one. Usually $\beta$ is assumed to be less than $1$, so that future utilities weigh less than the present one. But it is easy to see that if $\beta=1$, then we get exponential discounting as a special case where there is no present bias. With an appropriately chosen $\beta$, we can therefore reconcile the inconsistency in equations $(1)$ and $(2)$.


Difference between direct and indirect utility What is the difference between direct and indirect utility? Following  the advanced microeconomics textbook Jehle and Reny I can not understand either the intuition or the math definition. It confuses me.

Something that may help with the intuition:

U <-  Goods <- Income Prices

The direct utility is derived from the consumption of goods. Said it simply, money, on its own, is almost worthless in terms of utility (setting aside cases where people simply like having money). Goods, on the other hand, generate utility because they can be used or consumed directly.

Now, Goods can be obtained only with money, and based on their prices (how much you can buy). So, indirectly (notice the framework i started with), income does not generate utility, but it does generate utility "indirectly", because it allows us to buy goods.

HTH


Formulas or rules regarding End of Life for vehicle Are there formulas or rules when keeping a vehicle is no longer financially beneficial?
I understand the below needs to be considered:

Every time a purchase is made, sales tax will need to be paid.
Keeping a vehicle longer reduces the number of sales tax
transactions.
A vehicle, especially new vehicles of certain models,
depreciate quickly - exponential depreciation.
The retail book value comes into play as well as the age of vehicle on whether a repair should be made; 10%, 20%, not certain.

There is no one general standardized formula for the value of a car. That is not how prices work. The price of a used car is going to depend on what other people are willing to pay for it, not some depreciation formula that you can just plug numbers into. This inherently means there is some uncertainty in trying to determine the value of a used car.

With that said there are resources out there to approximate what people generally are able to buy/sell a used car for such as the Kelley Blue Book which records the average selling price for models of used cars after a certain number of years. These resources should give you an approximation for what a used car could go for but it will never be exact and is location and time dependent.


Sources on Educational intervention changing consumer preferences? I'm doing some research on how education can change a consumers preference for a given good or service. Im looking for more research papers or books that discuss such a topic.

I've looked around online a little bit and read
The Effects of Consumer Education on Consumer Product Safety Behavior by  Richard Staelin, however I'm looking for more sources on the topic.

Any suggestions?

I found research on this topic from the recent October 2016 issue of the American Economic Journal: Applied Economics. However I could not find the PDF online from the site however I got it from a different source.

Titled as
The Impact of High School Financial Education: Evidence from a Large-Scale Evaluation in Brazil it is learned that its possible to change consumers habits via curriculum design.

  We find significant treatment effects on spending behavior as well. In line with the concepts
  taught in the curriculum, the results show a 2.1-2.5 percentage point greater likelihood of
  comparison shopping before making purchases, and a 3.1-4.1 percentage point greater likelihood
  of negotiating price or payment method prior to purchases by students in treated schools. Further,
  the results show that 16 percent of students in treated schools made a list of monthly expenses as
  part of a budgeting exercise compared to 13 percent in the control schools in follow-up 1. These
  numbers are 17 percent and 14 percent respectively, in follow-up 2. All treatment effects are
  statistically significant at the 1 percent level.

  Overall, these results show a clear improvement in student behavior as a result of the financial education course, in line with concepts taught in the curriculum.

The article concludes

  Financial education in schools is an important policy focus in both developed and developing
  countries, yet its impacts are not well understood. This paper contributes to the literature by
  demonstrating that a financial education program targeted to youth in secondary school can
  improve both knowledge and behavior, as well as influence financial attitudes and preferences.

Excellent research, and a recommended reading.


What determines the exchange rate of two fiat currencies if the supply of each is known? In this blog post, economist Steve Landsburg posed a question about the value of Bitcoin which he didn't know the answer to.

Imagine a future in which Bitcoins (or some other non-governmental
currency) are widely accepted and easily substitutable for dollars, at
an exchange rate of (say) $X$ dollars per Bitcoin.
Then if there are $M$ dollars and $B$ bitcoins in circulation, the money
supply (measured in dollars) is effectively $M + X B$ .
Money demand is presumably $P D$, where $P$ is the general price level and
$D$ depends on things like the volume of transactions and the payment
habits of the community. (If it helps, we can write $D = T/V$ where $T$ is
the volume of transactions and $V$ is the velocity of money.)
Equilibrium in the money market requires that supply equals demand, so
$M + X B = P D$
Now $M$ is determined by the monetary authorities; $B$ is
determined by the Bitcoin algorithm, and $D$, as noted above, is
determined outside the money market.
That leaves me with two variables ($X$ and $P$) but only one equation.
What pins down the values of these variables?

As he suggests in parenthesis, this isn't a problem specific to Bitcoin, it's a general problem for non-governmental currencies that are perfect substitutes for dollars.
So does anyone know the answer to Landsburg's question?  Are there any models that shed light on what determines the exchange rate $X$ and the price level $P$ in a situation like this?

There isn't any good way to rehabilitate the quantity theory when there are other currencies that are perfect substitutes for dollars - so in that sense, there isn't any answer to Landsburg's question. Indeed, the irrelevance of the quantity theory under perfect substitutability - which has always been theoretically clear - has become a practical reality recently, as reserves become a perfect substitute for other short-term nominal assets once the nominal interest rate hits zero.

That said, I'd make two points.

1. Anything less than perfect substitutability rescues the quantity theory.

Suppose we replace the left side of Landsburg's quantity theory equation with the more general form
$$F(M,XB) = PD$$ where $F$ is a homogenous production function that produces aggregate "monetary services" using money $M$ and bitcoins (with value stated in terms of money) $XB$.

Landsburg's equation corresponds to the case of perfect substitutes, $F(M,XB) = M+XB$. In fact, there's another assumption that's implicit in Landsburg's formulation, which is that either $X$ is constant over time or, if $X$ varies, the risk-adjusted expected return on bitcoins relative to money is zero: otherwise, you'd strictly prefer to hold one or the other, whichever gives the highest return, given that they have equal transactional value. I'm going to continue assuming that this assumption holds for simplicity - but keep in mind that in a full-fledged dynamic model, allowing returns to differ and individuals to substitute on this basis might endogenously produce the extra equation that Landsburg seeks.

If money and bitcoins have the same returns, then anyone holding them will want to equate the marginal transactional value of the two, setting $F_M=F_{XB}$. This holds for any relative quantities of $M$ and $XB$ in Landsburg's perfect substitutes formulation, which is why he's struggling, but for general (homogenous) $F$ it will only hold for one ratio $M/XB$ of the two. This will pin down relative demand.

For instance, if $F$ is Cobb-Douglas, with $F(M,XB) = M^\alpha (XB)^{1-\alpha}$, then $F_M = \alpha F/M$ and $F_{XB} = (1-\alpha)F/XB$, and equating the two gives us $M/XB = \alpha/(1-\alpha)$. Suppose $\alpha=1/3$. Then we have $XB = 2M$, and it is trivial to solve for $P$ from $M$ and $D$:
$$F(M,XB)=PD\Longleftrightarrow M^{1/3} (2M)^{2/3} = PD\Longleftrightarrow P = 2^{2/3}\frac{M}{D}$$
Cobb-Douglas is just one parameterization I'm using for illustrative purposes, but we'll similarly be able to solve as long as $F$ has a declining marginal rate of substitution between $M$ and $XB$ - which would be true, for instance, if $M$ and $XB$ were almost perfect substitutes, but not quite. Landsburg's case of perfect substitutes is very much non-generic in this sense: it's probably not true that fiat currency and bitcoins will ever be perfect substitutes in absolutely every application.

By the way, the idea that two forms of currency combine in an imperfectly substitutable way to provide overall monetary services isn't just something I made up - you can see assumptions like this in the literature in a number of places, like equation (3) in Ireland (2011).

2. The central bank can pin down the price level in other ways, even without the quantity theory.

The modern view on monetary policy is that what really matters is the central bank's ability to set the short-term interest rate. Traditionally, this has been done by changing the supply of money through open-market operations, but that doesn't need to be the case. Indeed, Woodford's canonical text shows how it is possible to implement monetary policy even in a "cashless" world where there is no demand for money: the central bank simply pays interest on money. (By the way, this result is hard to escape when you try to microfound the "quantity theory" equation by writing down a dynamic, internally consistent model: you realize that the quantity theory operates in general equilibrium via the response of interest rates to money, and that by manipulating interest rates directly we can get the same outcome.)

Indeed, we're moving closer to Woodford's hypothetical world all the time: for instance, one of the options for the Fed when it decides to raise interest rates in the coming months will be to push up the rate of interest on reserves, while keeping its expanded balance sheet intact.

From this viewpoint, Landsburg's observation just isn't very relevant. The central bank is dedicated to price stability, and it'll enforce this by adjusting interest rates in response to deviations of inflation from trend. If it can adjust interest rates through the traditional method of adjusting $M$ via open-market operations, great. But if it can't do this (because we live in Landsburg's world of perfect substitutability), then the central bank will just adjust nominal interest rates by changing the interest it pays on reserves, and ultimately accomplish exactly the same thing.


The evolution of economic thought in the XX century While I was studying, I stuck into a great debate between what is called "modern macro" and Keynesian macro with a lot of interesting and actual insights. I have already read about "classical economics", I mean Smith, Ricardo and so on but I did not succeed in finding a book/paper talking about the actual debate and its roots.

Can you please suggest me some references in order to better understand the evolution of economic thought in the XX century and to make my own idea about the actual debate going on?

A reference in this topic is Michel De Vroey. He published a new book on A History of Macroeconomics from Keynes to Lucas and Beyond.

This book retraces the history of macroeconomics from Keynes's General Theory to the present. Central to it is the contrast between a Keynesian era and a Lucasian - or dynamic stochastic general equilibrium (DSGE) - era, each ruled by distinct methodological standards.

See also a paper on The History of Macroeconomics from Keynes’s
General Theory to the Present for the Handbook of the History of Economic
Analysis.


Thesis-advisor/student pairs that won the nobel prize I am trying to compile a list of winners of the Nobel memorial prize in economics whose thesis advisor also won the prize.

So far I have

Eric Maskin (advisor) / Jean Tirole (student)

Are there other pairs?

This seemed like a fun exercise, so using just the info on Wikipedia, I was able to compile this:

Honourable mentions, who I classify as economists who have at least two students who have won the Nobel include:

Wilson (Roth and Holmstrom)
Lovell (Prescott and Mortensen)
Tucker (Nash and Shapley)
Cassel (Myrdal and Ohlin)

Another interesting fact worth mentioning is that, while Krugman’s advisor, Dornbusch, did not win the Nobel, Dornbusch’s supervisor, Mundell, did. A similar comment applies so Lovell, who was Leontief's student, and had two students who won the Prize.

More interesting observations: predictably, for the vast majority of these pairs, the advisor won the prize before the student. Exceptions are Leontief and Samuelson; Fama and Scholes; and Hurwicz and McFadden.

Other triplets:

Miller-Fama-Scholes
Leontief-Samuelson-Merton
Leontief-Solow-Akerlof/Diamond/Stiglitz
Leontief-Schelling-Spence

We even have a quadruplet: Kuznets-Friedman-Markowitz-Sharpe.


Will inflation rise or fall when the Fed increase their interest rate? When the Fed lower the interest rate, there will be a rise in GDP and thus a decline in unemployment, which in turn cause the inflation to go up according to the Phillips curve. But Fisher’s equation tells me that real interest rate = interest rate - inflation. So if real interest rate does not change, an increase in interest rate should also cause a increase in inflation, a contradiction.

Any help or comment is appreciated.

Hint:

If you're keeping real interest rates constant in the second scenario, you should keep real interest rates constant in the first scenario.

If you do this, lowering the nominal interest rate will decrease inflation off the bat (by the Fischer's equation) by the same amount as the change in nominal interest rates.


Doesn't the Pareto-extension rule invalidate Eliaz's (2004) unified theorem of social choice? Eliaz (2004) uses social aggregators to provide a unique "meta-theorem" from which Arrow and Gibbard-Satterthwaite follow as corollaries. He defines social aggregators as follows. Let $\mathcal{P}$ denote the set of all n-tuples of linear (thus strict) orderings over the elements of set $X$, where $|X| \geq 3$, and $\mathbf{R}$ a set of binary relations on $X$. A social aggregator is a function $F: \mathcal{P} \rightarrow \mathbf{R}$. A social welfare function is a social aggregator satisfying acyclicality, completeness, and existence of a best alternative; a social choice function takes more work to define, but in short, completeness is only required for at least one alternative which is socially ranked at least as high as all others.
Eliaz then proves that no non-dictatorial social aggregator can satisfy acyclicality, existence of a best alternative, weak Pareto efficiency, and "preference reversal", which is basically an independence requirement by which a reversal of the social relation must follow the same reversal in the preferences of an individual. He then shows that from the conditions above follow all the conditions in Arrow and Gibbard-Satterthwaite, which are thus just special cases of the general meta-theorem.
I have two key questions:

To be a social welfare function à la Arrow, do we not require more than just acyclicality - in particular, transitivity? Is it correct that what Eliaz calls a social welfare function, is actually a social decision function?

If so, isn't Sen's (1969) Pareto-extension rule a counter-example to the meta-theorem? For strict individual orderings, the Pareto-extension rule works as follows: all conflicting profiles (i.e. all those profiles in which there are two $x,y \in X$ and two $i,j \in N$, $N$ being the set of individuals, such that $xP_i y$ and $yP_j x$), then $xRy$ and $yRx$, $R$ being the social relation. In other words, the Pareto-extension rule resolves all conflicts by ties. This rule should satisfy all condition imposed by Eliaz: acyclicality (it is actually quasi-transitive, a stronger condition), existence of a best alternative, non-dictatorship, independence (subsumed by preference reversal), and clearly, weak Pareto efficiency.

Acyclicality as defined by Eliaz is simply the condition that
the values of a social aggregator are transitive. It is different from the usual acyclicity condition according to which a relation is acyclic iff it has irreflexive transitive closure. The formulation of Eliaz is a bit cryptic, but he actually shows in his Observation 1 that his acyclicality implies transitivity. The converse is also easy; the simple details are below. The result of the Pareto extension rule need of course not be transitive.
Formally, acyclicality as defined by Eliaz says that for all $R\in\mathbf{R}$ and for every three alternatives $a$, $b$ and $c$ in $A$, if $aRb$ and $\neg(cRb)$, then $\neg(cRa)$.
But the condition that for every three alternatives $a$, $b$ and $c$ in $A$, if $aRb$ and $\neg(cRb)$, then $\neg(cRa)$ is simply the transitivity of $R$, formulated in a slightly weird but equivalent way.
Here is the simple proof: Assume that $R$ is transitive and $aRb$ and $\neg(cRb)$. If it were the case that $cRa$, then $cRb$ by transitivity, contradicting the assumption. For the other direction, assume that the condition holds and that $cRa$ and $cRb$ holds. We want to show that $cRb$. Indeed, if not then by the condition $\neg(cRa)$, contradicting the assumption.


Subset of Data in a gravity model In my last subject of studies I am analyzing trade costs in a gravity model, e.g. multilateral trade resistance and bilateral trade resistance terms. The gravity model assumes world trade. However, I want to analyse the effect of these trade resistance terms only on a subset of countries, , e.g. trade costs of war on LDC's. I therefore would drop all developed countries as exporters and would only analyse LDC's as exporters. Developed countries would be included as importers though. Would it be statistically misleading or would that regression work ?

This regression may work. Two issues, however.

How do you identify the "trade costs of war" given that trade and war are potentially endogenous?
Dropping the developed countries, which are the main exporters, may affect the estimates of the bilateral and multilateral trade resistance terms. But this is easy to check by comparing the estimates with and without the main exporters.


Regarding the units of the shift produced by subsidies on supply curve I am giving my first steps on microeconomics and I can't fully understand why by applying a per unit subsidy, the supply curve is shifted by a fixed amount. In wikipedia's words:

  Marginal subsidies on production will shift the supply curve to the right until the vertical distance between the two supply curves is equal to the per unit subsidy

But let's say that my supply curve is given by
$$ Q_s = -200 +3 \cdot P $$
If a per unit subsidy is applied, the new supply curve is now given by:
$$ Q_s = -200 +3 \cdot (P+50) $$
But if the unit of the subsidy is $[\frac{\$}{units}] $ the units of the equation don't match:
$$ Q_s [units] = -200[units] +3[\frac{units}{\$}] \cdot (P[\$]+50[\frac{\$}{units}]) $$
So shouldn't a per unit subsidy change the slope of the supply curve rather than shifting it?

The confusion stems from the fact that the price is also a $\frac{\$}{units}$


Identify whether a good is giffen good or not and under what condition Given the following partial information about a consumer's purchases.He consumes only two goods.
In year 1, $p_1^1=p_2^1=100,x_1^1=x_2^1=100$

In year 2, $p_1^2=100,p_2^2=80,x_1^2=120$

Over what range of quantities of good 2 consumed in year 2(i.e,$x_2^2$) could we conclude that good 1 is an inferior good.

I feel confused because I'm not informed the choices after a change in wealth under the same price system, neither under $(p_1^1,p_2^1)$ nor $(p_1^2,p_2^2).$

But the solution given by my TA is :
Since $x_1^1<x_1^2$, so we need $p^2x^1>p^2x^2$, that gives $0< x_2^2< 75$. I don't know where this argument comes from and whether it is true or not.

Any help are going to be appreciated.

Since the question is asking for clarification on a given answer, I don't think this question necessarily needs to be closed. To address your concerns:

You will recall Walras' Law states $p \cdot x = w$. That is, you spend all your money buying things, given some regularity conditions. So just figure out how much was spent in year 1 and that will give you wealth for that period. For year 2, you'll note that depending on the range for $x^2_2$, it will imply the consumer having different amounts of wealth. That will give you the information you need to find where good 1 is inferior.

It might be helpful to think about what ranges of good 2 would violate WARP, and what the ranges above and below it would mean. Hope this helps.


Is there any specific significance of inverse demand? Why do we need separate form of demand? Where do we use inverse demand form? concept only.

Inverse demand maps from quantity to value. It is useful to identify how much some units of the good are worth to the consumers. The central welfare concepts of consumer's and producer's surpluses rely on inverse functions in their definitions.

In addition there are special cases (e.g. perfectly inelastic demand) where defining inverse demand is just easier.


Risks asscoiated short term stimulus as interest rates approach zero TL;DR
Government interest rates are approaching zero.

What are the risks to borrowing large sums in the current enviroment? Would inflation occur?
Full Story
I was recently reading an article about Rishi Sunak's (UK Chancellor) aim to rein in public spending in the UK post pandemic, the implication being he was planning to do this much earlier than other countries.
Since the interest rates are so low borrowing appears very cheap. Conventional gilts (fixed interest) make up 75% of the UK government portfolio and the interest rates on these are approaching zero (see graph above). There is strand of thought that government ought to borrow lots while it can, this opinion appears to be widely held. The spending so far is short term stimulus such are furlough payments, not medium/long term investment.
Inflation
A turbo charged economy with low unemployment could lead to higher demand, higher prices and then inflation. However for countries hit hard by the pandemic unemployment is high (5% in the UK) and likely to increase as furlough measures are removed.
The Question
What are the risks to continuing to borrow large amounts ($100Bns)to spend on short term stimulus right now?
What economic reason would there be to not do so?

The potential risk of borrowing too much now is that interest rates will be higher when the debt has to be rolled over. Even though it is completely correct to say that most government securities have fixed interest rate, most of these securities are not perpetual, meaning they expire at some point.
For example, as mentioned on the UK Debt Management Office website:

Conventional gilts also have a specific maturity date. In the case of 1½% Treasury Gilt 2047 the principal will be repaid to investors on 22 July 2047. In recent years the Government has concentrated issuance of conventional gilts around the 5-, 10- and 30-year maturity areas, but in May 2005 the DMO issued a new 50-year maturity conventional gilt. In June 2013, following market consultation the DMO issued a new 55 year maturity conventional gilt.

This carries some potential risk. For example, suppose for the sake of argument government could borrow now $£ 1000$ with coupon rate $0\%$ (coupon rate is essentially the interest paid on face value of fixed income security), for 5 years. That is great deal now but in 5 years government will face the following problem, it will either have to repay the debt (which could be difficult to do for country with high level of debt) or instead roll it over meaning the government issues another $£ 1000$, but this time if interest rates are higher and government is forced to issue it with, let us say $20\%$ coupon rate that would be a problem because suddenly the cost of servicing debt to the government would skyrocket.
This being said, it is worth noting that even though the above is potential risk that should be taken seriously, most economists believe that governments should borrow more when the interest rates are low, especially if they do so long term (e.g. 10, 30 or 50 years) or even better some argue they could start issuing perpetuities i.e. debt instruments where principal never has to be repaid (see discussion in Corsetti, Erce, Pascual 14 May 2020).  This is because issuing long term debt or perpetuities locks the low interest rates on that particular debt for very long time or indefinitely meaning there would be plenty of time to consolidate public finances if interest rates were rising sharply. In addition, government has also other venues how to handle debt such as monetization of the debt although that can have some serious disadvantages as well but discussing that is beyond scope of this answer. Consequently, while it is definitely real risk as you pointed out in the question itself most economists would argue governments should take advantage of these low rates while they can.


Does Game theory consider opportunity cost? Morton Davis in his book Game Theory: A non-Technical introduction brings the
following example of a non-zero sum game (pg.73) :

A Buisness Partnership
A builder and an architect are jointly offered a contract to design and construct a building. They are offered a single lump sum as a payment and are given a week to decide whether they accept. The approval of both is required, so they must decide how the lump sum will be divided. The architect writes to the builder suggesting that the profits be divided equally. The builder replies, committing himself to the contract in writing provided he receives 60 percent of the profits. He informs the architect moreover, that he is going on a two week vacation, that he cannot be reached, and it is up to the architect to accept the contract on these terms or reject it entirely.
The architect feels like he is being exploited. He feels that his services are valuable as the builder's and that each should receive half the profits. On the other hand, the probable profit is large, and under different circumstances, he would consider 40 percent of such a total an acceptable fee. Should he accept the builder's offer? Note that the builder has no more options; on the architect has the choice- to accept or reject the contact. This is reflected in the payoff matrix shown:
$$\left[\begin{matrix}(0.40,0.60)\\(0, 0)\end{matrix} \right]$$

My question :
The way the case seems to be presented is that the architect is forced to choose 40 percent in light of the alternative where there is no profits to be gained. What about the architect's opportunity cost? Isn't there what to be gained from the architect when refusing this split of profits in a 40-60 split as far as opportunity cost in concerned?

Recall that Oppurtunity Cost is referred to the benefit forgone by choosing the other option.

In your example of a single player game, opportunity cost exists since the architect is completely in control of the benefit he receives. In this case the opportunity cost for signing the contract is 0 (and conversely -40 for not signing the contract).

However this is only applicable in a single person game.

In a case where the business owner and Architect were actively negotiating, it would appear that there would not be any practical ramifications for considering opportunity cost because the payoffs change depending on the other player and can only be seen after the fact.

for example consider a single period 2x2 game such that:
$$\left[\begin{matrix}(10,5)&(2,2)\\(2,2)&(5,10)\end{matrix} \right]$$

From the horizontal/vertical player's position his payoffs range from 10,5 and 2. He does not choose with respect to costs, he chooses based on what he thinks the payoffs will be.

To answer the broader question which  you are probably wondering about.
Opportunity cost is only considered when a buy in for a specific game is necessary

You'd have to consider expected value of a game compared to the cost. (however that only provides a fair price when the game is played infinity, you would also have to consider how many times you'd have to play a game and end up with a positive profit) using this formula:

$$n=\left(\frac{1.96\sigma}{p-\mu}\right)^2$$

I suggest reading up on Martingales and the St. Petersberg Paradox for more info.


Help with CES Utility Function exercise I am attempting to solve the following CES Utility Function problem:

However, I am running into issues when I get to 3).

For 1) I have $K = \left(\frac{\omega p_1}{p_2}\right)^{\frac{1}{p+1}}$

For 2) I get $X_2^M = \frac{m}{\frac{p_1}{K}+p_2} $

For 3) I find $\lambda^* = (K^\rho + \omega)^{-\frac1p-1} \cdot \omega \cdot p_2^{-1} $

and $v(p_1, p_2, m) = \left(\left(\frac{m}{p_1+Kp_2}\right)^{-\rho} + \omega(\frac{mK}{p_1+Kp_2})^{-\rho}\right)^{-1/\rho}$

I then divide $\lambda^*$ by $v(p_1, p_2, m)$, but when I do so I can't seem to fully cancel out $p_1,p_2,m,K$ and $\rho$ which I believe I would have to do to prove that they are proportional. I'm not sure if the issue is with my $\lambda^*$, my $v(p_1,p_2,m)$ or both...

Additionally, for 6) how does one demonstrate homogeneity of a given degree?

For question 3, I'm sure there are simpler solution than mine. I provide this version for your reference.

By definition,
\begin{align}
\lambda^* &= \frac{\frac{\partial u}{\partial x_1}(x_1^M)}{p_1} = \frac{\left[(x_1^M)^{-\rho}+ w(x_2^M)^{-\rho}\right]^{-\frac{1}{\rho}-1}(x_1^M)^{-(\rho+1)}}{p_1}\\
\\
v(p_1,p_2,m) &= u(x_1^M(p_1,p_2, m), x_2^M(p_1, p_2, m)) \\
& = \left[(x_1^M)^{-\rho}+ w(x_2^M)^{-\rho}\right]^{-\frac{1}{\rho}}
\end{align}
So
\begin{align}
\lambda^* &= v(p_1,p_2,m) \frac{1}{p_1\left[(x_1^M)^{-\rho}+ w(x_2^M)^{-\rho}\right](x_1^M)^{\rho+1}}\\
&= v(p_1,p_2,m) \frac{1}{p_1\left[x_1^M+ w\left(\frac{x_1^M}{x_2^M}\right)^{\rho+1}x_2^M\right]}\\
& = v(p_1,p_2,m) \frac{1}{p_1\left[x_1^M+ w\left(\frac{1}{\kappa}\right)^{\rho+1}x_2^M\right]}
\end{align}
Plug in the expression for $\kappa = \left(\frac{wp_1}{p_2}\right)^{\frac{1}{\rho+1}}$ to the equation above, we have

\begin{align}
p_1\left[x_1^M+ w\left(\frac{1}{\kappa}\right)^{\rho+1}x_2^M\right] &= p_1\left[x_1^M+ w\frac{p_2}{wp_1}x_2^M\right]\\
& = p_1x_1^M + p_2x_2^M\\
& = m
\end{align}
so $$\lambda^* = \frac{v(p_1,p_2,m)}{m}$$

To show a function $F(x_1, x_2, ... x_n)$ is homogenous of degree $k$, simply show that $$F(kx_1, kx_2, ...kx_n) = \lambda^kF(x_1, x_2, ... x_n)$$ For $\forall \;\lambda>0$


What is the difference between intensive margin and extensive margin in labor economics? What is the difference between intensive margin and extensive margin in labor economics, or general RBC model, where we talk about labor-hours supplied changing with extensive margin or intensive margin?

In Labor Economics, "Extensive margin" refers to "how many people work". "Intensive margin" refers to "how much a given number of people work, on average". To copy from a freely available recent study by Blundell, Bozio and Laroque 2011,

  "...we split the overall level of work activity into the number of individuals in work and the intensity of work supplied by those in
  work. This reflects the distinction between whether to work and how
  much to work at the individual level and is referred to, respectively,
  as the extensive and intensive margin of labour supply. At the
  aggregate level the former is typically measured by the number of
  individuals in paid employment and the later by the average number of
  working hours."

Evidently, it is an important distinction, especially when one wants to analyze changes in employment, measured say in total number of hours worked: Say, did they increase? Why? Because more people work, or because the same number of people work more? And if the answer is "both", then what portion is attributable to a change in the intensive margin, and what portion to a change in the extensive margin? (this is why the word "margin" is used).

Of course "intensity" as a word has a more general meaning, as for example the one mentioned in another answer here -it may be the case that people work "faster" and so in the same time interval, they produce more. Such changes are usually put under the concept of "changes in efficiency" (for example in Growth theory this is how they are called). In Labor Economics the terms have the meaning given above.


Doubt on the meaning of real money balances Mankiw defines real money balances, $\frac{M}{P}$, to be the quantity of goods and services a given amount of money can buy. On page 88 of Macroeconomics 7th edition, he illustrates the concept with the following example:

  Real money balances measure the purchasing power of the stock of
  money. For example, consider an economy that produces only bread. If
  the quantity of money is $\$10$, and the price of a loaf is $\$0.50$, then
  real money balances are $20$ loaves of bread. That is, at current
  prices, the stock of money in the economy is able to buy $20$ loaves.

It is very clear to me what real balances represent in such a simple example. However, I suppose in real life $P$ would be expressed as some index, right? If $P=1.52$ is the implicit price deflator for GDP in some year, for instance, and the quantity of money in the economy is $\$1.000$, what exactly does $\frac{M}{P}=\frac{1000}{1.52}\approx657.9$ represent? How do we interpret that number? Thanks in advance.

The level of a price index (like the GDP deflator) is essentially arbitrary. The usual choice is to set the reference date to 100, but it could just as easily be set to 1. So the level of the real money balance is essentially an arbitrary number. If you were using it in an economic model, you would need to adjust the scaling in the functions to account for this.

For an interpretation, pick a base time $t$. You then divide the monetary aggregate $M(t)$ by annualised nominal GDP at time $t$. This converts the money holding into a fraction of annual GDP. Since GDP is a flow, it has units of \$/(year), and the money number has units of \$. The ratio of the division has units of years. The interpretation is that the ratio is the number of years worth of the goods and services that go into the “GDP basket” that the monetary aggregate could buy. (For example, if the monetary aggregate was 0.5 of annual nominal GDP, it can buy 6 months worth of whatever goes into GDP.)

Let us fix the base period $t$. If we rebase the deflator $P(t)$ so that it equals annualised nominal GDP at time $t$, the “real money balance” using that deflator gives us that same ratio discussed above. (Since the level of the deflator is arbitrary, we can multiply the the entire time series by a constant, and nothing much changes. So in this case, set the scaling constant to be equal to the level of nominal GDP at tine $t$ divided by the value of the original deflator at time $t$. The result is that the new deflator is equal to nominal GDP at time $t$.) So we have an interpretation for the real money balance for period $t$.

If we go to the next period ($t+1$), the interpretation gets more complicated. The problem is that the mix of goods and services in GDP changes. So it may be that I am over-simplifying things here. (This does not happen for bread, which is presumed to be uniform over time.)

My interpretation of the real money balance is that it is volume of real GDP (in years) that can be purchased by the money balance $M(t+1)$ using the prices prevailing at time $(t+1)$, but using the time $t$ real GDP basket. So if moves to 0.75, that means that the money balance at time $t+1$ could buy 9 months worth of the goods and services that were produced at time $t$. However, this will probably not correspond to 9 months worth of the annualised production at time $t+1$, since real GDP may itself have grown (or shrunk, if there was a recession).

One can argue that this interpretation is complicated, but it reflects the difficulties with the definition.


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

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

Brian is right. The claim was that, if you took the cost per square meter of land area in Tokyo based on market rates, the Imperial Gardens in Tokyo were worth more than California.

Source: http://articles.chicagotribune.com/1989-11-19/business/8903110641_1_land-prices-national-land-agency-rockefeller-center

Obviously, this is a classic example of a fallacy that arises from extrapolation— if that additional land area had been made available for sale, it would have significantly increased supply and caused prices to drop accordingly.


How to interpret Whited Wu index (WW-index) I want to study financial constraints on companies of different groups and for that I try to use Whited-Wu index:
WW = - 0.091CF - 0.062DIVPOS + 0.021*TLTD - 0.044*LNTA + 0.102*ISG - 0.035*SG
Where TLTD is the ratio of the long-term debt to total assets; DIVPOS is an indicator that takes the value of one if the firm pays cash dividends; SG is firm sales growth; LNTA is the natural log of total assets; ISG is the firm’s three-digit industry sales growth; CASH is the ratio of liquid assets to total assets; CF is the ratio of cash flow to total assets (see Whited and Wu. Financial Constraints Risk. 2006).

Although I managed to compute it, I have difficulties with results interpretation. My idea was to compare different companies/groups of firms using this index. As written in one of the papers, "higher index values can be associated to higher need of external capital". So if in 2010, for "Toyota" I got value -0.9 and for "Fuji Technica Inc." -0.53, may I conclude that Toyota is more financially constrained (requires more external capital)? Similarly, if I get two industries - food and car producing - then the first have higher values of WW.

This is equation $(13)$ of Whited, T. M., & Wu, G. (2006). Financial constraints risk. Review of Financial Studies, 19(2), 531-559.

It is empirically estimated as regards the specific coefficient values. The important question is,

  What is the left-hand-side?

Looking at eq. $(12)$ of the paper the left-hand-side of $(13)$ is $\lambda_{i,t+1}$ which in turn is part of

$$\Lambda_{i,t+1} = \frac {1+\lambda_{i,t+1}}{1+\lambda_{i,t}}$$

$\Lambda_{i,t+1}$ is discussed in the middle of p. 536 (between eq. 5 and eq. 6). As the authors write,

  If the outside equity constraint is binding, the effects of external
  finance constraints show up in the term $\Lambda_{i,t+1} =
 (1+\lambda_{i,t+1})/(1+\lambda_{i,t})$, which is the relative shadow
  cost of external finance. In the absence of finance constraints,
  $\Lambda_{i,t+1}=1$. On the other hand, if the equity constraint
  binds, then generally $\Lambda_{i,t+1}\neq1$, unless $\lambda_{i,t+1}
 = \lambda_{i,t}$. As also noted in Gomes, Yaron, and Zhang (2004), this last observation implies that finance constraints can only affect
  investment if they are time varying. It is the shadow value of the
  constraint today, relative to tomorrow, that is important.

So $\lambda_{i,t+1}$ is the shadow cost of external finance at period $t+1$. Near the end of p. 538 the authors write

  The higher $\lambda_{i,t+1}$, the greater is the effect of finance
  constraints.

This is translated as "the higher $\lambda_{i,t+1}$, the more difficult (or costly) is for a firm to obtain external financing". It does not appear to relate to whether it needs more external financing or not.

Moreover, as the authors write in p. 540, it being a shadow value, it must be non-negative. So what do you make of the fact that you obtained negative values?


A profit maximization problem (whole problem has been solved, I just have question about interpretation) I would like to discuss with you about the following production function.

$$y=f(t_m, t_l)=\rho t_m^m(n+t_l)$$

where $0<m<1 $ and $n>0$ are fixed parameters.

$t_m$ is manager time.

$t_l$ is labour time.

The manager know the production function freely.

Also let’s define $w_m$=manager’s wage and $w_l$=labour’s wage for $w_m>w_l>0$

$\rho$ is the good’s market price.

Extra Notes:

• the manager’s outside option= the  manager wage in the economy

•the manager is going to  run his own company if he establishes one.

So far, I have defined the production function.

How I have two questions that I would like to discuss with you.

————————

How can I interpret the parameters $n$ and $m$? It is easy to interpret them mathematically, but I could not decide how to make a comment about these parameters in economic terms?

When I take derivatives

$\partial y/\partial t_l= t_m ^m>0$ which means that as labour’s time increases, production increases, revenue increases and so profit increases.

$\partial y/\partial t_m= m t_m ^{m-1}(n+t_l)>0$ which means that as manager’s time increases, production is diminshingly increases (since $m-1<0$) and revenue diminishingly increases so profit diminishingly increases. ( I did this comment. But I don’t think it is enough or correct in economic view. How can I say it correctly?)

———————-

My important question is that!

Under Which conditions does the manager establish a company and decide to enter the industry?

For that, I firstly establish the manager’s decision problem as follow:

Revenue = $\rho y= \rho t_m^m(n+t_l)$

Cost= $t_m w_m + t_l w_l$

Profit = $\pi = \rho t_m^m(n+t_l) -( t_m w_m + t_l w_l)$

So his decision problem:

$$\max \rho t_m^m(n+t_l) -( t_m w_m + t_l w_l)$$

Subject to $w_m>w_l>0$ and $0<m<1$ and $n,p>0$

When we solve it

$\partial \pi/\partial t_m= \rho m t_m ^{m-1}(n+t_l) -w_m=0 $

$w_m= \rho m t_m ^{m-1}(n+t_l)$

$\partial \pi/\partial t_l=\rho t_l ^m-w_l=0$

$w_l= \rho t_m ^m$

So we know that $w_m>w_l>0$

$$ \rho m t_m ^{m-1}(n+t_l)> \rho  t_m^{m}$$

$$n+t_l>{t_m\over m} $$

I only find this condition in order to establish a company. ( I am not sure but I hope it is true) But I cannot say something about it in economic view.

I solved everything, just discuss what I did. Is it correct or false? Or how can I interpret them in economic aspect?

Thanks a lot.

EDIT

From the above maximization problem, I obtained the following solutions:

And from $w_l= \rho t_m ^m$

I get $$t^*_m=(w_l/\rho)^{1/m}$$

From $w_m= \rho m t_m ^{m-1}(n+t_l)$

I get $$t^*_l= {w_m\over m}p^{1-m/m}w_l^{1-m/m}-n$$

When I insert these two $t^*_l$ and $t^*_m$ into the profit function, I get

$$\pi^*=w_l^{1/m}w_m \rho^{1-m/m} {1\over m} (2-mp^{1/m-1})-nw_l$$

Then, when I compare this with the outside option $w_m$, then I get

$$\pi^*=w_l^{1/m}w_m \rho^{1-m/m} {1\over m} (2-mp^{1/m-1})-nw_l>= w_m$$

But this result doesn’t make sense. I could not make any reasonable interpretation.

Your production function is basically a Cobb-Douglas function of the form $y=A(t_m-a)^\alpha(t_l-b)^\beta$. Therefore, the parameters $\alpha$ and $\beta$ measure the intensity with which inputs are needed for production. The smaller the value of such parameters, the smaller the marginal productivity of the inputs is. In your context, the company is more labor intense than managerial intense, since $\alpha=m<1$ and $\beta=1$. Finally, the parameters $a$ and $b$ measure the minimum level needed by the company of each input in order to operate. In your case, $a=0$ so the company needs a management to operate. However, $b=-n$ so the company can produce even if $t_l$ was equal to zero. Notice that the larger the $n$, the less the company needs of labor.

In fact, though you found two equations that characterize equilibrium I think you want to solve for $t_m$ and $t_l$ in terms of parameters only (you will see that if  $n$ is very large, the optimal $t_l$ is zero. After that, I would plug in the results into the profit function, that will tell you how much profit the manager will get if he decides to enter the industry, and you can compare that to the outside option.

Solution:

For the manager to operate the company, the profit function must be larger than the outside option. I will assume that if she operates the company, since she is the manager, she does not need to pay herself, so the costs are only $w_lt_l^*$, but her outside option is equal to $w_mt_m^*$, the labor income she will earn working for a similar company  that would demand the optimal management labor.  Therefore, she operates the company iff the profit $\pi =\rho t_m^m(n+t_l)-w_lt_l-w_mt_m\geq 0$.

Case 1: (Assume that $t_m^*,  t_l>0^*$)

Solving the FOC's, we get $$t_m^*=\left(\frac{w_l}{\rho}\right)^{\frac1m} \qquad t_l^*=\frac{w_m}{m \cdot w_l}\left(\frac{w_l}{\rho}\right)^{\frac1m}-n$$

$$\pi^*=\frac{w_m}{m}\left(\frac{w_l}{\rho}\right)^{\frac1m}-w_m\left(\frac{w_l}{\rho}\right)^{\frac1m}-w_l\left(\frac{w_m}{m\cdot w_l}\left(\frac{w_l}{\rho}\right)^{\frac1m}-n\right)=w_ln-w_m\left(\frac{w_l}{\rho}\right)^{\frac1m}$$
Therefore, $\pi^*\geq 0$ iff  $$w_ln\geq w_m\left(\frac{w_l}{\rho}\right)^{\frac1m}$$ However, we assumed that $t_l^*>0$ so
$$\frac{w_m}{m}\left(\frac{w_l}{\rho}\right)^{\frac1m}\geq w_ln$$

The two inequalities can hold since $1 > m$. These are necessary conditions for the manager to operate the company and demand strictly positive labor. I would interpret them as $w_ln$ needs to be intermediate.

Case 2: ($t_m^*>0$ and $t_l^*=0$)

This case occurs if
$$\frac{w_m}{m}\left(\frac{w_l}{\rho}\right)^{\frac1m}\leq w_ln$$
Notice that (after doing some algebra) the optimal profit function $\pi^*$ is still bigger than zero iff
$$w_ln\geq{w_m}\left(\frac{w_l}{\rho}\right)^{\frac1m}$$
In this case, if the first inequality is satisfied, the second holds too.

Conclusion Putting the two cases together we conclude that the manager operates her company if and only if
$$w_ln\geq{w_m}\left(\frac{w_l}{\rho}\right)^{\frac1m}$$
She will sometimes hire workers in her company (if $w_ln$ is not  too large) and sometimes she will not.


How do the factors of production map to the GDP identity? How do the 4 factors of production (nature / capital / labour/ entrepr.) map to the GDP components in:
$$Y=C+I+G+(X-M)$$

To me it seems that all factors map to all GDP components, simply because it's fully a different perspective to breakdown the GDP. Is that correct / why?

thanks!

They all map through production function to output $Y$. Since output is produced from these factors we have

$$Y=f(K,L,E,N,...)$$

Where, $K$ would capital, $L$ labor, $E$ would be entrepreneurship and $N$ nature - you can also include any arbitrary number of factors and also note while entrepreneurship is in some textbooks considered factor, nature is often just included under the land label.

The right hand side of the identity is all determined by output.

Consumption is determined by output as its function of disposable income based on output. A simple undergraduate example would be:

$$C=c_0+c_1(Y-T)$$

Where $c_0$ and $c_1$ are parameters $Y$ is output and $T$ taxes. You can have more complex consumption functions but they will all be functions of $Y$.

Investment $I$ depends on the $c_1$ parameter which determines what proportion of income people save. That is $(1-c_1)Y=S$ where $S$ is saving and $I=S$ (assuming balanced budget).

$G$ is again determined by the output - in the long run government can only spend maximum what the society can produce and what government can extract from society through taxes $G=T$.

$X-M$ tracks the movement of some of the home output abroad and import of some of the foreign output.

So to sum up, the factors of production map to GDP as they through production function map to $Y$ and the right hand side of the equation is just all determined by what $Y$ is.


Why is price dispersion from Inflation called relative price “distortion”? I know what relative price is and that it fluctuates more frequently in times of Inflation. But what I don’t understand is why it is called “distortion” when relative price dispersion is caused by inflation.

According to various textbooks such as Mankiw’s, relative price is what enables rational consumer decisions and effective resource allocation, but inflation leads to its “distortion” which results in resource misallocation.

Now “distortion” usually means a phenomenon that misleads people into making wrong decisions. But where does distortion exist in relative price fluctuations? isn’t it natural for people to buy more goods that increase in terms of relative price, and buy less that decrease in relative price?

I don’t understand what bad decisions people are making here, and why it leads to resource “misallocation”.

Even if there isn’t inflation, relative price fluctuation exists all the time, and consumers always make decisions based on that. We don’t really call THAT a distortion - it’s a perfectly normal thing that causes a substitution effect which makes us buy more things that are relatively cheaper. So wouldn’t decisions based on relative price usually actually lead to better resource allocation?

So my question is, what “distortion” is happening when relative price fluctuations happen from inflation, and why does that lead to “resource misallocation”? Is there an excess supply or excess demand that results from people taking action based on relative price fluctuations? If there isn’t, why is it resource misallocation?

I would really appreciate it if someone could give me a good explanation on this. I’ve tried to solve this curiousity for days searching the internet and stuff but I’ve been unable to find satisfying answers. Detailed examples would be extremely helpful :)

The word "distortion", (as used in e.g. the Ramsey–Boiteux pricing), is not intrinsically negative.

It simply means that people change their consumption behaviour because of changes in price(s).

For example, a tax on oxygen would not (and cannot)  be distortive because people have no choice but consuming oxygen.

A contrario, a tax on tabacco is distortive, and is actually precisely implemented because of this very trait: it will change the consumption behaviour of smokers.

Put differently, the notion of distortion is strongly related to the notion of price elasticity.

Also, constraining markets equilibrium can generate deadweight losses, which is likely the reason why people think of the word "distortion" as negative. Is changing behaviour via price signals negative per se? Is trying to make people quit smoking negative per se ? No.

The word "distortion" is probably one of the most misconceived/misused notion in economic theory, especially when it is used in the political sphere. But originally it has, I repeat, no negative connotation. And I really think that this is how Mankiw uses/perceives it.

  Why is price dispersion from Inflation called relative price “distortion”?

It is called so because consumption behaviors do not change if all increases of prices in the economy are of the same relative magnitude $\iff$ the dispersion is null. E.g. a tax on, say, tobacco, has to be distortive to be useful, i.e. it has to be greater than inflation, even if such intervention can actually generate deadweight losses.


Does Russia Prevent Gold Exports? The Sirius Report tweets:

  Surprises me how anyone imagines that #Russia only has 1800+ tons. Just look at the fact that they never export #gold production and what they have annually produce for years. That is just for starters,

Soviet Union aside, from wiki, we see that gold production in Russia (graph) seems to have stayed above 100 metric tons a year (minimum of 100 x 20 years would be 2000).  I can't find any support for "Russia doesn't allow gold exports" or that they've ever done this, though it's possible they did this during the Soviet Era.  I can find Russian gold coins (latest year) on GovMint, so it seems like they are allowing non-Russians to buy gold, or is this gold from other countries?

Is there any evidence that Russia does not allow gold exports and circumstances which may warrant exceptions?

No, there is no such evidence, because Russia does export gold, though it also adds to its reserves

For example Sputnik News (established by the Russian government-controlled news agency Rossiya Segodnya) reported

  Exports of fine gold from Russia increased 2,5 times to 56,6 tons (1,82 million oz) last year, compared to 22,4 tons in 2016, according to the Russian State Assaying Chamber under the Ministry of Finance.

  ...

  Russia's precious metals refineries reportedly produced 306,9 tons (9,867 million oz) of gold in 2017, which is 6,4 percent more than 288,6 tons produced in 2016. 18,4 percent of all the gold produced in the country was exported, while the rest 224 tons of the metal were purchased by the Central Bank of Russia to add to the country's gold and foreign currency reserves, RIA Novosti reported.

  ...

  "The exports (of gold) in 2017 were not as high as they were in 2014 — 140 tons", the expert told RIA Novosti.


Simple Regression With Dummy Variable Consider a simple linear model:

$Y = \beta_1 + \beta_2 MALE + u$

where $MALE$ is a dummy variable. $MALE = 0$ if female, $MALE = 1$ if male.

A model is fitted:

$\hat{Y} = \hat{\beta_1} + \hat{\beta_2} MALE$

$\bar{Y_F}$ and $\bar{Y_M}$ are the sample means of $Y$ for females and males respectively.

Prove that:

$\hat{\beta_1} = \bar{Y_F}$, $\hat{\beta_2} = \bar{Y_M} - \bar{Y_F}$

If the points are plotted in a scatter block, there will be two vertical clusters of points at $MALE = 0$ and $MALE = 1$, as shown:

It seems intuitively obvious that the total residual sum of squares ($RSS$) is minimized by minimizing the $RSS$ separately for the female and male points. This is achieved by fitting a point at the mean of these points, $\bar{Y_F}$ and $\bar{Y_M}$. Fitting a line between these point yields the correct values for $\hat{\beta_1}$ and $\hat{\beta_2}$.

I wish to prove this algebraically.

Find $\hat{\beta_2}$:

$$\hat{\beta_2}=\frac{\Sigma(Y_i-\bar{Y})(MALE - \overline{MALE})}{\Sigma(MALE - \overline{MALE})^2}$$

Assuming m males in a sample of n people, $$\overline{MALE}=\frac{m}{n}$$

We can say:

$$MALE - \overline{MALE}=\begin{cases}-\frac{m}{n} & \text{if }MALE=0\\\\\frac{n-m}{n} & \text{if }MALE=1\end{cases}$$

With some algebra, the numerator of $\hat{\beta_2}$ becomes:

$$\Sigma(Y_i-\bar{Y})(MALE - \overline{MALE})=\frac{m(n - m)}{n}(\bar{Y_M} - \bar{Y_F})$$

The numerator of $\hat{\beta_2}$ becomes:

$$\Sigma(MALE - \overline{MALE})^2=\frac{m(n - m)^2 + m^2(n - m)}{n^2}=\frac{m(n - m)}{n}$$

Dividing the two gives the correct answer:

$$\hat{\beta_2}=\bar{Y_M} - \bar{Y_F}$$

Find $\hat{\beta_1}$:

$$\hat{\beta_1}=\bar{Y}-\hat{\beta_2}\overline{MALE}=\frac{m\bar{Y_M}+(n - m)\bar{Y_F}}{n} - (\bar{Y_M} - \bar{Y_F})\frac{m}{n}=\bar{Y_F}$$


Vocabulary/Name for Utility of a Set of Choices I am trying to find if there is some litterature or definition of the concept of the Utility of a set of choices. My google searches return nothing, and I expect it is because I do not know the right word.

Here is an example to illustrate what I am looking for.

Consider the following items; a very nice sport car, Car1, the same model of car, only without some options such as no A/C and slightly worse seats, Car2, and a worn off pickup, Truck.

Say that all those vehicles have some associated utility, say

u(Car1) = 500, u(Car2) = 490, u(Truck) = 100

While Car2 is very good in isolation, it is dominated by Car1 and very unlikely that anyone would pick Car2 over Car1. The Truck, on the other hand, has a low value but might be picked over Car1 under some circumstances.

Hence, the utility of the set of choices {Car1, Truck} should be higher than the value of the set {Car1, Car2} even if it contains lower quality items as the truck might actually be helpful.

The assumption here is that the single value of utility associated with the item does not tell us exactly how the user makes its choice. We could assume for example that the utility of a vehicle is 2-dimensional and consists of Niceness of the vehicle and Carrying capacity.

The total utility of the vehicle is the sum of the utility provided by those two features, but the decision process might be more complicated and not follow the Independance of Irrelevant Alternatives/Luce Choice Axiom and would follow a model where correlation among options is possible.

What you seem to be interested is the subfield of decision theory that goes by the name of "menu choice." The starting point of this literature is the paper

Kreps, David M. "A representation theorem for preference for flexibility." Econometrica: Journal of the Econometric Society (1979): 565-577.

This paper might be directly relevant to the problem you want to address.


Total Differential of a Utility Function Subject to a Budget Constraint I am trying to fully understand the process of maximizing a utility function subject to a budget constraint while utilizing the Substitution Method (as opposed to the Lagrangian Method). I am following the work of Henderson and Quandt's Microeconomic Theory (1956).

My confusion lies with obtaining the total differential of the generalized utility function after substituting in the budget constraint. For example, suppose you have the following utility function:

$$U=f(q_1,q_2)$$
Subject to:
$$y^0=p_1q_1+p_2q_2$$

The total differential of this utility function is:

$$dU=f_{q_1}dq_1+f_{q_2}dq_2$$

where $f_{q_1}$ and $f_{q_2}$ are the partial derivatives of $U$ with respect to $q_1$ and $q_2$, and $dq_1$ and $dq_2$ are the changes in $q_1$ and $q_2$.

Substituting the budget constraint into the utility function results in:
$$U=f(q_1,\frac{y^0-p_1q_1}{p_2})$$

I am struggling to calculate the total differential of the above function. Would the total differential just be the partial derivative of $U$ with respect to $q_1$ multiplied by the change in $q_1$? Below is my attempt:

$$U=f(q_1,\frac{y^0}{p_2}-\frac{p_1}{p_2}q_1)$$
$$dU=f_{q_1}dq_1-\frac{p_1}{p_2}dq_1$$

The next step in the book (after skipping the above total differential) is:
$$\frac{dU}{dq_1}=f_1+f_2(-\frac{p_1}{p_2})=0$$

Obviously, my intermediate calculation is incorrect (probably in multiple ways). Can someone identify and clarify my mistakes in progressing from the substituted utility function to the above equation? I understand that this process is used to equate the marginal rate of substitution to the goods price ratio and I am aware of its interpretation. My question lies simply with the mathematical derivation.

In the second term of the intermediate calculation we must find the partial derivative of the entire second parameter of the $f$ function.  Hence
$$dU = \frac{\partial f}{\partial{q_1}}dq_1+\frac{\partial f}{\partial (\frac{y_0-p_1q_1}{p_2})}d(\frac{y_0-p_1q_1}{p_2})$$.  Obviously this is a substitution of $q_2$ into the original total differential derivation you had.  My point is that you tried to do the partial differential of $f$ with respect $q_2$ by assuming that this would equal $$\frac{dq_2}{dq_1}$$ when this may not always be the case.  For the final equation that you have may want to consider the chain rule.  The way you have it, we have defined $$U=f(q_1, q_2)$$ and $$q_2(q_1)=\frac{y_0}{p_2}-\frac{p_1}{p_2}$$  Then according to the chain rule you have $$\frac{dU}{dq_1}=\frac{\partial f}{\partial q_1}\frac{dq_1}{dq_1}+\frac{\partial f}{\partial q_2}\frac{dq_2}{dq_1}$$  Then we evaluate $$\frac{dq_1}{dq_1}=\frac{d}{q_1}q_1=1$$  Then we get $$\frac{dU}{dq_1}=\frac{\partial f}{\partial q_1}+\frac{\partial f}{\partial q_2}\frac{dq_2}{dq_1}$$  Then, $$\frac{dq_2}{dq_1}=-\frac{p_1}{p_2}$$ Finally we end up with $$\frac{dU}{dq_1}=f_1+f_2(-\frac{p_1}{p_2})$$


What's the relationship between IS-LM model and loanable funds model and what's the differences? Are the two models compatible?

Consider the situation: consumers lost their confidence in the economy so that they consume less and save more, hence the IS curve shift down. Since the consumers save more, there should be more loanable money in the bank.

So, why doesn't the LM curve as well as the interest rate shift down when there is more lonable money？

(I can tell the two models apart.But I think it is natural for the interest rates to go down when people save more/consume less)

The LM-curve is completely independent from the loanable funds market. This is because the loanable funds market is entirely determined by the real side of the economy. Therefore, it is linked to the IS curve, not the LM curve. Even more, equilibrium in the loanable funds market for given $Y$ allows you to derive the IS curve, just as the keynesian cross allows you to do.

To see this, consider both relationships in the loanable funds market. The demand side of loanable funds is given by the demand for investment (negatively related to the real interest rate $r$) and the supply side is given by all savings available (positiveley related to $r$). For equilibrium it is required that $S=I$ holds. Which is exactly the equilibrium condition represented by the IS curve: what are the combinations of $r$ and $Y$ for which savings equals investment.

To derive the negative IS-relationship from the loanable funds market, just go through the following reasoning. Suppose that the loanable funds market is in equilibrium. This equilibrium holds for a given $Y$. If $Y$ increases, and the marginal propensity to consume is smaller than unity, the level of savings will increase for each $r$, so that the savings curve shifts to the right. More income does not affect investment, so that a new equilibrium requires a lower $r$. Conclusion: if $Y$ increases, a lower $r$ is needed for $S=I$ to hold. This is the IS-curve.


How to Calculate Price Elasticity of Demand When Perfectly Elastic? When we have perfect elasticity, the demand curve is a horizontal line and the elasticity of demand coefficient is equal to infinity.

How do we arrive at a solution equal to infinity?

We know that

  Elasticity of Demand Coefficient = Change in Quantity Demanded /
  Change in Price $x$

If we change price by $x$, how do we get what the change in quantity demanded is if there is no quantity demanded at the new price?

$$\epsilon_D=\frac{\% \Delta Q_D}{\% \Delta P}$$
A perfectly elastic demand curve is horizontal, meaning we quantity demanded can change by any amount without changing price (any quantity can be sold at the price corresponding the vertical intercept). Hence, for any change in quantity, $\% \Delta P=0$. While we cannot strictly divide by zero, in the limit, the ratio is infinity.


What is structural estimation compared to reduced form estimation? I've heard a lot of definitions given for structural estimation. But it's never seemed entirely clear to me. Some times I've heard that what one person might call "reduced form" estimation should actually be called structural estimation. Sorry I don't have an example to illustrate, but I was wondering if somebody could clarify, hopefully with a link to a paper or some other source. What is structural estimation compared to reduced form estimation? Does the potential outcomes framework count as a structural equation?

Structural estimation is a term coined by the Cowles commission which at the time seems to have been dominated by Haavelmo, Koopmans and a few others. The motto of the Cowles commission (after 1965) was: "Theory and Measurement". The phrase represents the underlying rationale of structural modelling, that measurement cannot be done without some kind of theory. To my knowledge, the phrase was first used by Koopmans in "Identification Problems in Economic Model Construction":

  Systems of structural equations may be composed entirely on the basis
  of economic "theory." By this term we shall understand the combination of (a) principles of economic of behavior derived from general observation--partly introspective, partly through interview or experience--of the motives of economic decisions,(b) knowledge of legal and institutional rules restricting individual behavior (tax schedules, price controls, reserve requirements, etc.), (c) technological knowledge, and (d) carefully constructed definitions of variables.

Structural equations are then equations that come from an underlying economic (or physical, or legal) model. Structural estimation is precisely estimation which uses these equations to identify parameters of interest, and inform counter-factuals. Importantly, these parameters are usually taken to be invariant, and therefore counter-factuals taken from their estimates will be completely "correct". Counter-factuals were the main unit of interest to the Cowles commission.

Koopmans also discusses reduced form estimation:

  By the reduced form of a complete set of linear structural equations... we mean the form obtained by solving for each of the dependent (i.e., nonlagged endogenous) variables, and in terms of transformed disturbances (which are linear functions of the disturbances in the original structural equations).

The linearity is an artifact of the times (this was published in 1949!) but the point is that reduced-form equations are equations written in terms of economic variables which do not have a structural interpretation as defined above. So, a linear regression will be a reduced-form of some true structural model, because linear regression usually does not have a true economic interpretation. This does not mean that reduced form equations cannot be used to identify parameters in structural equations - in fact this is precisely how indirect inference works - just that they do not represent a deeper model of the data generating process. Reduced forms can (in principle) be used to identify structural parameters, in which cased you are still performing structural estimation, just through using the reduced form.

Another way to look at this is that structural models are generally deductive, whereas reduced forms tend to be used as part of some greater inductive reasoning.

For a comparison of this kind of Cowles commission structural modelling with Rubin causal modelling, check out this awesome set of slides by Heckman.

For other resources I'd check out more of what Koopmans wrote, the book Structural Macroeconomics by DeJong and Dave, these lecture notes by Whited, this paper by Wolpin (written for the Cowles Foundation, in honour of Koopmans) and a response by Rust.

Addendum: A simple example of reduced form and structural models.

Suppose we were looking at data on the prices, $p_t$ and quantities, $q_t$ produced by a monopolist. The monopolist faces a series of unknown costs in the future, and a linear demand curve (this would really have to be justified). Let's say the $\hat q_t$ and $\hat p_t$ we observe are measured with some kinds of mean-zero error, $e_t$, and $v_t$

Noting that both price and quantity seem to be associated with changes in cost, a reduced form equation for this model might be:
\begin{align}
\hat q_t &= \gamma - \lambda c_t + \epsilon_t\\
\hat p_t &= \alpha + \beta c_t + \nu_t
\end{align}
Because this is a reduced form model, it needs no justification other than that it might work empirically.

On the other hand, a structural model would start by specifying the demand curve (again to be strict this should start at the level of individual utility), and the monopolist's problem:

\begin{align}
\text{Demand curve: }&p_t=a-bq_t\\
\text{Producer's problem: }&\max E\left[\sum_{t=0}^\infty\delta^t (p_t-c_t)q_t(p_t)\right]\\
\text{Measurement equations: }&\hat q_t = q_t + e_t\\
&\hat p_t = p_t + v_t
\end{align}

From this further structural equations could be derived (structural because they are still representative of principles of economic behavior):

\begin{align}
\hat q_t&=\frac{a-c_t}{2b} +e_t\\
\hat p_t&=\frac{a+c_t}{2} + v_t\\
\end{align}

This is a case where a reduced form equation will have a meaningful structural interpretation, as consistent estimates $\hat a$ and $\hat b$ can be formed:

\begin{align}
\hat a&= 2\hat\alpha \\
\hat b&= \frac{1}{2\hat \lambda}
\end{align}

Another case of identification of structural parameters from reduced forms is the logit model in the case of valuations with extreme value errors (see McFadden (1974)). In general it is unlikely a given reduced form model will have a structural interpretation.


Fundamental equations in economics For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important equations that underly the subject which I should introduce and attempt to explain?

Instead of proposing specific equations, I will point to two concepts that lead to specific equations for specific theoretical set ups:

A) Equilibrium
The most fundamental and the most misunderstood concept in Economics. People look around and see constant movement -how more irrelevant can a concept be, than "equilibrium"? So the job here is to convey that Economics models the observation that things most of the time tend to "settle down" -so by characterizing this "fixed point", it gives us an anchor to understand the movements outside and around this equilibrium (which may be changing of course).

It is not the case that "quantity supplied equals quantity demanded" (here is a foundational equation)

$$Q_d = Q_s$$

but it is the case that supply tends to equal demand (of anything) for reasons that any economist should be able to convincingly present to anyone interested in listening (and deep down they all have to do with finite resources).

Also, by determining the conditions for equilibrium, we can understand, when we observe divergence, which conditions were violated.

B) Marginal optimization under constraints
In a static environment, it leads to the equation of marginal quantities/first derivatives of functions.
Goods market: marginal revenue equals marginal cost.
Inputs market: marginal revenue product equals marginal reward (rent, wage).
Etc. (I left "utility maximization" out of the picture on purpose, because, here first one would have to present what this "utility index" is all about, and how crazy we are (not), by trying to model human "enjoyment" through the concept of utility).

Perhaps you could cover it all under the umbrella "marginal benefit equal marginal cost" as other questions suggested:

$$MB = MC$$

Economists live in marginal optimization and most consider it self-evident. But if you try to explain it to an outsider, there is a respectable probability that he will object or remain unconvinced, instead usually proposing "average optimization" as "more realistic", since "people do not calculate derivatives" (we don't argue that they do, only that their thought processes can be modeled as if they were). So one has to get his story straight about marginal optimization, with convincing examples, and a discussion about "why not average optimization".

In an intertemporal setting, it leads to the discounted trade-off between "the present and the future", again "at the margin" -starting with the "Euler equation in consumption", which in its discrete deterministic version reads

$$u'(c_{t})=\beta(1+r_{t+1})u'(c_{t+1})$$

...and one cannot avoid the theme of utility, after all: $u'()$ is marginal utility from consumption, $0<\beta<1$ is a discount rate and $r_{t+1}$ is the interest rate

(don't consult wikipedia article on Euler's equation in consumption, the concept behind it is much more generally applicable and foundational than the specific application that the wikipedia article discusses).

Interestingly, although dynamic economics are more technically demanding, I find this more intuitively appealing since people seem to understand way better "what you save today will determine what you will consume tomorrow", than "your wage rate will be the marginal revenue product of all labor employed".


Migration wage differential, Borjas (2013) textbook Basic calculus question here! I started reading the textbook Borjas, G. J. (2014). Immigration economics. Harvard University Press and am confused already with the first result.
Background: He frames the migration decision in terms of wage differences between two countries $i \in \{0,1\}$ in each country (home is 0)
$$
log (w_i) = \mu_i + v_i
$$
where $\mu_i$ is the average wage in home and potential destination and $v_i $ is an i.i.d normally distributed random variable with mean 0 and variance $\sigma^{2}$. If $i=1$ is destination country, then migrant will pay a cost $C$ to move there.
Calculation: Okay, the simple algebra is then to combine these elements into an index
$$
I = log \left(\frac{w_1}{w_0+C} \right) \approx (\mu_1 - \mu_0 - \pi) + (v_1 - v_0)
$$
with $\pi = C/w_0$.
Steps: So I did some log manipulations (see below) and think I arrive at this if the $log\left(1+\frac{C}{w_0}\right) \approx log\left(\frac{C}{w_0}\right)$. Is this an approximation one does? If yes, do you background at to why? Or is the simplification different?
$$
log \left(\frac{w_1}{w_0+C} \right) = log (w_1) - log(w_0+C) + log(w_0) - log(w_0) = log (w_1)  - log(w_0) - log\left(1+\frac{C}{w_0}\right) = e^{log(\mu_1 + v_1)} - e^{log(\mu_0 + v_0)} - e^{log\left(1+\frac{C}{w_0}\right)} \approx (\mu_i - \mu_i - \pi) + (v_1 - v_0)
$$

Yes, that is an approximation one does. You have stumbled upon the log-approximation, which is very commonly used in Economics.
It states that $log(1+x)≈x$, for very small $x$. Hence, typically $x$ is a fraction. It is also used in macro to approximate growth rates.
There are lots of resources out there that explain it, e.g. here.
The way I remember it is that $log(1) =0$ so $log(1+x)≈x$ for small $x$. This is mathematically totally wrong, but I find it to be a useful memory device personally.


Stock vs flow variables How could I decide from a variable exactly, that is stock or flow type?

  Variables, which are measured at a point of time are called stock
  variables whereas variables measured over a period of time are flow
  variables. This means that stocks are non-recurring in nature whereas
  flows are recurring in nature.

I found, that number of unemployed people is stock and amount of salary is flow. As I know, salary is a fixed amount of money, but number of unemployed people can be changed really fast.

A stock represents a quantity measured at one specific point in time, which  may have accumulated in the past.

According to the Bureau of Labor Statistics, the US unemployment rate stood at 4.1 percent in February 2018. This represented a stock of 6,706,000 unemployed workers in February 2018. But from January to February, we observed a flow of workers going in and out unemployment.

  A flow variable is thus measured over an interval of time, e.g., hours, days, weeks, months or years. It has time dimension.

Because of inflows and outflows of workers going in and out unemployment, between January and February, the stock of unemployed workers was a bit higher in January 2018 (=6,684,000).

A year before, in February 2017, the unemployment rate was about 4.7%, representing a stock of 7,486,000 unemployed workers at that particular time. This means that a net flow of 7,800 (=7,486,000 - 6,706,000) US workers went out unemployment between February 2017 and February 2018.

Your wage in February 2018 is a flow because it's the money you earn between Feb 1st and Feb 28. (by the way, this amount is not necessarily fixed from one month to another).


Is investment a type of saving or expenditure I am confused that if investment is a type  of saving or a expenditure .if investment is a type of expenditure then is  saving is what is left after subtracting consumption and investment from income

In simplistic national accounts terms $$Y=C+I+X-M$$ is an  expenditure identity while $$Y=C+S$$ is a use of income identity.

Implicitly this gives $$S-I=X-M$$ suggesting an excess of saving over investment in an open economy corresponds to a trade surplus in the current account, which in turn corresponds to an outflow in the financial account: the excess of savings over investment leads to an increase in overseas assets.

In a closed economy with no exports, imports or international financial flows, this forces $S=I$ and so no excess of saving over investment. Any production not used for consumption or normal investment has the effects either of increasing stocks (another form of investment) or of being valueless (so not counting towards income or saving).


What is the concrete meaning of Britain saying they export Banking Services? Today I read:

  One of Britain’s chief exports is Banking Services.

Now I presume that doesn’t mean consumer savings accounts.

I presume it means investment loans to companies and equities holdings in foreign companies. (Some might argue these are similar)

But if a bank has holdings in a foreign company, is it really exporting Banking Services? Isn’t that just owning things?

My question is: What is the concrete meaning of Britain saying they export Banking Services?

Exports of banking services  means that banks in the UK charge companies and people abroad for banking services, which might include for money transfer, foreign exchange and other broking, wealth and asset management, merger and acquisition services, and other things that banks do. It may include their interest rate margins between taking deposits and making loans, as an implicit fee for financial intermediation

It does not include actual foreign investment, such as direct investment, portfolio investment or financial investment: those do not count as exports of services in the Balance of Payments though income from them do count as primary income in the Balance of Payments current account

Nor does it take into account that many of the banks in London are in fact predominately foreign owned or that many of their staff are foreign.  If they operate from London then they are treated as British banks for these purposes, though their profits may then count as an outward flow to their owners in the Balance of Payments

In 2017 UK exports of financial services (excluding insurance and pension services) were worth about £61 billion; imports of financial services were almost £11 billion


Mathemtical Economics Question regarding Profit Maximization I'm studying Mathematical Economics and there's this question that I'm unable to understand.

Q. Suppose a firm faces a demand curve for its product $P = 32 - 2Q$, and the firm's costs of production and marketing are $C(Q) = 2Q^2$. Find the following:

(f) What would the competitive price and quantity be, assuming $C(Q) = 2Q^2$ represented the industry cost function?

Actually the question has 5 more parts but I was only stuck on this last one (f). In the other parts I calculated Profit formula, price and quantity that maximize total revenue and the price and quantity that maximize profit (if by any chance these are related to the last part)

Any help will be appreciated!

Well, it's very straightforward question. You have a cost function, from which you can get a Supply Curve, by taking its first derivative. You'll find competitive price and quantity when the supply curve you got meets the demand curve.

First, our supply curve: $$P = 4Q$$
Then, the demand curve:

$$ P = 32- 2Q$$

Competitive $Q$ is:

$$ 32 - 2Q = 4Q $$
$$Q = \frac{32}{6} \approx 5.333$$

So, competitive price is:
$$ P = 32 - 2 * 5.333 \approx 21.333$$


Intuition: Can someone explain me this contradiction please? (This is about price elasticity of demand) Both figures are demand curves. In figure 1, the curve includes both high elasticity (|E|>1) and low elasticity (|E|<1) but in figure 2, the curve is either high elasticity or low elasticity. How should I explain this contradiction?

Figure 2 is a bit misleading. Both demand curves have an elastic and an inelastic region, just like the one in Figure 1. The meaning of "High elasticity " and "Low elasticity" in Figure 2 is that the steeper line has a much lower magnitude of elasticity than the flater line at the same quantity level.


Destroying the dollar Let's destroy the USD dollar: I am the government of a small, economically and geopolitically unimportant country that has its own currency and a local central bank. I order the local central bank (at gun point, if need be) to lend me dollars. Is there a technical problem to do this? No, this is just an exchange of papers and electronic messages -we can write on them anything we want, especially with a gun in our head. We can attach to these electronic records any three-letter code we want, so why not "USD"?

Now I have a bank account with a balance of gazillions and gazillions of dollars- and USD ones, the heavy stuff.

I can pay off my public debt, make every citizen rich (or just those that I like), import all the luxuries in the world, buy as much energy as I want, whatever. After all, I will be paying in USD dollars right? I will be wire-transferring from a bank account, an electronic signal that will contain some digits and the code "USD" attached.

So let's hear it from the experts: what kind of checks has the international community in place in order to effectively avoid such a situation?

And what if, as the most long-lasting counterfeiters know, we were to do this modestly, just a little at the time to help a tad with the local government budget, but without "showing-off riches" to the rest of the world??

I think you misunderstand what "electronic money" is - moving electronic money around isn't simply a matter of sending the right "codes" - it is ultimately about asking the central bank of that currency to move money around.

Sure you can open up excel and write in it "I have \$100" but that isn't USD, much as writing \$100 on a piece of paper doesn't make it a \$100 bill.

In order to lend you dollars I actually have to have some dollars to lend you.  That means I need a reserve account with one of the 12 Federal Reserve banks.  There are no electronic USD that are not ultimately in a Federal Reserve Account.

The "ultimately" in that sentence is there because banks can (and do) form hierarchies.  Only the largest ("Tier 1" banks, sometimes called "clearing banks") actually have a reserve account with the central bank in a given currency.  Other, Tier 2, banks will simple hold accounts with Tier 1 banks.  Smaller local banks may even be Tier 3.  When it comes to foreign currency dealing, you could be even further down the chain (i.e. a small bank in Australia may be Tier 4 for USD)

Because of this hierarchy a certain amount of electronic banking can be done without moving reserves.  A transfer only needs to progress up the hierarchy until it gets to a common bank between the two customers.

So for example:

A payment between two accounts at the same bank, can be done on that bank's systems.
A payment from an account at a Tier 2 bank, to a different Tier 2 bank might be done using a shared Tier 1 bank.  The Tier 2 bank's are "customers" of the Tier 1 bank, and so the Tier 1 bank can do the transaction on their system.
A payment between customers that ultimately fall under two different Tier 1 banks must be done by at a Federal Reserve bank.
The US adds an extra complication, because there are 12 Fed Reserve banks - if two Tier 1 banks don't bank with the same Fed Branch, then the Fed Reserve System also has to go "one step higher" and the New York Fed acts as the very top bank: "How do reserves move between the 12 federal reserve banks?" explores exactly how that is done.

So the problem in your scheme is you couldn't get your central bank "into" this pyramid of banks.

Your central bank's computer can show $1tr on screen but the only way to transfer to another bank, would be to instruct YOUR Fed bank to take money out of YOUR fed reserve account and put it into the other bank's account.  Your central bank can't make reserve dollars.

Aside:  An alternative way of looking at this, for those familiar with how BitCoins work, is to note that the important feature of electronic money is to prevent double spending.  BitCoin does this with the BlockChain; the USD equivalent of the block-chain is held on the Fed Reserve computers.  You can't just declare yourself to have billions of bitcoins - to spend them you have to get your transactions onto the BlockChain.  With electronic USD you have to get your transactions onto the Fed ledger.  Only the Fed has a copy of this and their say is final.  There would be no way for your central bank to change the Fed ledgers.


Price Elasticity of Demand - elastic demand and impact of price reductions on total revenue A question in relation to Price Elasticity of Demand.

My understanding is that when demand is elastic, a price reduction will increase
total revenue.

If the price of a product changes from \$100 to \$80 (20% decrease) and quantity demanded increases from 1000 to 1240 (24% increase), PED = 24/-20 = -1.2 (elastic).

Total revenue at the original price (\$100) and quantity demanded (1000) = \$100,000 Total Revenue after the price change is \$80 x 1240 = \$99,200 so total revenue has actually fallen

Can anyone reconcile this with the point that when demand is elastic a price reduction should increase total revenue?

Like anything derived from calculus, the statement is guaranteed to hold true only for infinitesimal change. Unfortunately, since I don't know the entire demand function, I can't say much more than this.

A clear example of why this wouldn't work: starting at the same point \$100 and Q = 1000, we can decrease price to zero and total revenue would go down.


Marginal productivity of aggregate labor relation to wage I know that $f'(l)=w$. But if i have that the aggregate production is $Y=AL^{1-α}$  with $L=N*l$ (The number of workers, $N$, multiplied by the labor force). So basically I want to find an expression for $w$ (the wage.).

Full problem:

Consider a one period economy, with aggregate technology given by: $Y=AL^{1-α}$ ,$0<α<1$. $L$ denotes the aggregate labor. The economy is integrated by $N$ identical agents, that offers labor force for a remuneration $w$. Also each person receives an Nth part of the earnings $π$ that generates the aggregate production. The objective of each agent is:

$\max \qquad γ\ln(1-l) + \ln(c)$.

$\text{subject to} \qquad c = wl + \frac{1}{Nπ(w)}$

So the firm's problem is, letting $L=Nl$

$\max_{L} Y-Lw\implies w=(1-\alpha)AL^{-\alpha}, \pi(w)=\alpha AL^{1-\alpha}$

Consumer's problem: substitute out c and only choose l, taking $\pi$ and $w$ as given

$\max_l u(l, wl+1/(N\pi))\implies -\gamma/(1-l)+w/(wl+1/(N\pi))=0$

Now substitute in the values for w and profit from the firm into the consumer's FOC and you will solve for labor supply (=labor demand as we are in eq) in terms of exogenous parameters ($\gamma, N,\alpha, A)$.


What are the implication of state-run oil production vs. private production from leases? I'm not any kind of expert in this area, so please be gentle.

It seems that we speak of oil (and other natural resources) as though control of output and revenue from extraction adheres to the national government (as in "Saudi" oil), but is this true of countries like the US as well? Is it accurate to speak of "US" oil in the same way we speak of "Saudi" oil, given that from what I gather the US does not directly control production and does not directly sell product, while the Saudi government controls oil extraction as a state-owned monopoly?

What if any are the implications of the apparent differences here?

Like many international markets, the crude oil market is a mix of private and public participants.

From most perspectives, it really doesn't matter whether oil production is state-run or run by private leases. Both, ultimately, are combinations of public and private forces - just different blends. Both are trying to optimise the outcomes for their owners. They're all suppliers that respond to demand.

They're all largely price takers; the larger they are, the more they contribute to being a price maker - same as any other market. Nominally, Saudi Arabia as the main force in OPEC carries the market force of the entire cartel: but as Saudi is by far the largest producer in OPEC, the supply levels of the other cartel members don't carry anywhere near as much weight, and there is some evidence that they haven't always implemented fully proportional cuts when Saudi has called for cartel-wide production cuts.

So Saudi Aramco is just another market player, albeit the single largest one, and has some additional leverage via other OPEC members.

Many myths surround Saudi's oil policy; many widely-held assumptions are wrong. The most accurate thing I've heard said of it, credited to various folks is: the people who talk about Saudi intentions, know nothing; and the people who do know the intentions, say nothing.

Footnoe: the products are not completely fungible: different crudes have different chemical compositions (sweet crude has low sulphur content, sour crude has high)


Substitution effect on investment due to tax credit Suppose we are in an economy with only two kinds of investment, business investment and residential investment. Suppose also that government gives tax-credit on business investment. Will there be a substitution effect like the one happens in microeconomics where the demand curve for residential investment is shifted downwards and the demand curve for business investment is shifted upwards? I mean, a textbook would say there will be an upward shift for business investment demand curve and no changing in residential investment curve. Any comments will help!

I think we should regard these more like supply curves. Moreover, I will regard this economy being composed of agents with heterogeneous levels of profitability ratios between business and residential investment.

In the business side, there will be an average return on investment curve, and at lower investment levels, there will be higher returns and vice versa, which makes this look more like a demand curve. Moreover, this might be regarded as an exogenous curve in your scenario.

From the perspective of investors, when the average return on investment is low, only those who have higher levels of private returns to investment (compared to residential investment) will invest in business and more people will be attracted to business investment as the return increases.

A similar picture would hold for the residential investment. The economy arrives at an equilibrium when each of these markets are in equilibrium.

A person would allocate his wealth among his choices based on the additional gains per cost of each alternative. Here, when you have lower the cost of business investment by reducing taxes, all agents will find business investment comparably desirable, and there will be less people investing in residential industry.

So the supply in residential investment will be lower simultaneously with the increase in supply of the business investment.

Of course you can consider scenarios in which an investor's optimal decision requires diversifying to some degree, but as long as the complementarity is not extremely strong, which would be expected in this case, the economy-wide supply curves would shift in opposing directions.


Intertemporal Utility Maximization Suppose an economic agent’s life is divided into two periods, the
first period constitutes her youth and the second her old age. There
is a single consumption good, C, available in both periods. The
agent’s utility function is given by

$$U(C_{1},C_{2}) = \frac{C_{1}^{1-\theta }-1}{1-\theta }+\frac{1}{1+\rho}\frac{C_{2}^{1-\theta }-1}{1-\theta }$$

with $0<θ < 1,ρ > 0$, and where the first term represents utility from consumption during youth. The second term represents discounted utility from consumption in old age, $1/(1+ ρ )$ being the discount factor.

During the period, the agent has a unit of labour which she supplies
inelastically for a wage rate $w$ . Any savings (i.e., income minus
consumption during the first period) earns a rate of interest $r$,
the proceeds from which are available in old age in units of the only
consumption good available in the economy. Denote savings by $s$. The
agent maximizes utility subjects to her budget constraint.

$i)$ Show that $θ$ represents the elasticity of marginal utility with
respect to consumption in each period.

$ii)$ Write down the agent’s optimization problem, i.e., her problem
of maximizing utility subject to the budget constraint.

$iii)$ Find an expression for s as a function of $w$ and $r$.

$(iv)$ How does s change in response to a change in $r$? In
particular, show that this change depends on whether $θ$ exceeds or
falls short of unity.

$(v)$ Give an intuitive explanation of your finding in $(iv)$

I am not being able to solve this problem. I proved the first part $i$.

$$C_{2}= (w-C_{1})(1+r)$$

So, $ii)$ Optimization Problem =

$$\frac{C_{1}^{1-\theta }-1}{1-\theta }+\frac{1}{1+\rho}\frac{C_{2}^{1-\theta }-1}{1-\theta }+\lambda (w-C_{1}-(w-C_{1})(1+r))$$

$iii) s=w-C_{1}$ How do we express this int terms of $w$ and $r$?

Any help with this sum will be appreciated.

What you have is basically the Fisher Two-Period Optimization Problem. (Fisher)

For iii)
You first need to find the Euler equation, which tells you how to optimally trade off first-period and second-period consumption.

For starters, your optimization problem is set up incorrectly:
$$\frac{C_{1}^{1-\theta }-1}{1-\theta }+\frac{1}{1+\rho}\frac{C_{2}^{1-\theta }-1}{1-\theta }+\lambda (w-C_{1}-\frac{C_{2}}{1+r})$$

You find the Euler equation by deriving and equating the first-order conditions of both consumption terms.

$$\frac{1}{1+r} C_{1}^{-\theta }= \frac{1}{1+\rho}C_{2}^{-\theta }$$

Then just solve for $C_{1}$, substitute $C_{2}=s(1+r)$, and plug into $s=w-C_{1}$, which gives:

$$
s=w-(1+r)^{\frac{\theta-1}{\theta}}(1+\rho)^{\frac{1}{\theta}}s \\
s=\frac{w}{1+(1+r)^{\frac{\theta-1}{\theta}}(1+\rho)^{\frac{1}{\theta}}}
$$

The derivative, giving the response to a change in $r$, is:
$$
\frac{\partial s}{\partial r}= -\frac{(\theta -1) w ( 1+\rho)^{1/\theta } (1+r)^{1/\theta }}{\theta  \left((\rho +1)^{1/\theta }+r (\rho +1)^{1/\theta }+(r+1)^{1/\theta }\right)^2}
$$

The derivative for $0<\theta<1$ is positive, indicating that a higher return on saving will lead to an increase in the amount saved. Preference for first period consumption is still low enough, so that the consumer is willing to save more to consume it later. Here the substitution effect dominates the income effect.

When $\theta>1$, the derivative is negative, meaning that preference for first period consumption is so high that the consumer is willing to lower savings for current period consumption. Here the income effect dominates the substitution effect.