The social welfare of a unique general competitive equilibrium in an exchange economy The first theorem of welfare economics states that "Every Walrasian Equilibrium (WE) is Pareto Efficient (PE)" - Microeconomic Theory Nicholson, Synder 11th ed. p477. But PE is quite a weak condition. Is WE a stronger condition or is does WE just mean any PE allocation?

I was specifically wondering; suppose we have an exchange economy with agents $N$, and there is a unique competitive equilibrium (WE) solution, $q^*$. Does this also maximize aggregate social welfare amongst possibly many PE outcomes? Where aggregate social welfare is defined as:

$$
  SW(q^*) = \sum_i^N U_i(q_i^*)
$$

To ask this question only makes sense if WE $\subset$ PE allocations, because if there is a single PE allocation then it must by definition maximize aggregate social welfare, because there is no other feasible solutions.

Any solution maximizing social welfare has to be PE, but not all PE solutions are SW maximizing. For example, at a given PE allocation agent $i$ could lose 1 util in exchange for agent $j$ gaining 2.

Using the 'utility monster' critique of aggregate utility maximization it is pretty easy to show that gen. comp. eq. does not always maximize aggregate utility.

Imagine a pure exchange economy with two agents, $A$ and $B$ and two types of goods, $x_1$ and $x_2$. Agent $A$ has nothing whereas agent $B$ has one unit of each good. The agents respective utility functions are
$$
U_A(x_1^A,x_2^A) = 2x_1^A + 2x_2^A \hskip 20pt U_B(x_1^B,x_2^B) = x_1^B + x_2^B.
$$
Trivially the initial distribution is a competitive equilibrium and also trivially it does not maximize aggregate utility.

EDIT:

I am not sure I understand @spinkus's comment, as obviously not every solution maximizes the aggregate utility, but I will address the other point: Not trading. That is not at all important for me, I just wanted to make the example trivial.

Suppose given some strictly monotonic utility functions $U_A,U_B$ and some initial endowments $w_A,w_B$ some allocation $a^*$ is a competitive equilibrium. If this allocation does not maximize aggregate utility we are done. If it does, consider the following monotonic transformation of $U_B$:
$$
\hat{U}_B \triangleq c \cdot U_B
$$ where $c$ is a positive number. In a pure exchange economy with $U_A,\hat{U}_B$, initial endowments $w_A,w_B$ the competitive equilibrium will again be $a^*$ as the preferences are unchanged. Yet even if $a^*$ maximized $U_A+U_B$, it clearly will not maximize $U_A + \hat{U}_B$ if $c$ is small enough.


What is excess demand/ excess supply? I've been reading up on Walras' Law and thought I understood it pretty well. However one of my friends asked me point blank what is an example of excess demand or excess supply is and I had some difficulty answering and realized I had no clue.

What are examples of excess demand and excess supply?

Definition 1. Excess supply is supply minus demand.

Definition 2. Excess demand is demand minus supply.

Example 1. A baker posts a sale price of \$2 per loaf of bread.

At this price, he is willing to sell up to 300 loaves of bread (per day), but consumers are willing to buy only 200.

We say that quantity supplied and quantity demanded (at the price of \$2) are 300 and 200 and write $$S(\$2) = 300\text{ and }D(\$2) = 200.$$

Excess supply is then $$ES(\$2) = S(\$2) − D(\$2) = 300 - 200 = 100.$$ (If we'd like, we can also say that excess demand is −100.)

Example 2. A baker posts a sale price of \$1 per loaf of bread.

At this price, he is willing to sell up to 100 loaves of bread (per day), while consumers are willing to buy 250.

We say that quantity supplied and quantity demanded (at the price of \$1) are 100 and 250 and write $$S(\$1) = 100\text{ and }D(\$1) = 250.$$

Excess demand is then $$ED(\$1) = D(\$1) − S(\$1) = 250 - 100 = 150.$$ (If we'd like, we can also say that excess supply is −150.)

In the real world, the baker may not know precisely how many loaves of bread he's willing to sell at each and every price. Nonetheless, if it is the case that QS obviously greatly exceeds QD (or vice versa), he will either notice this and respond accordingly or go out of business.


Why is Land not considered as a fixed capital? As far as I know 'Fixed Capital' includes things which don't deteriorate or get used up upto a long, e.g. tools, machinery and building etc. My question is that since Land fulfills this criteria, why is it not considered as a Fixed Capital?

The distinction between land and physical capital is based on some of their economic properties, particularly relating to investment: whether it can be reproduced or not; whether it has a finite lifetime (compared to the human lifetime).

Almost all land is not reproducible, and does not have a finite lifetime.

Physical capital is reproducible, and does have a finite lifetime.

Hence, almost all land is not physical capital.

There are corner cases, where land is reproducible, and may appear and then disappear again in less than a handful of human lifetimes: in those very rare cases, that particular land behaves more like physical capital rather than how land generally behaves, and so could be classed as such.


Lump sum taxation in the overlapping generations model I am working through my textbook's problems, using the overlapping generation's model. In this economy, people are endowed with $y$ goods when young, and nothing when old. They will choose to exchange some of their endowment for money, and hence real money demand is given by
$$N(y-c_{1, t})$$
for the population $N$ of young people, and the value $v^t$ of money.

In this question, the money supply is shrinking such that $M_{t+1} = zM_{t}$ with $0<z<1$. The old are taxed $\tau$ goods by the government, payable in terms of fiat money. It then destroys this revenue.

I have already found that the rate of return of money is given by
$$\frac{v_{t+1}}{v_t} = \frac{1}{z} > 1$$

The question asks for proof that this situation will not maximise individuals' welfare. I first find the lifetime budget constraint:

$$c_{1, t} + zc_{2, t+1} \leq y - z\tau$$

and then find the feasible set for consumption for each individual:

$$c_1 + c_2 + \tau \leq y$$

When I now compare the first and second period consumption intersections, I appear to find that consumption for both periods will be more than is feasible. For instance my feasible set intersections are

$$c_1 = y - \tau, c_2 = y - \tau$$

whereas for the equilibrium, I get

$$c_1 = y - z\tau, c_2 = \frac{y}{z} - \tau$$

both of which are more than their feasible equivalents, since $z < 1$. What have I done wrong here?

If I understand correctly the set up, the government does not destroy real goods, it just collects fiat money and destroys it to reduce the available quantity of money (since money is in the hands of the individuals). The fact that the government calculates the amount of fiat money to collect by using a real-goods base, $\tau$, does not alter this fact. But then, all endowment is consumed and the government's actions just affect the price level.

Some assumptions:
a) population is constant at $N$ per generation
b) all individuals are identical, so we can carry the analysis by setting $N=1$
c) There are no altruistic motives, so no inheritance
d) Individuals do not carry over periods real goods: they consume some of their endowment, and what they do not consume, they sell in exchange for money
e) the subscript $1$ denotes consumption when Young, and the subscript $2$ consumption when Old.

Assume that we are in economy's period $t+1$. The Young come to the Goods market as suppliers, bringing with them $y-c_{1,t+1}$ goods. The Old come to the Goods market as buyers, bringing with them fiat money.

Market clearing implies in real terms that all real goods will change hands, and then that the Old that bought them will consume them. So we obtain

$$c_{2,t+1} = y- c_{1,t+1} \implies c_{2,t+1} + c_{1,t+1} = y  \tag{1}$$
In nominal terms equilibrium requires that Total Revenue of Suppliers equals Total Expenditure of Buyers. Total Revenue is

$$TR_{t+1} = p_{t+1}(y-c_{1,t+1})  \tag{2}$$

The Old will want to spend all their available money (since money is not consumed per se, and they don't leave any inheritance). The money they got in the previous period (prior to being taxed) was Total Revenue of Suppliers in period $t$. The tax is paid on $t+1$, has a real base $\tau$ and so its nominal value is $T_{t+1} = p_{t+1}\tau$. So Total Expenditure is

$$TE_{t+1} = p_t(y-c_{1,t}) - p_{t+1}\tau  \tag {3}$$

Equating $(2)$ and $(3)$ we get

$$p_{t+1}(y-c_{1,t+1}) = p_t(y-c_{1,t}) - p_{t+1}\tau \implies p_{t+1}(y-c_{1,t+1} +\tau) = p_t(y-c_{1,t}) $$

and using $(1)$ we obtain an expression that involves the components of life-time consumption of the same individual

$$p_{t+1}(c_{2,t+1}+ \tau) = p_t(y-c_{1,t})\tag{4}$$

We are moreover told that what fiat money the government collects as taxes, it destroys, targeting a fixed rate of reduction. So we have

$$m_{t+1} = m_t - T_{t+1} = m_t - p_{t+1}\tau = zm_t$$

$$\implies m_t = \frac {p_{t+1}\tau}{1-z} ,\;\; 0<z<1 \tag {5}$$

We know that $m_t = p_t(y-c_{1,t})$, so we obtain

$$p_t(y-c_{1,t}) = \frac {p_{t+1}\tau}{1-z} \tag {6}$$

Combining $(4)$ and $(6)$ we see that consumption of Old is determined exogenously

$$ (4), (6) \implies p_{t+1}(c_{2,t+1}+ \tau) = \frac {p_{t+1}\tau}{1-z}$$

$$\implies c_{2,t+1} = \frac {z}{1-z}\tau \tag{7}$$

Since the endowment $y$ is also exogenous, consumption when Young is also determined exogenously (from $(1)$)

$$ c_{1,t+1} = y-\frac {z}{1-z}\tau \tag{8}$$

But if $z$ and $\tau$ are constant over time, then the time subscripts become irrelevant. Each generation consumes exactly the same when Young and when Old as the previous and the next ones:

$$c_1 = y- \frac {z}{1-z}\tau ,\;\; c_2 = \frac {z}{1-z}\tau \tag{9}$$

Using $(9)$ together with $(4)$ we can determine the evolution of the price level

$$(4), (9) \implies p_{t+1}\left(\frac {z}{1-z}\tau+ \tau\right) = p_t\frac {z}{1-z}\tau$$

$$\implies \frac {p_{t+1}}{p_t} = z <1 \tag{10}$$

as should be expected. Constant amount of goods with shrinking amount of fiat money $\implies$ deflation.

As regards the issue of whether the equilibrium here is welfare maximizing.

Eq. $(4)$ combined with $(10)$ gives us the life-time budget constraint. Assuming logarithmic utility, the individual would solve

$$\max V = \ln(c_1)+  \frac 1{1+\rho}\ln(c_2)\\
s.t. \;\; y - zc_{2} - z\tau  = c_{1} \tag {11}$$

The first order condition with respect to $c_2$ is

$$-z\frac 1 {c_1} + \frac 1{1+\rho}\frac 1 {c_2} = 0 \implies c_1 = (1+\rho)zc_2 \tag{12}$$

Combining with the life-time budget constraint as well as $(9)$ we end up with a quadratic in $z$ in order for the equilibrium to be utility-maximizing.

$$(11), (12) \implies (1+\rho)zc_2 = y - zc_{2} - z\tau \implies (2+\rho)zc_2^* = y  - z\tau \tag{13}$$

$$(9), (13):\;\; c_2^{eq.} = c_2^* \implies \frac {(2+\rho)\tau z^2}{1-z} = y  - z\tau$$

$$ \implies (1+\rho)\tau z^2 +(y+\tau)z - y = 0$$

This has a single positive real solution

$$z^* = -\frac {y+\tau}{2(1+\rho)\tau} + \left[\left(\frac {y+\tau}{2(1+\rho)\tau}\right)^2+\frac {y}{(1+\rho)\tau}\right]^{1/2} $$

Now, for this value of $z$ to be feasible, not only do we want it smaller than unity, but we must also consider the non-negativity constraint on the level of consumption of the first period.

We want
$$c_1 > 0 \implies y- \frac {z}{1-z}\tau > 0 \implies z < \frac {y}{y+\tau} <1 $$

So one should check whether
$$-\frac {y+\tau}{2(1+\rho)\tau} + \left[\left(\frac {y+\tau}{2(1+\rho)\tau}\right)^2+\frac {y}{(1+\rho)\tau}\right]^{1/2} < \;? \; \frac {y}{y+\tau}$$

which holds. So $z^*$ is feasible, and for this single value the imposed allocation of consumption will equal the utility-maximizing solution (at least for logarithmic utility).


Social welfare in terms of preferences How does one define a social welfare in terms of individuals’ preferences $\succeq_i$?
If we have utility functions $u_i$ then a social welfare maximizing outcome $x$ is simply one that maximizes $\sum_i u_i(x)$. How does one specify a social welfare maximizing outcome in terms of preferences?

Usually one tries to construct a Social Welfare Function (SWF), i.e. a general rule how to aggregate individual preferences to a social preference relation. Then various axioms are formulated that a useful SWF should obey, and some such SWF is selected. A social welfare maximizing alternative would then be one which is weakly preferred to all other alternatives by society.
However, if there are at least three alternatives and the axioms include Universal Domain, the Pareto Criterion, and Independence of Irrelevant Alternatives, then Arrow's Impossibility Theorem shows that the only SWF obeying all three of these axioms is a dictatorship.


Link between supply of domestic assets and monetary policy From Treasury's Oct'2016 FX policies report:

  Switzerland’s economic policy situation is distinctive given its relatively small stock of domestic assets, which limits monetary policy options to address persistent deflation in the context of significant safe haven capital inflows.

What is the link between stock of domestic assets and monetary policy options?

Monetary policy is conducted by the Swiss Central Bank. The Swiss Central Bank has a monopoly over the issue / production of Swiss francs.

The purpose of the Swiss Central Bank is to produce / supply Swiss francs to the Swiss public if the Swiss public wants to hold more Swiss francs and to purchase Swiss francs of the public if the Swiss public wants to hold fewer Swiss francs. If it doesn't bad things will happen but that's outside of the scope of this question.

The Swiss Central Bank does this by either purchasing domestic assets with newly created Swiss francs and selling domestic assets for previously created Swiss francs.

The reason that the Swiss Central Bank does this by purchasing and selling domestic assets is that it is often not appreciated if one country's government interferes in the economy of another country's government and the Swiss Central Bank is considered to be part of the Swiss State.

The problem the Swiss Central Bank faces is that the Swiss currency and Swiss domestic assets are considered to be good stores of value by foreigners. The function of a currency is a unit of account, store of value, and a medium of exchange. So the Swiss currency fulfills the second function, store of value, for foreigners. But this leaves fewer Swiss francs for the Swiss public to use as a medium of exchange. And if there are fewer Swiss francs but the demand of the Swiss public is the same, then this results in deflation. Swiss francs become relatively more valuable compared to other goods. The prices of other goods, in terms of Swiss francs drop. At the same time there are fewer domestic assets that can be exchanged for newly created Swiss francs because these have been purchased by foreigners.

This is highly simplified, but I hope that this answers your question.


Is weak sustainability (Hartwick's rule) possible on a global scale? Hartwick's rule postulates that an economy is sustainable if all rents obtained from the extraction of non-renewable resources are re-invested in produced capital (Source). A typical example would be the Norwegian Sovereign Wealth Fund that invests the resource rents obtained from oil into equity, real estate and fixed income. (Source)
In generic terms the investments that the fund makes will be in capital (e.g. machinery) or land and other rent-generating assets (e.g. land, patents, etc.). However, the produced capital will depreciate over time and the rent-generating assets do not involve the production of a new asset but the purchase of the rent attributable to the rights over an existing asset.
How then would weak sustainability (Hartwick's rule) be possible on a global scale? Presumably this would have to involve investing every cent of resource rent into capital investments with a lifespan that is at least as long as the lifespan of the resource that it substituted?

First of all Hartwick's rule has originally been derived under rather specific assumptions, among others a Cobb-Douglas production function and constant population and technology. Therefore copying it one on one to the real world would require a huge leap of faith.
Although it has later been generalized to broader classes of production functions, people have also pointed out that instead of a prescriptive rule (invest resource rents in man-made capital to realize constant consumption), it is in fact a descriptive result. If we observe constant utility then resource rents must have been reinvested.
Asheim, Buchholz and Withagen (2003) show among others that it is perfectly possible in a world with constant technology and population not to have zero net investment, and still constant utility over time, as well as situations where we follow the Hartwick rule and have non-constant consumption (and hence non constant utility).
Blindly following the Hartwick rule, on a global scale or on a regional scale for that matter would therefore not be a good idea. That notwithstanding several papers have shown strong links between savings in the past allowing for constant or even growing consumption in the (far) future (e.g. here, here and here).
Intuitively it makes sense that saving rents from non-renewable resources to make-up for lost production capacity is a good policy measure. Whether or not it will be enough is a different matter, and very much depends on degree of substitutability and technological progress.


Solving a system of equations using R I'm trying to use R for my Macro practise and model solve for the equilibrium price where the inverse demand curve PD(q) and supply curve P.
How do i do this?
Thanks!

Note 1.: It is rude to edit a question after it was answered; I had to make significant edits to make my answer consistent.

Note 2.: this is not a system of equations. There are two functions defined, but only one equation:
$$P_D(q) - P_S(q) = 0$$

What helps here is that inverse demand is decreasing in quantity while inverse supply is increasing. So given any $q$, if $P_D(q) > P_S(q)$ we know that $q$ is under the equilibrium value of $q^*$, and if $P_D(q) < P_S(q)$ then $q > q^*$.
You can also narrow down the range $q^*$ can be found in. Clearly $q^* \geq 0$.
Also $P_D(q)$ should not dip into negative territory, so you can find a very large $\bar{q}$ for which $P_D(q) \leq 0$. One can do this easily by starting from $\bar{q} = 1$, evaluating $P_D(\bar{q})$, and doubling $\bar{q} = 1$ iff $P_D(\bar{q}) > 0$.
Given the interval $I = [0, \bar{q}]$ which we know contains $q^*$, you can now apply interval halving.
An algorithm for approximating $q^*$ with a desired level of precision $\epsilon$:

Define the interval $I = [0, \bar{q}]$.
Start of LOOP
Select the midpoint of the interval as a "guess" for $q^*$. (In the first iteration this is $q = \bar{q}/2$.)
Evaluate the statement $P_D(q) > P_S(q)$.
If true, then

$q^*$ should be smaller, the solution is in the lower half of the interval, so in the next iteration we will use that as our new interval $I$.
If false, then

$q^*$ should be larger, the solution is in the upper half of the interval, so in the next iteration we will use that as our new interval $I$.
Evaluate the statement new interval is very small, i.e. has length less than $2\epsilon$.
If true, then
select its midpoint and say that you have approximated $q^*$ with reasonable precision, end program.
If false, then
Go to start of LOOP.


How can an outcome be Pareto efficient but not Kaldor-Hicks efficient? An policy is a Pareto improvement if it makes some people better off and no one worse off.  And a policy is a Kaldor-Hicks improvement if it can be turned into a Pareto improvement by redistributing money.  Every Pareto improvement is a Kaldor-Hicks improvement, but not every Kaldor-Hicks improvement is a Pareto improvement.

Now an outcome is called Pareto efficient if there are no possible Pareto improvements of it, and Kaldor-Hicks efficient if there are no Kaldor-Hicks improvement of it.  Now clearly every Kaldor-Hicks efficient outcome is Pareto-efficient, because if a Pareto improvement were possible it would also be a Kaldor-Hicks improvement.  But my question is, why is the converse not true?

Here is my argument for why the converse is true.  Suppose that X is a Pareto-efficient outcome which is not Kaldor-Hicks efficient.  Then there exists a Kaldor-Hicks improvement which can be turned into a Pareto improvement by a redistribution of money.  But then that Kaldor-Hicks improvement together with that redistribution is a Pareto improvement, so there exists a possible Pareto improvement of X, contradicting the fact that X was Pareto efficient.  Where am I going wrong?

Example. Each month, God gives Adam $60$ apples and Eve $40$ (for a total of $100$ apples). Let's write this allocation as $X=(60,40)$.

The Devil now comes along and offers to increase their total monthly allotment of apples to $101$, but on the condition that the allocation must be $Y=(59,42)$.

Observe:

$X$ is Pareto efficient but not Kaldor-Hicks efficient.
$Y$ is both Pareto efficient and Kaldor-Hicks efficient.
$Y$ is a Kaldor-Hicks, but not a Pareto improvement over $X$.
Through imaginary redistribution, we could get from $Y=(59,42)$ to $Z=(60,41)$. And $Z$ would then be a Pareto improvement over $X$. But the problem is that the option of making the redistribution $Y\rightarrow Z$ doesn't actually exist. And so, while $X \rightarrow Z$ would indeed be a Pareto improvement, the problem is that it does not exist and is not a possibility. It is merely something we or Adam and Eve may have imagined.

So let's see where you went wrong in your argument:

  But then that Kaldor-Hicks improvement together with that redistribution is a Pareto improvement

This is correct. Using the above example, $X \rightarrow Y$ is the Kaldor-Hicks improvement, $Y \rightarrow Z$ is the imaginary redistribution, and $X \rightarrow Z$ is the Pareto improvement.

  so there exists a possible Pareto improvement of X

The error is here. The redistribution $Y\rightarrow Z$ is imaginary and does not exist. So, the reallocation $X \rightarrow Z$ is also imaginary and does not exist.

(In this case the redistribution  $Y\rightarrow Z$ isn't possible due to arbitrary constraints set by the Devil. But in the real world there will be other constraints.)

Edit: Another example

Suppose you and I are neighbors. I really like practicing the drums at 9 am on a Saturday. You really, really, like sleeping until 10 am on Saturdays, which is, of course, significantly disrupted by my drumming. Suppose I value drumming at \$10, and you value sleeping at \$20. What are the efficient outcomes?

The clear Kaldor-Hicks efficient outcome is for me to not drum. Sure, I lose (the equivalent utility of \$10 to be precise), but I lose less than you gain. If desired, you could compensate my loss, and still be better off than if I drum.

The set of Pareto efficient outcomes is bigger. It's Pareto efficient for me to either not drum (letting you sleep), or drum away at 9 am!

Of course, we could come to a mutually agreeable resolution where I don't drum and you pay me some amount between \$10 and \$20. However this adds another layer of complexity that we didn't include: that enforceable agreements and transfers are possible (and costless). In the real world, where there are many other pragmatic issues (such as enforcement, positive transaction costs, lack of information about who the "gainers" and "losers" are, etc.), these payments might not be possible, and hence, we're reduced to considering the initial problem.


Why stochastic dominance is "stochastic"? I think the CDF is pretty much fixed, so the FOSD (first order stochastic dominance) is pretty much non-stochastic. Why does it have a "stochastic" in its name?

In the below figure, CDF $F(\cdot)$ is first-order stochastically dominated by $G(\cdot)$. But $X_1$ and $X_2$ fall within the support of both distributions. So it would be possible to draw $X_1$ from $F$ and $X_2$ from $G$, or to draw $X_2$ from $F$ and $X_1$ from $G$.

More generally, if $X_G$ is a draw from $G$ and $X_F$ is a draw from $F$ then $X_F-X_G$ will sometimes be positive and sometimes negative. In this sense, the dominance is only stochastic: $G$ produces larger draws than $F$ on average, but not all of the time.


Consumer preferences I want to know under what preferences relation will I not want to consume all of my budget. Because if my preferences are strictly monotonic, strictly convex or convex, even LNS or continuous. I would consume all of my budget. Are they any situations where I would not?

Edit: when I meant preferences I am treating each individual case i.e. if it is LNS it is not convex (necessarily)

Yes. Suppose the consumer has the following utility function:

$$u(x) = - \sum_{i=1}^n x_i$$

Here's a different example, where commodities are goods instead of bads:

$$v(x,y) = -(x-a)^2 - (y-b)^2$$

When the consumer's budget $m$ is strictly greater than $p_x a + p_y b$, then the consumer will not consume all of their budget.


Identifying Nash equilibria in extensive form game Is there a systematic way of identifying all (pure strategy) Nash equilibria (not just the subgame perfect ones) in an extensive form game? In the following Entrant v Resident example, there are three NEs, two of which ($(OF,F),(OA,F)$) are not subgame perfect. What I've been doing is to convert the extensive form to normal form, and then find NEs there. While reliable, this method is time consuming, and gets complicated as the number of actions/players increases. For example, I suspect that it'd be much easier to spot NEs in a four-player extensive game (each with two action, say) than its normal form equivalent.

I'd be interested to know if there's any procedure that we can use to find pure NEs in a reasonably simple extensive form game.

As far as I know, No.

While I am not sure why you would want to find non-subgame perfect Nash equilibria in an extensive form game, I am sure you would need to convert it to normal form to do it. Extensive form of a sequential game carries more information than normal form, specifically which moves do not exist within the sequence. In a normal form representation of the sequential game you have to show every possible move available to every player, even the moves that do not exist. So basically when you convert a sequential game from extensive form to normal form, it becomes another game where you then look for Nash equilibria.

If you are doing a two player game where each player gets one move, you can do it in your head just by looking at the game tree, but if the game is any more complex, you would need to do it step by step, first converting it into a normal form.


Unintended consequences from "fixing" the US financial system Last year, I read the book The Bankers' New Clothes: What's Wrong with Banking and What to Do about It.  The book explained some of the causes of the recent financial crisis of 2007-2009 and gave some steps to prevent a similar crisis from occurring again.  Some of the steps were

  1) eliminating the FDIC,
  2) increasing the capital requirements of banks (up to ~30% instead of the current 2%-3%), and
  3) having liability rest completely on bank owners and decision-makers within the bank (i.e. no government bailouts, depositors receive a certain number of cents on the dollar rather than 0, etc.).

However, economics in plagued by the law of unintended consequences.  If these three points were implemented into the US financial system, what are some unintended consequences that could result?

1) Would lead to the return of general panic led bank runs, and introduce additional instability to the system.

It´s not generally appreciated, that 19th century bank runs were not just a symptom of insolvency or illiquidity, but were also occasionally triggered by competitors (other banks) spreading rumours. Generally this is a bad idea that rests on the fallacy that banks are just another business.

2) They are typically rather more than 2-3%, 10-12% was the average at the crash, and Basel 3 is moving this up to above 15%. It´s generally a good idea, but it depends on the type of capital - more loss provisions are good, but simple holding extra share capital not so much. There are also side effects with respect to economic growth while the increase is occurring.

3) This seems a little confused. Depositors are not decision makers in banks - they are the customers. Owners, managers and shareholders of the banks are not necessarily the same people, but making in particular the managers and owners stand behind the banks with their entire assets might be interesting. As in ´may you live in interesting times´ interesting. Scottish banking in the 18th-19th century was regarded as more stable by the English since the entire property of the bank´s owners would be seized if the bank failed. In today´s world though, expect that to cause issues, if Banks are the only type of company that this kind of punitive ownership encumbers, then one might imagine that relatively few people will want to own one, or creative ways will be found around the requirement.

Banks are also usually regarded as a fairly safe investment (between major credit crises at least), and a good investment for pension funds and retirees, as their dividends provide a steady stream of income. Blowing those institutions up, might not be entirely desirable.

All of this not withstanding, the main issue with banks, and the answer to why they are not just another company - is that they provide the money supply. The problem posed by any banking crisis, and any proposed reform, is how does this avoid or solve monetary and credit supply contraction in the event of loan default failure. 1 & 3) in particular would be likely to cause significant monetary contraction, and return the financial system to the instabilities of the 19th century, where not to put to fine a point on it, it was bouncing up and down like a yo-yo. Wikipedia has quite a nice list:

List of Banking Crises


Can saddle path not go through the origin in Ramsey model? In my case, the utility function is CEIS and discrete, the production fuction is $f(k_{t})=k_{t}^\alpha$, the budget constraint is $f(k_{t})+(1-\delta)k_{t}=c_{t} + k_{t+1}$. I use Jacobian matrix and Schur factorization to get the linearized policy function for consumption, therefore i can plot saddle path and unstable arms. In the end they look like below. However I read that saddle path must go through the origin, which is not right in my plot.

So my question is: does saddle path always go through the origin?

I guess you already went trough the algebra below, but just for context, the problem you're trying to solve is

$$
\max_{c}\sum_{t=0}^{+\infty}\beta^t u(c_t) \\
\text{s.t.}~~ f(k_t) + (1- \delta)k_t = c_t + k_{t+1} \tag{1}
$$

where $f(k_t) = k_t^\alpha$ and

$$
u(c_t) = \frac{c_t^{1-\gamma}}{1-\gamma} - 1 \tag{2}
$$

The problem in (1) can be cast into the two coupled equations

\begin{eqnarray}
u'(c_t) &=& \beta[1 + f'(k_{t+1}) - \delta]u'(c_{t+1}) \\
k_{t+1} &=& f(k_t) + (1-\delta)k_t - c_t \tag{3}
\end{eqnarray}

where $u'(x) = x^{-\gamma}$, and $f'(x) = \alpha x^{\alpha-1}$. These first of Eqns. (3) can be inverted to obtain an expression for $c_{t+1}$ in terms of $(k_t,c_t)$, leading to

\begin{eqnarray}
c_{t+1} &=& \beta^{1/\gamma}c_t [1 + \alpha[k_t^\alpha + (1-\delta)k_t - c_t]^{\alpha-1} - \delta]^{1/\gamma} \\
k_{t+1} &=& f(k_t) + (1-\delta)k_t - c_t \tag{4}
\end{eqnarray}

Which can be expressed as

$$
{\bf x}_{t+1} = {\bf F}({\bf x}_{t})~~~\mbox{with}~~~ {\bf x}_t = \left(\begin{array}{c}c_{t}\\k_{t}\end{array}\right) \tag{5}
$$

A fixed point ${\bf x}^*$ of the map ${\bf F}$ is such that

$$
{\bf x}^* = {\bf F}({\bf x}^*) \tag{6}
$$

that is, a point for which the system does not evolve. If you use $\gamma=2$, $\beta=0.9964$, $\alpha=0.36$, $\delta=0.025$ this point is (found by solving Eq. (6)),

$$
{\bf x}^* = \left(\begin{array}{c}c^*\\k^*\end{array}\right) = \left(\begin{array}{c}2.84829\\52.2808\end{array}\right)  \tag{7}
$$

which is clearly different from zero! You can linearize ${\bf F}$ around ${\bf x}^*$ and write the result as

$$
{\bf y}_{t+1} = {\bf J}{\bf y}_t ~~~\mbox{where}~~~ {\bf y}_t = {\bf x}_{t} - {\bf x}^*, ~~~ {\bf J} = \left.\frac{\partial{\bf J}}{\partial {\bf x}}\right|_{{\bf x} = {\bf x}^*} \tag{8}
$$

Is this last system the one that has a saddle point at ${\bf y} = 0$


Can individual consumers ever be price-makers, and can they thereby have major effects on welfare? Suppose there's a big demand shock on some good X. As long as X has fairly standard supply and demand curves, that'll raise the price. And all of the buyers who would have bought at the lower price will be slightly harmed -  they all have to pay a bit more for the good. And the producers are benefited - they make a greater profit. And the new buyers would presumably benefit from buying the good as well.
In \$ terms, this should balance out to be slightly positive. But, in welfare terms, it seems like it might not be. The buyers could all be a lot poorer than the producers, so an extra \$1 in profit might be far less valuable to the producers than it was to the buyers, so the demand shock could overall be a bad thing - it's effectively a transfer from the poor to the rich. Or it might be other way around, with producers poorer than buyers, in which case the demand shock would be a great thing - it's a transfer from the rich to the poor. Is that right?
But here's the actual question: do individual consumers ever trigger price changes like this? If I choose to go to the supermarket and buy an apple (rather than not do so), is there any probability at all that that very slight increase in the demand for apples will trigger a price rise on all apples, even for a short time? Or if I choose to buy and consume a bit more gas, which is much more divisible than apples, could I potentially raise the price of gas by $0.01, whether the price rise just happens at my local gas station or the world over?
I realise that, even if it's possible that this could happen, it'd be extremely unlikely. That's okay. I'm curious about whether I could have even a 1 in a billion chance of having this sort of effect. After all, raising the price of, say, rice or wheat by even \$0.01 across the entire world could have enormous welfare impacts. For at least some of the extreme poor, a \$0.01 price difference may mean that they go hungry for the day, or that they can't afford other essential goods, like medicine. So, is there any probability at all of individual consumers having this effect?
If you know of any papers which look at this sort of phenomena, I'd love some recommendations! Likewise, any papers which look at which individual goods are overwhelmingly produced by the poor and consumed by the rich, or vice versa. (I'm guessing there might be some stuff in the literature on trade?)

Answer to the Question on Welfare
The welfare analysis is not as simple as that.  First, let us set aside for a second any inequality considerations (we can add them on later but there are some misconceptions about welfare analysis that have to be corrected first).
Welfare in supply-demand analysis is conventionally measured by amount of consumer and producer surplus. These are defined as the difference between maximum price consumer is willing to pay and price consumer actually gets to pay in case of consumer surplus and in case of producer surplus as the difference between the price consumers actually pay, in both cases summed across all consumers and producers. Graphically, the consumer surplus is given by the blue area and producer surplus the red area on the picture below:

Given this the expansion of demand can very well lead to increase of not just overall welfare but consumer welfare as well, even if price increases. Consider a trivial example:
Suppose demand is given as: $D=100-10P$ and supply as $S=6P$. Given this assumptions market price and quantity will be $P_e = 6.25, Q_e = 37.5$ which will gives us the following producer and consumer surplus: $PS = 117.1875, CS = 70.3125$.
Now suppose the demand increases (i.e. shifts to the right) which can be represented by new demand function $D = 120 -10P$ and supply remains the same. Now the market price and quantity will be  $P_e = 7.5, Q_e = 45$ which will gives us the following producer and consumer surplus: $PS = 168.75, CS = 101.25$.
As clearly demonstrated by the simple stylized example above increase in demand even when it leads to increase in price can very well leave consumers better off even measured in just consumer welfare terms.  Note the above is just example, the size of both consumer and producer surpluses crucially depend on shape of supply and demand, so in some situation consumers could be worse off. The point is that already from the start the assertions made about consumer welfare from shocks to demand are simply invalid.
Next, if we would want to start discussing inequality and similar issues then yes the above welfare analysis would change. If we would for example denote all producers poor and all consumers rich (or vice versa), assume that interpersonal welfare comparisons are possible etc., we would additionally have to scale the consumer and producer surplus accordingly to reflect that. Nonetheless, this does not necessarily change outcome of the above welfare analysis, the inequality would have to be severe enough so that scaled CS/PS would be lower in the new equilibrium.
However, the simple partial equilibrium generic supply-demand graph/model is not suited for analysis of inequality. For example, the stylized supply-demand model above does not explicitly model factor prices (e.g. wages, capital etc). The reason why supply is upward sloping is that the more producers produce the more factors they need to employ (e.g. more workers) which puts upward pressure on wages. Just because factory owner is rich that does not mean workers are so in more involved analysis we would try to model also supply demand changes on labor markets or some alternative partial equilibrium analysis that focuses specifically on people's incomes/wealth whether they are consumers or producers etc. Since this heterogeneity is not captured by simple stylized supply and demand you simply cannot do any serious welfare analysis that takes into account inequality simply from  supply and demand shifts on a given goods market. You need more complex model for that (see discussion in any public economics textbook for example Stiglitz, Economics of the Public Sector, 3rd ed. is good place to start).
Answer to the Question on Individual Consumers Changing Prices
Yes individual consumer demand can change market price unless we have special situations (e.g. situation where supply is completely elastic so increase in demand wont affect equilibrium price). I mean this is on some level trivial. The demand function is nothing more than an aggregation of individual demands, hence if demand and supply function are such that increase in demand leads to  change in price, then individual consumers can affect the market price.
You can of course have special situations such as 'step-like' supply because it might be simply too costly for suppliers to adjust prices just because one extra person demands one extra good (your example of shopper in general store).  An exaggerated case of such situation is plotted below.
In the case as shown below the demand will affect price only if it shifts sufficiently to point where supply is elastic. The probability of some individual consumer being the proverbial 'last straw' will depend upon parameters of the model. For example, if we assume that quantity demanded must increase by $100$ to create change in price, and if we assume this increase in demand is caused by $100$ individual consumers each raising their demand exactly by 1, then the probability of any single randomly selected consumer being the one that caused the price change would be $\frac{1}{100}=1\%$.    This is of course oversimplified because in reality one consumer my increase their demand by 10 another just by 1, this would make the probability calculation more complex but not impossible in principle.
This being said, I do not know of any research that would try to calculate the above. Normally when it comes to demand researchers do not have data on individual demand of every single customer. Even the demand curve has to be estimated as only equilibrium demand can be observed, but this is doable and can be done with reasonable precision. So I would be surprised if there would be some situation where there is enough data to realistically calculate this. However, we know that demand as a whole affects prices - there is whole literature on estimation of supply-demand systems (see  MacKay & Miller; 2019 for review and sources cited therein for particular examples) which shows that changes in demand change the prices and since demand is just an aggregation of individual demands individuals have an effect on this. Since demand curve can shift only when individual demands shifts there will always be someone on the margin responsible for triggering price change.


what is the difference between microeconomics and microfinance? what is the difference between microeconomics and microfinance?

I cannot understand the difference between the two terms

Kind of a good question, but it's to do with etymology, nitpicking or something. While economics is the allocation of scarce resources and finance is the allocation of scarce resources over time, microeconomics is a study while microfinance is a provision of financial services.

Thus, the 'micro' in microeconomics refers to the scope of study namely that microeconomics studies the behaviors of individuals and firms instead of state issues of growth, inflation, and unemployment.

However, the 'micro' in microfinance refers to the scope of recipients of financial services.


A national accounting calculation The question that I am trying to answer is as follows:

  For a given year, South Africa's Gross Domestic Expenditure (GDE) is R 3 251 414, imports are R 987 781, and exports are R891 562. The table below lists the taxes and subsidies applicable to the South African economy:
  $$\begin{array} {|l|rr|}
\hline
\text{Taxes on production} & \text{R} & 54\ 166 \\
\hline
\text{Taxes on products} & \text{R} & 338\ 792 \\
\hline
\text{Subsidies on production} & \text{R} & 14\ 358 \\
\hline
\text{Subsidies on products} & \text{R} & 18\ 684 \\
\hline
\end{array}$$
  The gross value added at factor cost is

  A. R 2 795 279

  B. R 2 863 543

  C. R 2 835 087

  D. R 3 155 195

  E. R 3 347 633

My Answer is R 2 891 498, because I took the GDE and added subsidies and subtracted taxes. I did that because I assumed that the GDE was given at market prices. I disregarded the information about imports and subsidies because I assumed that GDE was calculated using the equation Y=C+I+G+X-M.

I disregarded the information about imports and subsidies because I assumed that GDE was calculated using the equation Y=C+I+G+X-M.

This is where I went wrong. GDE is calculated as C+I+G, but to get GDP at market prices, I need to add nett exports.


General equilibrium - exchange economy with time and perishable goods I am attempting to solve a general equilibrium problem from the textbook Jehle and Reny. However, I am slightly confused if my approach is correct. The question is as follows.

Consider an exchange economy with one good and two time periods. Two consumers have the following utility functions:

$U_A (x_{A1}, x_{A2}) = \sqrt{x_{A1}} + \sqrt{x_{A2}}$

$U_B (x_{B1}, x_{B2}) = \sqrt{x_{B1}} + \sqrt{x_{B2}}$

where $A1$ corresponds to time period 1 and $A2$ corresponds to time period 2.

Each consumer is endowed with one unit of the good at time period 1, BUT only B is endowed with 1 at time period 2 (A is endowed 0 at time period 2). Note that storage of the good is not possible, but consumers can engage in trade in period 1. Calculate the competitive equilibrium allocations.

I am not sure if I am overthinking the problem, but since the good is perishable. Will both agents just consume their endowments (e.g., agent 1 consumes 1 in the first period, and agent 2 consumes one in the first and one in the second).

Is there a scenario where agent 1 would want to sell some of his endowment in period 1 to purchase some in period two? Given his utility function I believe this would be the case, but showing it seems much different than the typical GE problems I have been solving.

Thanks

Of course, note that in general, consumer B is willing to increase her consumption in period 1. it is a matter of simply solving the problem in the regular way. i.e, MRS=p and find the $p$ which "clears" the market.

Normalize the price of the current period good to $1$ and let $p$ be the price of the second period good, then the optimum for player $A$ is:
$\max_{x_{A1},x_{A2}} \sqrt{x_{A1}}+\sqrt{x_{A2}}$ s.t $x_{A1}+px_{A2}\le 1$
Clearly the constraint is binding and thus the problem becomes:
$\max_{x_{A1}} \sqrt{x_{A1}}+\sqrt{\frac{1-x_{A1}}{p}}$
Calculate the first order condition, repeat the process for consumer B etc...


Where can I find data on bilateral trade? Where can I find data on bilateral trade between countries in the world over time?
I heard that only International Trade Center has access to this data, but I guess there's a public source. I tried but didn't succeed, for example this one.

Many thanks.

For aggregated trade, there is a excellent database from CEPII called histtrade. It covers data from the first industrial revolution. The site also has data covering disaggregated  trade but only with limited observations.

http://www.cepii.fr/CEPII/en/bdd_modele/bdd_modele.asp

A second data set is the Barbieri Data set, that can be downloaded from the COW project.

http://www.correlatesofwar.org/data-sets/bilateral-trade


Where can I find data on income and social mobility over time? How far back is data available? I'm interested in income and social mobility. I understand that Piketty's research deals with the the distribution of income over a long time period. I have also seen some of Chetty and Saez's research concerning income and social mobility in the US. I'm wondering, what data do Chetty and Saez work use? What other data is potentially available and how far back does it go?

It would be nice to see who could find the data that goes back the farthest. (Also, the data does not necessarily have to be US data.)

Maybe check Clark's work. He allegedly uses long time series.
http://jasoncollins.org/2014/09/30/the-genetic-basis-of-social-mobility/


Question about skill-biased technical change, Acemoglu I am writing about skill-biased technical change, and in particular the 2001 Acemoglu (http://economics.mit.edu/files/283) paper on the topic, in which there is a part I am very stuck on.

In the paper he suggests there is a market size effect and a price effect which directs technological change. The price effect directs technological change to areas which are relatively more expensive, and the market size effect to areas which are relatively bigger. The elasticity of substitution between two factors plays an important part, so that a low elasticity between two inputs will result in the price effect dominating, since in this situation scarce factors are relatively more expensive and innovation will intend to economise on this. With a high elasticity, the market size effect dominates, since scarce factors do not have a different relative price, so innovation will make widely used factors more efficient.

He applies this to skill biased technical change, in which he says one of the reasons the skill premium has increased so much over the past 60 years is because of the influx of skilled workers (i.e. the market size effect is dominating), so that with more skilled workers, innovation is directed at making them more efficient and they enjoy a higher wage. On page 18 under section 4.2 he states that this will happen with no reference to the degree of substituability between skilled and unskilled workers.

This is where I am stuck. I am trying to explain the theory, in words like I have above, so that it would read something like this: with a high degree of substitutability, technical change favours the more abundant factor (the market size effect). Skilled and unskilled labour have a high degree of substitutability, so an increase in the supply of skilled workers will direct innovation towards complementing that factor. But surely skilled and unskilled workers have a low degree of substitution? In which case surely the price effect would dominate?

I would greatly appreciate any help on this, I am sure I am making a big error somewhere, since it makes sense for the market effect to dominate here due to the empirical evidence of the increasing wage premium over the years... I also hope what I am asking makes sense. I wouldn't have written such a long question, but I feel it wouldn't have made sense without the context of the theory.

I won't replicate the model -interested readers should read the link the OP provides.

Acemoglu's argument as to when a high relative supply of skilled labor will lead to skill-biased technological change is laid out in page 13 (below eq. $(18)$), it includes the all-important condition eq. $(19)$ and ends in the middle of page 14. Here the author explains what must hold in order to observe this phenomenon.

Then at the the bottom of page 18 the author writes

  "Moreover, recall that when condition ($19$) is satisfied, equation $(18)$ traces an upward-sloping long-run relative demand curve for
  skills. Therefore, the induced skill bias of new technologies can be
  sufficiently pronounced that the skill premium may increase in
  response to a large increase in the supply of skills."

So here, the author simply invokes the necessary theoretical condition obtained previously.
So what is this condition? It reads

$$\sigma > 2- \delta \tag{19}$$

where $\delta$ is an index raging in $[0,1]$ (and serving some purpose) and  $\sigma$ is the elasticity of substitution between skilled and unskilled labor.

So we see that in order to obtain skill-biased technological change together with high relative supply of skilled labor in the model (as appears to be the historical experience), namely, in order for condition $(19)$ to hold, we must have, as a necessary but not sufficient condition $\sigma >1$ according to this model.

Now, at the bottom of page 9, we see

$$\sigma \equiv \varepsilon - (\varepsilon-1)(1-\beta), \;\;\; \beta \in (0,1)$$

and where $\varepsilon$ is the elasticity of substitution of the two goods that are combined in private consumption (though not directly in the utility function as the author writes somewhere -see eq. $(6)$).

So for our necessary condition $\sigma > 1$ we must have

$$\sigma > 1 \implies \varepsilon - (\varepsilon-1)(1-\beta) > 1$$

$$\implies (\varepsilon-1) > (\varepsilon-1)(1-\beta)$$

which will hold iff $\varepsilon >1$.

So the real-world rationalization is shifted

from "is there high substitutability between skilled and unskilled labor"

to "is there high substitutability in final product/consumption between intermediate products made using skilled labor and intermediate products made using unskilled labor"?

...because if there is such high substitutability at this "second" stage, then indirectly, skilled and unskilled labor acquire a high degree of subsitutability, even though looking directly at a single production function, it would appear reasonable that they should not be highly substitutable.
In other words, here "substitutability" emerges as an even more economic, rather than mainly an engineering/technical concept.

I will leave to the OP the task of contemplating further.

ADDENDUM

Responding to a comment by the OP, in the specific model, "intermediate goods" are combined at the consumption level. In real life of course, in almost all products, skilled and unskilled labor are combined to reach the ready-for-consumption good. For example consumers consume services of a building as a whole, not design services and/or brick-laying services separately.

One way to rationalize this is by thinking in quality terms: degree of substitution between buildings made by mediocre craftsmen alone ("unskilled" labor), against buildings made using experienced builders and engineers. Since the substitution degree is a preference parameter, not taking into account prices, one could reasonably argue that the degree of substitution between similar products of different quality can be high (again, as a tendency coming from preferences, the actual consumption decisions will also depend on prices of course).


Interpretation of multinominal logit regression (Stata) I have a few questions about mlogit. I have a set of independent variables and a categorical, but ordered, dependent variable with three categories (Disagree, Neutral and Agree). The assumptions for ologit were not fulfilled. I chose Neutral as the base category. The coefficient of one of the independent variables X (a dummy taking the values 1 or 0), so the multinominal log odds, is negative for both Agree and Disagree, so the two effects are in different directions. The coefficient for Disagree is -1.264 and for Agree it is -0.672. If I calculate the corresponding probabilities, the change in probability of Agree is higher than the change in probability of Disagree, when taking the difference between X=1 and X=0 (using the equation on page 6: https://www.stata.com/manuals/rmlogit.pdf). This indicates that the effect on Agree is actually larger than the effect on Disagree, even though the absolute value of the coefficient is smaller.
Can the change in probability of an outcome compared to the base be higher than the change in probability of another outcome compared to the base, even though the absolute value of the coefficient (or log odds) is smaller for the former?
Also, what is the difference between the change in probability of an outcome relative to the base (as described on page 6 of https://www.stata.com/manuals/rmlogit.pdf) evaluated at X=1 and X=0 and the marginal effect (margins dy/dx), which also describes the probability of the outcome?
Thanks

You have that:
$$
\begin{align*}
\ln\left(\frac{\Pr(D|X = 1)}{Pr(A|X = 1)}\right) &= \ln\left(\frac{\Pr(D|X = 0)}{\Pr(A|X= 0)}\right) -1.264 + 0.627,\\
&\le \ln\left(\frac{\Pr(D|X = 0)}{\Pr(A|X= 0)}\right)
\end{align*}
$$
So taking exponents, we have that:
$$
\frac{\Pr(D|X = 1)}{\Pr(D| X = 0)} \le \frac{\Pr(A|X = 1)}{\Pr(A|X = 0)}.
$$
What you find is that:
$$
|\Pr(A|X=1)- \Pr(A|X = 0)| > |\Pr(D|X = 1) -\Pr(D|X = 0)|
$$
These two are not necessarily in conflict.
For example:
$$
\Pr(D|X= 1) = 0.1\\
\Pr(D|X = 0) = 0.3\\
\Pr(A|X = 1) = 0.4\\
\Pr(A|X = 0) = 0.677
$$


why is the term fiat money or fiat currency and is it the same as legal tender or are there any differences? I learnt some very basic economics learning about 2, 2.5 decades back. Recently, while reading some article on the web, I came to know about 'fiat money' and 'fiat currency' but have been unable to understand if the two terms are same as what is known as legal tender in most countries or does it have different, subtle implications ? A little bit of contextual and historical context may go a long way in understanding where both these terms came from. Are they recent or rooted in 19th, 18th century or before ? I am not sure of the tags hence using ones which seem to be more appropriate. Please fix if something else is better.

Difference between money and currency in general (i.e. in any monetary arrangement -fiat money, gold standard etc.) is as follows:

Currency: is the money in the strictest sense of a word. It includes coins and bank notes in the circulation. In foreign exchange the word is also used to as a synonym for unit of money (e.g. $ €) but from your question I think you are looking for the first meaning.

Money: is the whole stock of money in economy, hence not just coins and paper notes which are only small part of all money but also money on accounts etc.

Legal tender: is a money that must be accepted if offered in payment for debt. So for example in principle any debt can be repaid let’s say with labor or with some commodity, but the creditor can say no to all those things unless you had some specific contract but can’t say no to legal tender of the country. Legal tender again does not need to be fiat money it could be some gold backed money or fiduciary money etc.

Fiat money: following the Mankiws definition from his principles of economics (p 220). It is: “money without intristic value that is used as money because of government decree”. So there is a connection to legal tender all fiat money is also a legal tender by definition but it’s a necessary condition not sufficient one as it also has to have no intristic value. Fiat currency is just the coin and note part of the fiat money.

The origin of the word fiat is from Latin: “let it be done”. In modern English it’s synonymous to government decree, edict or act.

The earliest reference to fiat money I could find is in John Maynard Keynes’ treatise on money (1930). But I am unable to say if the word was not used before that.


Remittance: Migrant workers sending money to their families I wonder about the role of migrant workers in a general economic context.

Migrant working appears all over the world and on many time and space scales:

around cities (e.g. commuters)
inside countries (more and better paid work in the North than in the South (e.g. Italy) or in the West than in the East (e.g. Germany))
continent wide (e.g. Europe: West-East, North-South)
world wide (e.g. Europe-Africa, North America-South America)

Overall, migrant workers who send some money back to their families seem to make use of arbitrage, i.e. taking "riskless advantage of price and loan differences". (This doesn't mean that the advantage is effortless: The workers and their families pay the heavy price of being torn.)

But this is not the issue of my question. My question is more general and concerns national economics in general and sustainability.

For the (richer) "host countries" (where the money is earned) the economical effect of sending money out (deflation) may be negligible, but for the (poorer) "home countries" (where the money is sent to) the effect may be significant:

inflation (more money than goods)
social conflicts (envy-driven)
accelerated emigration (of workers and experts)
in sum: an economical downward spiral

There's just one positive effect that I can imagine:

compensation of otherwise economic injustice (by historical or actual reasons)

Is there a general opinion about migrant working seen economically from the perspective of the "home countries" (where the money is sent to)? To which extent and how long does this way of economic exchange work? I'd like to learn more about this.

There are actually more pros then cons for the "home countries" in my opinion, and I have official/credible sources to back this opinion up.

Financial remittances have been recognized as an important developmental vehicle associated with migration. Financial remittance flows have steadily increased in volume from the 1990s to the present day. In 2017, migrants sent an estimated $466 billion to families in developing countries. Money sent home from abroad is shown to be more stable than both private debt and portfolio equity flows, and several times larger than international development aid.

An estimated 800 million people worldwide are directly supported by remittances from relatives and loved ones abroad, according to the International Fund for Agricultural Development (IFAD). Remittances lift families out of poverty, improve health and nutrition conditions, increase education opportunities for children, improve housing and sanitation, promote entrepreneurship and reduce inequality.

However, apart from financial remittances, transnational communities also contribute by way of 'social remittances' - the flow of skills, knowledge, ideas and values that migrants transmit home. The impact of social remittances was most strongly felt in areas such as education, health, employment, business and aspects of governance, found a study conducted by IOM in Tanzania in 2014.

In short, there is a lot work to be done. IOM, UN Migration Agency, in partnership with specialized organizations, civil society, academia and the private sector, have engaged in several concrete projects and initiatives aimed at improving knowledge of social and financial remittance usage and corridors. They have conducted studies on the impact of remittances on families and communities, and worked to enhance the development impact of remittances, financial inclusion and diaspora engagement.

EDIT to address cons:
There are indeed cons; let's look at the ones you pointed out:             inflation: I think most people would say this form of inflation is insignificant when you compare it the global economic perspective. There is a literal currency war between most if not all of the worlds nations, going on for a while now, where advanced economies are technically importing inflation to emerging market economies. These amounts are huge and when you factor in our topic here, it makes our topic a bit insignificant in comparison. See: https://en.wikipedia.org/wiki/Currency_war
James Rickards also has a great book on the subject.

As for social conflicts, this is a pretty micro oriented con, and a bit political as well. I'm afraid I don't have much knowledge on this one.

For accelerated emigration, this is perhaps the biggest con, but is easily countered in the long run. Here's why:

I think it is commonly accepted that most of the skilled workers in the long run wish to return to their home country/their families. When these workers leave their home countries, the country loses the potential GDP input of said workers. What do they gain in return? Cash inflow. Which we already accepted doesn't have much of a significant effect on inflation. What that cash inflow does do is increase consumption and investment a little bit, which promotes the prosperity potential of the country in the long run. Assuming this consumption and investment is aimed at long term growth for the home country, the workers would eventually come back(their original goal in the first place) to a stable economic system(that they inadvertently helped create) and provide further.


Term for fraction of economic value earned? Is there a term for the fraction of economic value earned by a person in their labor that is due to their creation?

For example, a car factory laborer who's work creates:

Economic value created = $500,000

Income Paid = $50,000

Would have a value of 0.1

At the other end of the spectrum, the CEO might be

Economic value created = $2,000,000

Income paid = $1,500,000

Fraction = 0.75

You seem to be looking for the phrase 'wage share' or 'share of labour compensation'.

Wage share:

  The wage share (or labor share) is the ratio between compensation of employees (according to the system of National accounts) and one of the following variables:

  gross domestic product at market prices
  gross domestic product at factor cost
  net domestic product at factor cost (domestic income at factor cost)

Here is some US data on share of labour compensation.


Value function iterations with hyperbolic discounting I am currently working to the numerical solution of a model similar to the consumption-savings decision model with hyperbolic discounting as in Krussel et al. (2003).

Even if hyperbolic discounting implies that the value function does not generally have the standard contraction property, some solutions to the problem have been implemented; for example Judd (2004) proposed perturbation methods from the exponential case and a local solution for small departures of hyperbolic discounting.

I have already implemented the basic model without hyperbolic discounting, using value function iterations on discretized policy grids.

Do you have suggestions for the extension to hyperbolic discounting? Is it possible to extend the basic model without moving to iterations in the Euler equation? Any advice or reference is welcomed.

  Krusell, Per, and Anthony A. Smith Jr. "Consumption–savings decisions
  with quasi–geometric discounting." Econometrica 71.1 (2003): 365-375.

  Judd, Kenneth L. "Existence, uniqueness, and computational theory for
  time consistent equilibria: A hyperbolic discounting example." (2004).

Refer to Harris-Laibson 2001.
They show the validity of the contraction mapping theorem in a neighborhood of the exponential consumption path.


What will be the additional investment? I recently encountered upon this question:

Suppose, in  an economy,autonomous consumption is Rs 100 crore and autonomous investment is Rs 60 crore. Imagine that in this economy,with every increase in income 80 °/° of it is spent on consumption .  If the full employment level of income is Rs 1000 crore,what will be the additional investment?

So, the MPC is 0.8 and so the multiplier would be 5 times.
The consumption function is C =  Autonomous consumption + MPC.y
Hence, C = 100 + (0.8)1000 = 900 crore.
But then given that the multiplier is the ratio  change in income to change in investment, how to proceed further?

I think you use the inverse (1-MPC) of the MPC to derive the marginal propensity to save (MPS) and create the investment function.  So, I= 60 + .2*1000 = 260, or an additional 200 from the autonomous level.


Price and cross price Elasticity of demand The question is: Prove or disprove, if the price elasticity of a demand of a good is unitary then the cross price Elasticity of demand of that good is zero.

Any hints on how to approach this?

$P_XX+P_YY=M$

Differentiating w.r.t. $P_X$,

$\frac{\partial X }{\partial P_X}P_X+X+\frac{\partial Y}{\partial P_X}P_Y=0$

Divide the whole term by $X$, considering $X\neq 0$

$\varepsilon _X+1+\frac{\partial Y}{\partial P_X}\frac{P_Y}{X}=0$

$\varepsilon _X=1$(Given)

$2+\frac{\partial Y}{\partial P_X}\frac{P_X}{Y}(\frac{P_Y}{X}\frac{Y}{P_X})=0$

Here, $$P_X,P_Y,X,Y> 0$$(ASSUMPTION)

Therefore, Cross- Price elasticity is $-2$ (some positive no.) and not $0.
So, this statement is not true.


Long Term Impacts of Austerity Measures Is there much research into the long term impacts of government fiscal contractions.

I have heard about 2nd generation unemployed as a result of Thatcher's policies but that is very much anecdotal. What does the literature have to say on the matter?

I have left the interpretation of government fiscal contraction open so as to capture a broad variety of policies.

There are many articles focusing on short term impacts, not so much long term impacts

This set of lecture notes cites a bunch of great studies.

Effectively, this lecture said that fiscal consolidation (austerity) might have been expansionary (good). The Federal Reserve, however says:

  fiscal consolidation is not likely to be expansionary today.

The deciding factor seems to be whether Monetary Policy can offset short-term effects, thogh the Fed goes on to close with:

  In summary, economists have not definitively answered the question of whether and when austerity is likely to be beneficial. Much of the debate ignores the question of whether implementing austerity is feasible in nations with nonexistent records of long-run fiscal consolidation or that rely on foreign sources of deficit financing. The economic volatility of recent years provides a ripe area of future study regarding the true effects of fiscal contractions.

Or, "We'll see..."


revealed preference given an uncertain environment? classical revealed preference is about a situation where we assume an agent has a preference over some set of possible choices $X$. We then construct a revealed preference relation on $X$ from choices made given choice sets $C\subseteq X$.

But is there a theory of revealed preference for the case where the agent doesn't inherently care about his choice $x\in X$, but cares about outcome $o\in O$, where there is a function $f:X\to O$? This function $f$ may possibly be uncertain, or may vary over time?

EDIT: I am asking for a literature on the question of how we infer $u$ in this context, not on how do we infer the   induced preference on $X$.

Revealed preference theory is essentially about the observable empirical content of theories. Now if we look at the classical model of utility maximization, if there is a fixed function $f:X\to O$ and a utility function $u:O\to\mathbb{R}$, utility maximization amounts to maximizing with respect to the utility function $v:X\to\mathbb{R}$ given by $v(x)=u\big(f(x)\big)$ for all $x\in X$. There is nothing new here.

If $f$ can change or is uncertain, you are looking at a form of changing preferences or uncertain preferences. Since revealed preference theory is about the observable empirical content of theories, you need some theory about changing preferences or uncertain preferences. The task is then to identify the empirical content of the theory. For this to be an interesting exercise, there needs to be some relation between different decision problems. One example is the work of Gul and Pesendorfer on the empirical implications of the Strotz multiple self model of changing preferences with consistent planning in

  Gul, Faruk, and Wolfgang Pesendorfer. "The revealed preference theory of changing tastes." The Review of Economic Studies 72.2 (2005): 429-448.


Why was activity analysis abanadoned as a field of research? Activity analysis was a thriving research area in the 1940's and 1950's. It was fruitful enough to earn the Nobel prize for Tjalling Koopmans. But it seems to have been abandoned altogether. Mas Colell, Whiston and Greene (1995), Microeconomic Theory, Oxford University Press, only devotes a seven page appendix to it and refer the interested reader to Gale (1960): The Theory of Linear Economic Models, McGraw-Hill. Based on this, my guess is that not much additional work has been done in the area since 1960 and I wonder why.

In  Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General), 120(3), 253-281.
which is widely seen as the starting point of systematic Efficiency and Productivity Analysis, the author writes, referring to what he is about to present:

Similarly, although the treatment of the efficient production function is largely inspired  by  activity  analysis (see for example
Koopmans 1951), no  reference is made  to  this in the exposition. The
professional economist can easily draw the  necessary parallels for
himself, as indeed,  he can  note  the similarity  of the measure  of
"technical efficiency" and Debreu's "coefficient of resource
utilization"(Debreu,1951).

I would suggest that "activity analysis" has been subsumed into "Efficiency and Productivity Analysis", eventually living someplace inside Data Envelopment Analysis.
As for the reason why it did not stay in the "general microeconomics core" I believe it is because it was not a framework for economic models (that include behavioral hypotheses, incentives etc), but mostly a framework for quantitative measurement and analysis. As such it was more of a tool for applied decision making than for providing theoretical insights.


When to use a lagrange multiplier? I have a question in regards to the use of Lagrange multipliers in macro models.

I have seen that when writing a Lagrange there are two ways to write the Lagrange multiplier: 1) Indexed or 2) Unindexed. For example, in order to solve the Ramsey model in discrete time, in the simplest possible version, one would write the Lagrange as follows:

$$
L=\sum_{t=0}^{\infty}\bigg\{\beta^t u(C_t)-\lambda_t[C_t+K_{t+1}-(1-\delta)K_t-w_t-r_tK_t]\bigg\}
$$

and here the Lagrange multiplier is indexed in time and written as $\lambda_t$.

But when solving a simple lifetime consumption problem for an individual, one would write the Lagrange as follows:

$$
L=\sum_{t=0}^{\infty}[u(C_t)+\lambda(A_0+Y_t-C_t)]
$$

and here the Lagrange multiplier is not indexed in time, so we write it just as $\lambda$.

Hence, my question is when is it appropriate to use each type of multiplier?

Thank you.

I wish I could leave this as a comment, but the first formulation is a solution to a maximisation problem of the form
$$
\max_{C_t} \sum_{t} \beta^{t} u(C_t) \\
\text{s.t. } \quad C_t +K_{t+1} \leq (1-\delta)K_{t} + w_{t} + r_tK_t \quad \forall t
$$

The second formulation is a solution to a maximisation problem of the form
$$
\max_{C_t} \sum_{t} \beta^{t} u(C_t) \\
\text{s.t. } \quad \sum_{t} C_t \leq \sum_{t} (A_0 +Y_t)
$$

In a way, the first is a sequential problem, while the second is a time zero problem. In some instances the approaches are equivalent, but I'm not an expert on this.


Regression with Dummy Variables When I analyzed a data set with two categories, I used a dummy variable $z=1$ for category 1, and 0 otherwise, and added the extra term $\beta z$ to the regression model. Suppose the least squares estimate for $\beta$ is $b$. I tried to calculate some prediction intervals for the two categories. For category 1, since $z=1$, I needed to count the variance for $b$, but for category 2, since $z=0$, I did not count this variance. It then appeared that the variance for category 1 includes an additional variance because I happened to code it as $z=1$. I am new to study econometrics. Could anyone please help with this puzzle? Am I missing anything here?

That is natural and you are not missing anything.

Let $y=\alpha + \beta z + u$. Your prediction of $y$ given $z=1$ is $\hat{y} = a + b$, where $a$ and $b$ are the OLS estimates. The prediction error ($y - \hat{y}$) for $z=1$ is, thus, $(\alpha - a) + (\beta-b) + u$, which is involved with $b$. On the other hand, for $z=0$, the prediction of $y$ is $a$ and the prediction error is $(\alpha-a) + u$, which has nothing to do with $b$. As you said, the former depends on $b$, while the latter does not. (Perhaps it would help to remember that the value of $z$ is given for the prediction, and thus the prediction intervals depend on the value of $z$.)

(Calculation of the prediction intervals:) You can calculate the prediction intervals using the formula $(a+b) \pm se((\alpha-a)+(\beta-b)+u) \cdot \textit{critical value}$ for $z=1$, and the formula $a \pm se((\alpha-a)+u) \cdot \textit{critical value}$ for $z=0$. which is fine. Note that these two prediction intervals can also be written as $(a+b) \pm se(a+b+u) \cdot cv$ and $a\pm se(a+u) \cdot cv$, respectively, because $\alpha$ and $\beta$ are constant (nonrandom). How to estimate the standard errors can be found in Wooldridge's textbook (the "Prediction and Residual Analysis" section; 6.4 in 5ed).


Understanding General Least Squares From what I understand, we have our OLS estimator in matrix form which is,

$$\beta_{OLS} = (X'X)^{-1}X'Y$$

What we want to do is transform this, as the assumption that we have constant variance is not met. So we take a vector, p, for which,

$$\Omega = pp'$$

$$\Omega= \begin{bmatrix}\sigma_1^2&0&...&0\\0&\sigma_2^2&...&\vdots\\\vdots&\vdots&\ddots&0\\0&...&0&\sigma_n^2\end{bmatrix}$$

The we use this to transform $\beta_{OLS}$ to get $\beta_{GLS}$ :

$$\beta_{GLS} = (X'P^{-1}P^{-1}X)^{-1}X'P'^{-1}P'^{-1}P'y$$

My question is one to do with understanding, I don't get what p intrisically is, I get that it is being used to transform our estimate to obtain a variance term which meets the GM assumptions, but how would one actually go about finding what p is in a paractical sense?

Is the point of the $\Omega$ matrix to show what we are working to find, i.e. the actual variances?

Thank you.

The Ω matrix is the matrix of the variance of the error term for each observation. Since we do not observe the true error term, we cannot find the true Ω, but we can try to estimate it.

There are different ways of estimating Ω, and there is some debate in econometrics as to which method is the best but the most common method I think would be to take the square of the observed error divided by (1-h) where h is the projection matrix of your matrix X.


Retailer Price Setting for Existing Inventory in the Event of an Increase in Price Paid for the Good If you are a retailer, and the price you pay for one of your retail goods goes up, how do you price the inventory you already had (which you paid a lower price for)?

Here is an example of a TFD (True, False, Debatable) type question for this idea:

Suppose you run a hardware store, and the price you pay for sidewalk de-icer increases. You raise the price on the remaining stock of sidewalk de-icer in your store, for which you paid a lower price.

I think the answer to this question is false. Increasing your price on the inventory you already had violates the PMP, so any other price would lower profits.

At the time period in which you buy the new retail goods, the cost of having bought the old inventory goods is now a sunk cost. Your pricing decision I don't think should be based on the price of the old inventory. The new point where marginal cost equals marginal benefit (assuming competitiveness) is now the price of the new stock (more expensive).

Without competition though, the result will probably change, since the quantity you supply will now matter in affecting demand.


Collusion, deviation from equilibrium Two firms can produce either low (L), medium (M) or high (H) quantity. The payoff matrix is given by:

What is the outcome of this game if firms play only once?
Suppose the game is played for infinite periods and $\delta = 1/2$. Is it possible for firms to collude and choose $(L, L)$? Is it possible for firms to collude and choose $(M, M)$?

From the picture we can see that if the firms play once then the outcome is $(H,H)$. However I don't really know how to solve the second part and would really appreciate some help. What I do know in repeated infinite games that may be useful for this problem is the following.

Lets take the case of deviating from $(H,H)$ to $(M,M)$ for firm 1.

Equilibrium payoff = $3+3\delta+3\delta^2...=\frac{3}{1-\delta}$

Deviation payoff (I think that if firm 1 deviated and played $M$ then firm 2 would play L since they have higher payoff $(10)$ and so we would have)= $5+2\delta+2\delta^2... = 5+\frac{2\delta}{(1-\delta) }  $

Where $\delta$ is the interest rate after the first round. I feel that this portion is irrelevant, however, since we are talking about collusion and should consider both firms, instead of just firm 1's strategy.

Converting my comments into an answer...

In the infinitely repeated game, if the players want to collude on $(L,L)$, then there needs to be an incentive for each to stick to the plan, i.e. a punishment if one of them deviates from playing $L$.

As you have figured out, this amounts comparing the discounted payoffs from playing $(L,L)$ with a one-shot deviation of playing $H$ against $L$, and then playing $(H,H)$ forever.


Is it possible for Gross value added be negative on a company level? In National Accounts production approach, can there situations whereby the Output of a company is far lower than the Intermediate consumption therefore the Value added is negative?

Yes, it can happen if a company is selling things for less than it cost it to produce them, though for obvious reasons this doesn't happen very often (or at least not over any great length of time) as it usually doesn't make sense to continue producing in those circumstances.

You might see it occasionally, for example, in small farm businesses.  These can have high subsidies on production to begin with (which get subtracted in the calculation of GVA, narrowing the loss needed to bring it below zero), have few or no employees (just a self-employed farmer, so no or low fixed wages/CoE to be paid out), and a bad harvest or loss of livestock could result in the business not producing enough output to make GVA positive for a particular year.


Free market vs high income While answering this question I was doing some research and found that

the high-income world has Free Markets.

Is it that because they are high-income, they have free markets, Or, is it that their free market made them high-income?

A supplementary question is: if the latter is true, why don't all low-income countries adopt Free Markets?

Capitalism works best when there is elasticity- the price can go up or down by a marginal unit without running into the problem of plateauing supply or demand.

In extremely wealthy or extremely poor places, the market can experience inelasticity- where a change in the price will not affect demand.

Cheap item inelasticity:
E.g. The water is free at restaurants but we don't see people drinking insane quantities of water, though supply/$0 should equal infinite demand.

Expensive item inelasticity:
Someone is stranded in the desert and has no water. A vending machine offers him water for 100 gold coins. Even though the price is very high, the man still needs water. To save his life, the man would pay 100 or even 200 coins, doubling the price without reducing the demand. As it happens, the man has only one coin and dies because the vending machine was unable to adjust its price to make a sale.

Cheap item inelasticity is rarely a problem because if a country is stuck with undesirable surplus, it could just burn it or throw it in the sea.

Expensive item inelasticity is more prevalent in poorer places where more of the population is unable to afford important goods. A country could A) allow its people to starve B) subsidize goods for the poor C) set a maximum price for the item.

B and C are not free-market options.

A poorer economy is more likely to run into the problem of Expensive Item Inelasticity and is thus more likely to attempt to resolve it.


What would be the practicality of a widespread open-source approach in an economy? I'm not sure how to tag this so feel free to add any tags you see as relevant.

The question here is about anything that uses a proprietary approach today and applying open-sourcing to it.

What if someone open-sourced their work in such a way that it can be used by absolutely anyone on condition they put a bit of money in to keep a project going?

This instead of intellectual property or copyright sometimes heavily restricting usage and where there is not necessarily a benefit to the community.

Hope you get the gist and please comment below for me to clarify if necessary.

So suppose there is new technology $A$ that only 1 person has access to. If there are multiple firms with production technology $y=k^\alpha$ then obviously if that new technology was available to them at low/no cost, the overall productivity of society would increase (each firm has $y=Ak^\alpha$)

The problem is that it is likely the case that $A$ requires expenditure to make. You need some way to incentivize the production of that technology (at least in a basic neoclassical framework). So if you make it proprietary then the other firms may have to pay for it, or you can give it copyright so that only 1 firm has access to it.

In Romer's endogenous growth model, firms have an R&D cost to produce their final good, but they have monopolistic power in the intermediate step to ensure that they can make a profit. If they didn't have this patent then they would not produce the technology.

There are newer/more advanced models in law & economics that discuss different kinds of IP arrangements. A great question is how are things like WIkipedia so prevalent where most of the authors see no profit for their effort but they do it anyway. Ostensibly they achieve some sort of utility for it. But then they are producing a 'public good' and in that case others will freeride (so its only sustained if their utility from it is really high).


Matching in Blanchard-Diamond (1994) Setup Blanchard-Diamond (1994) have a model where each unemployed has a single ball (application) that she tosses into urns (vacancies). With probability $a$ the application lands in the urn - the unemployed manages to fill out the form, and his application is "valid".

Vacancies are open for a fixed period and then evaluate their application pool, leading to multiple applications per vacancy. Under some conditions, the distribution of applications per vacancy (denoted as $g(x)$) will be Poisson with expected value $au/v$.

Firm-based job-finding rate The number of matches is hence given by the measure of vacancies that have at least one application, times the number of vacancies

$$M = (1-g(0))v$$

and the job-finding rate is given by

$$ M/u = (1-g(0))v/u$$

Unemployed-based job-finding rate Instead of looking at the firms, one can look at the unemployed. As firms randomly draw from the pool of applicants, the average chance of an unemployed matching is the probability of matching times the inverse of the number of contestants that he will face:

$$ f = a\frac{1}{E[x | x > 0]} \\
= a\frac{1}{\frac{E[x]}{1-g(0)}}\\
= a\frac{1-g(0)}{au/v}\\
= (1-g(0))v/u$$

Which is turns out to be the same job-finding rate as calculated from the firm's perspective. This makes sense, as it needs to be an identity.

Firm-state-based job-finding rate Finally, to the part where I am struggling: An alternative way of computing this job-finding rate should be

$$ \tilde f = a \sum_{x=1}^\infty Prob(\text{applicant matches with firm with $x$ many applications} | \text{ she matched}) \frac{1}{x}$$

Which basically has the same logic, but is more detailed. This is interesting when one wants to analyze the $x$-component to the job-finding rate (i.e.: How relevant are firms with 5 applicants to the job-finding rate). However, the probability appears to be complicated. How do I compute this job-finding rate?

The total number of matched applications is

$$\sum_{x=1}^\infty g(x)xv = E[x]v$$

The number of applications matched with vacancies with $x$-many applications is

$$g(x)xv$$

Hence

$$Prob(\text{matching with x} | \text{matched} = \frac{g(x)x}{E[x]}$$

Using this in the equation in the question gives

$$ \tilde f = a \sum_{x=1}^\infty \frac{g(x)x}{E[x]}\frac{1}{x}\\
= E[x]a \sum_{x=1}^\infty g(x) \\
= \frac{v}{u} (1-g(0)) = f $$


Can absence of inflation be accounted for by a reconfigured class structure? A previous and oft-heard question asked why no inflation results from the Fed pumping money into the economy.

Are we simply seeing a methodical wage suppression, thus no official "inflation," while prices soar in certain sectors dominated by "shareholders," non-wage income, and the "one-percent" or whomever?

The money moves first into the financial industry, where actual production investment is less attractive. It seems that as long as no money gets locked into "sticky" labor contracts, the Fed can pump away and the results are not deemed "inflation." The money does not cycle up in wages or wage-earner goods.

In other areas, however, we do see soaring prices: art, luxury goods, high-end urban real estate, philanthropic gestures, political campaign funding, ivy educations, high-tech medicine, hedge fund fees, dividend payouts, tax-avoidance cash hoards, stock bubbles, etc.

Can the absence of official "inflation" be explained in large part by the "disaggregation" of labor, middle-class debt, and a new class configuration since the late 1970s? More like a "redistribution" or even a "customizing" of inflation.

Quantitative easing without high inflation can be explained by low velocity of money.

Think about a property tycoon who sees times are hard and instead of investing all his money in a development project, he buys gold which he keeps in a vault. The property project would have provided employment, and the wages would be used by workers to buy other things in the economy (high velocity). The gold in his vault just sits there (low velocity).

Economic troubles result in low confidence and low velocity of money. Central banks pumping money into the economy somewhat offsets this. As long as the overall velocity of money matches the productive capacity of the economy, there won't be high inflation. One concern of course is that central banks cannot control the velocity of money, so if all this new money gets velocity we could get high inflation that central banks cannot control.

Now think about where you mentioned soaring prices. Many of these are places where rich people can store wealth at low velocity: real estate, fine art, gold, etc. So yes, the effects very much are connected.


Impact of government subsidy on labour supply If the government pays a certain amount $b>0$ to every person who is not working, what is the impact of this subsidy on labour supply? How does it alter the reservation wage? Is your answer modified when payments are restricted to persons who are looking for a job?

My attempt: Suppose $A$ is an individual in the labour force. For an individual who is not in the labour force, there is no impact on labour supply. Therefore, it makes sense to apply the analysis to a person in the labour force.

In the income-leisure ($i$-$l$) diagram (of a week) for an individual $A$, without any government aid, let $w_R$ be the reservation wage. Suppose $G$ represents $A$'s other sources of income. Let $T=168$ be the number of hours in a week. Our analysis is done in the interval $[0,T]$ of the $l$-axis. We have the line $i=G+w(T-l)$ or $$i+wl=(wT+G).$$ At $l=T$ and $w=w_R$, $A$ is most happy (maximum utility) to not work at all. However, $w_R$ is the maximum wage rate at which $A$ doesn't work (by definition).

With the given government intervention, $A$'s original line shifts upward by $b$. $A$ comes to a higher utility point (than in previous case without government intervention) whether he is working or not. It is impossible to tell how the $w_R$ will be altered in this case. It is possible that if $A$ was working before, $A$ is not working now and vice-versa.

Am I correct?

The individual has a utility function over consumption and leisure

$$U(C, \ell) = U(C, T-L)$$
and to keep this static, it has the no-savings/no-credit budget constraint

$$C = G + wL$$

He wants to maximize utility. Inserting the budget constraint into the utility function the first-order condition is (maximizing with respect to $L$)

$${\rm (f.o.c)} :\;\; U_c(G+wL, T-L)\cdot w - U_{\ell}(G+wL, T-L) = 0 $$

This will hold in all optimal solutions. Set $L=0$ to express the reservation wage, (i.e. ask "what is the wage consistent with zero work?")

$$L=0 \Rightarrow U_c(G, T)\cdot w - U_{\ell}(G, T) =0$$

$$\Rightarrow w_R = \frac {U_{\ell}(G, T)}{U_c(G, T)}$$

Then

$${\rm sign} \left\{\frac {\partial w_R}{\partial G}\right\} = {\rm sign} \left\{U_{\ell c}(G, T)\cdot U_c(G, T) - U_{cc}(G, T)\cdot U_{\ell}(G, T)\right\}$$

We see that

A) If preferences are assumed separable between consumption and leisure, i.e. if  $U_{\ell c} = 0$, then under the usual assumption that  $U_{cc} <0$ we see that $\frac {\partial w_R}{\partial G} >0$.

B) If separability is not assumed, then it is usually assumed (and reasonably) that $U_{\ell c} >0$, in which case we again obtain $\frac {\partial w_R}{\partial G} >0$.

In both cases, an increase in $G$ (which is what happens when the government pays the amount $b$), increases the reservation wage. If we assume that wages are the same before and after the government subsidy, then if the person did not work, he will continue not to work, while if the person worked previously, he may now stop, given the government subsidy.

Of course, making the problem dynamic by introducing intertemporal utility maximization and a consumption-savings decision, requires an analysis on its own.


What is a bilateral currency swap line? Please explain in simple terms. How exactly does it function?

A bilateral currency swap line allows two central banks to immediately swap currencies directly between each other up to a specified amount. The swap allows Central Bank A to immediately buy Central Bank B's currency at the official exchange rate. The currency never leaves each Central Bank; it is just reassigned to a new owner.

Crucially, the two banks also agree that Central Bank A has to buy back its currency at the same rate plus interest at a specified future date. Central Bank B never assumes any risk for Central Bank A's newly purchased reserves and is no party to any agreements which make use of the funds.


Difference between a multiple regression and several linear regressions? Context: I'm an undergrad who took Intermediate Econometrics more than a year ago and I'm trying to brush up on some of the skills.

As I was reviewing multiple regression, I realized I didn't quite understand what makes the regressor coefficients different when doing a multiple regression vs doing a univariate regression. For instance, if I were to regress wages on years of education, why would the coefficient on years of education be different than when I regressed wages on years of education and test scores?

The data might be correlated which can lead to simple and multiple linear regression models giving different results.

Which goes against the assumption of no multi-collinearity:
Multicollinearity occurs when independent variables in a regression model are correlated.

When modeling years of education to wages, the results may show significance but modeling both years of education and test scores could show years of education as not significant because years of education and test scores are correlated.

Try  plotting years of education and test scores.


What was Paulus's "famous definition of price"? Schumpeter (1912 [1954]) mentions

  the famous definition of price by Paulus.

What does this refer to?

Julius Paulus Prudentissimus, circa 230 CE

"material was selected which, being given a stable value by the state, avoided the problems of barter by providing a constant medium of exchange.
That material , struck in due form by the mint, demonstrates its utility and title not by its substance as such but by its quantity, so that no longer are the things exchanged both called wares but one of them is termed the price.
An today its is a matter for doubt  whether one can talk of sale when no money passes. "

https://books.google.com/books?id=NgZKDwAAQBAJ&pg=PT123&lpg=PT123&dq=Julius+Paulus+Prudentissimus+economics+++definition+of+price&source=bl&ots=0FXjkqEeus&sig=ACfU3U2ZKnUHIoR4DXwLnTMmDpCKRyD0PQ&hl=en&sa=X&ved=2ahUKEwjjqZOAhdTpAhUETd8KHXXJBuQQ6AEwAXoECAoQAQ#v=onepage&q=Julius%20Paulus%20Prudentissimus%20economics%20%20%20definition%20of%20price&f=false


Disaggregated data on prices in US I have seen several papers that refer to the CPI Research Database, which contains micro-level data on prices in the US. For example, the data was used by Klenow and Kryvtsov (2005) and Nakamura and Steinsson (2007).

The only similar thing I found is Average Price Data on the site of the Bureau of Labor Statistics. Unfortunately, this dataset is quite small. First, only food and fuel are presented there. Second, average consumer prices for food are available for the U.S. city average and four regions only. However, Nakamura and Steinsson (2007) write that prices of food are collected monthly in 87 areas.

So, there potentially is a more informative dataset which contains information on prices in all areas.

Can I get it? What is the CPI Research Database? Is it available for the general public?

A paper published in 2009 by the Federal Reserve Board gave a brief description

  The BLS surveys about 85,000 items a month in its Commodities and Services Survey. Individual prices are collected at around 20,000 retail outlets across 45 large urban areas. The survey covers all goods and services other than shelter, or about 70 percent of the CPI based on BLS consumer expenditure weights. The CPI Research Database (hereafter CPI-RDB) maintained by the BLS Division of Price and Index Number Research contains all prices in the Commodities and Services Survey since January 1988. We use the CPI-RDB through May 2008, for a sample of "1988-2008".

  The BLS collects consumer prices monthly for food and fuel items in all areas. The BLS also collects prices monthly for all items in the three largest metropolitan areas (New York, Los Angeles, and Chicago). The BLS collects prices for items in other categories and other urban areas only bimonthly.

Details may have changed since then but essentially the database is an detailed dataset of prices for a wide range of selected items charged by a large sample of individual retailers at different points in time

It is not available to the public.  In particular, it contains commercially sensitive information about individual retailers

It is available to some academic researchers who reach an agreement with the Bureau of Labor Statistics putting restrictions on how they handle and how they use the database and on the locations where they access the data; BLS also charges a fee.  BLS provides details on Restricted Data Access on its website


Is clustered standard errors the best way for all regressions that uses clustered data? Using clustered standard errors assumes that the regression coefficients are the same for all the clusters in the data, right? What if they are not the same. For example, I have used F-test to compare regression coefficients across the 3 clusters in the plot below. The null is rejected that the regression coefficients are the same across the three regression models. So my intuition is that I cannot do something like "regress A B, cluster(C)", for example in STATA, right?. Thus, I should do a regression for each cluster instead? I will read on clustered standard errors later, so a hint will help.

Using clustered standard errors in Stata doesn't impose any additional restrictions on your coefficient estimates. The coefficient estimates are independent of the vce() option you choose.
If you have reason to believe your standard errors should be clustered, it means you think that there is some association between the cluster variable and your outcome. If that's the case, then you should absolutely include the cluster variable in the regression itself, at least as a fixed effect. Typically, it's most efficient to do that using xtreg orareg. Both allow the vce(cluster clustvar) option.
If you only include your cluster variable as a fixed effect, then you are implicitly assuming that the coefficients across clusters are the same but allowing for different intercepts - that's not a consequence of clustering the standard errors, but of the underlying parametric model. If you want to allow for varying coefficient estimates between clusters, you could include interactions between your independent variables and your cluster variables.