What is a supply side shock in macroeconomics? I was hoping someone could clarify what exactly is meant when someone refers to a country as having undergone a 'supply-side shock' and generally speaking when one is evaluating the health or growth of an economy, what is meant by the supply side of the economy vs. the demand side of it? Which components of GDP are considered as which?

Despite a lot of googling, it has been pretty difficult to find answers to this as most results are either in a micro-context or fail to provide examples of these things as well as their consequences.

In the framework of the ISLM model, a supply shock would be defined as any exogenous force that affects the ability of an economy to produce its natural level of output, this ability is represented by a production function that often relies on available resources and production technology. Therefore, any factors affecting the availability of resources or technology will be considered a supply shock (e.g. Drought and crops).

On the other hand, a demand shock acts on aggregate demand by influencing planned expenditure by economic actors or the amount of real money balances that economic actors desire to hold.

In short, if it affects available production inputs or production technology, it's a supply shock.

Notice that the GDP is just a measure of all goods and services produced in an economy for a given period of time. If you use the expenditure approach to GDP (Y = C + I + G + NX), a supply shock will not immediately act on this formula, rather it affects the formula Y=F(X) (where X is a vector representing production inputs). But note that the two formulas, meaning the two "Y"'s must equal each other, therefore, there will be changes in the first equation to match the second equation at some level of Y. However, you can't differentiate these changes from changes arising due to a demand shock unless you have the whole story. You can't just look at "C" for instance, and assume that any changes in "C" resulted from a supply shock.


How does capital accumulation raise the demand for labor in "Artificial intelligence, Automation and Work" by Acemoglu and Restrepo, the authors write:

  Capital accumulation: As our framework in the next section clarifies, automation corresponds to an increase in the capital intensity of production. The high demand for capital triggers further accumulation of capital (e.g., by increasing the rental rate of capital). Capital accumulation then raises the demand for labor. This may have been an important channel of adjustment of the British economy during the Industrial Revolution and of the American economy in the first half of the 20th century in the face of mechanization of agriculture, for in both cases there was rapid capital accumulation (Allen, 2009; Olmstead and Rhode, 2001).

The sentence "Capital accumulation then raises the demand for labor." is left unelaborated. I fail to understand why one should necessarily lead to the other. Can anyone explain?

Good question! Here Acemoglu and Restrepo discuss one of the many possible effects of automation, such that automation is likely to induce additional usage of capital in the sector or additional capital accumulation, which can increase labor demand.

They elaborate on this effect on their 2018 AER paper "The Race between Man and Machine: Implications of Technology for Growth, Factor Shares, and Employment".

In a static version of their model where capital is fixed and technology is exogenous, automation reduces employment and the labor share, and may even reduce wages. Their full model endogenizes capital accumulation and the direction of research toward automation and the creation of new tasks. If the long-run rental rate of capital relative to the wage is sufficiently low, the long-run equilibrium involves automation of all tasks. Otherwise, there exists a stable balanced growth path. Stability is a consequence of the fact that automation reduces the cost of producing using labor, and thus discourages further automation and encourages the creation of new tasks. The response of capital ensures that the productivity gains from both automation and the introduction of new tasks fully accrue to labor (the relatively inelastic factor).


Expected Utility and Jensen's Inequality Consider two random variables (costs and valuations) distributed $v\backsim G(.)$ and
$c \backsim F(.)$ with pdfs $g(.)$ and $f(.)$. Let the supports of $c$ and
$v$ be $[x,y]$. Let $x<a=E(v)<b<y$, so $[a,b]\subset\lbrack x,y]$. Now
consider a strictly concave (twice differentiable and continuous) utility function
$u(.)$, with $u^{\prime}(.)>0$, $u^{^{\prime\prime}}(.)<0$, and $u(0)=0$
(passes through the origin). Establish sufficient conditions such that the
expression
$$\int_{a}^{b}u(E(v)-c)f(c)dc-\int_{a}^{b}\int_{x}^{y}%
u(E(v)-v)g(v)f(c)dvdc\geq0,$$ where $E(v)=\int_{x}^{y}vg(v)dv.$

Things I've tried:

$\int_{0}^{\bar{v}}u(E(v)-v)g(v)dv\leq0$ by Jensen's inequality. To see
this, let $E(v)-v=t$. But $E(t)=E_{v}[E(v)-v]=0$, and so $E(u(t))\leq
u(E(t))=0$, since $u(0)=0$ by assumption.
Clearly, $\int_{a}^{b}u(E(v)-c)f(c)dc\leq0$, since we are integrating the
integrand $(E(v)-c)$ from $a=E(v)$ to $b$.
Intuitively, a variant of Jensen's inequality should apply if $c$ and $v$
are i.i.d. Let $c$ and $v$ be i.i.d. with identical supports. Then the
integrands are the same, and we have the expression
$$\int_{a}^{b}%
u(E(v)-v)f(c)dc-\int_{a}^{b}\int_{x}^{y}u(E(v)-v)g(v)f(c)dvdc.$$
However, we
can't apply Jensen's inequality directly since $\int_{a}^{b}u(E(v)-v)f(c)dc$
is not $u(E(x))$, even if we "factor out" the outer integrals. $\int_{x}%
^{y}u(.)g(v)dv$ seems to be a form of $E(u(x))$.

At a loss as to what to do here. Any help would be greatly appreciated. Thank you!

Didn't manage to get to a definitve answer in one shot, but it seems to me that Jensen inequality is not going to help much.

Build up:

You are essentially asking that

\begin{equation}
   E_v \left(u(a - v) \right) \leq E_c \left(u(a-c) |a\leq c \leq b\right)
\end{equation}

for a function $u$ increasing and concave and $[a, b] \subset Supp_v = [x,y]$.

In the language of measures, the above condition can be rewritten as

\begin{equation}
   \int_x^a u(a-c) dG(c) + \int_b^y u(a-c)dG(c) \leq \int_a^b u(a-c) \cdot \left[\frac{f(c)}{F(b)-F(a)} - g(c) \right]dc.
\end{equation}

First term on the left is certainly positive, second term on the left is certainly negative. The term on the right is of undetermined sign: $u(a-c)$ is negative in the integration interval, but $\frac{f(c)}{F(b)-F(a)}$ cannot be uniformly lower than $g(c)$ on $[a,b]$, as the former on this interval must sum up to 1 and the latter to $G(b)-G(a) \in (0,1)$.


Calculating income-expenditure multiplier? If planned aggregate expenditure in an economy can be written as: PAE = 5000 + 0.8Y, what is the income-expenditure multiplier in this economy?

My Attempt:

Y = 5000 + 0.8Y
Y - 0.8Y = 5000
0.2Y = 5000
Y = 25000

Since the marginal propensity to consume (MPC) is equal to ΔC / ΔY, where ΔC is change in consumption, and ΔY is change in income.

25000 / 20000 = 1.25

Do I take this further using multiplier = 1 / (1 - MPC) = 1 / (1-1.25) = 4

No, that is not correct. In the Keynesian model, the only variable that reacts to output is consumption. Other components of the aggregate demand do not.

For instance, in a closed economy, aggregate demand is $C+G+I$. Here, $C=c_0 + c_1Y$, where $c_0$ is autonomous consumption and $c_1$ is the MPC.

Hence, planned expenditure is

$$ Y^e = c_0 + G + I + c_1Y$$

which can be condensed to

$$ Y^e = a + bY $$

This is the equation you are given. Thus, the MPC is 0.8. This is actually the slope of the PAE curve in the Keynesian Cross diagram. It is usually lower than one. Calculation of the multiplier goes as normal.


Difference between GDP and GNI in this exercise Based on domestic production we observe the following income flows in a period:

  labor income of domestic residents: 150\$
  capital income received by foreign residents with a foreign citizenship: 5\$
  capital income of domestic residents with a foreign citizenship: 15\$
  capital income received by foreign residents with a domestic citizenship: 25\$
  capital income earned by domestic citizens with a domestic residence: 20\$

  Calculate the Gross Domestic Product (GDP) and the Gross National Income (GNI) of the economy:

Not sure how to solve this problem. As I understand GDP = 1+3+5, GNI = 1+4+5

I don't think that I understand how to treat foreign residents with foreign citizenship.

GDP refers to income associated to particular geography (or residence).

GNI refers to income associated to a particular set of individuals (citizens), regardless of where they earn their income.

Since geography and citizenship do not fully overlap, they might be different:

I think this is enough to help you answering the question.

(code for reproducing the figure here)


Expected Value of a Infinite Process Assume $x_t$ is an unit root process. Write first difference of $x_t$  as

$\Delta x_t$ =$\rho$ $\Delta x_{t-1}$+ $\epsilon_t$

Where $\epsilon_t$ is a white noise process.

How can we calculate $ E_t [x_{t+j}]$ when $j \rightarrow \infty$.

Suppose:

$a_t$= $x_t$ +$z_t$

$\Delta x_t$ =$\rho$ $\Delta x_{t-1}$+ $\epsilon_t$

$ z_t$ =$\rho$ $z_{t-1}$+ $\eta_t$

How can we calculate $ E_t [a_{t+j}]$ when $j \rightarrow \infty$.

You are asking about the expected value of the leading term of a sequence. There can be no general answer given the assumptions you make, since for example

$$x_{t+1} = x_{t} + v_{t+1}, \;\;\;E(v_{t+1}) = 0,\;\;\; x_0 \;\; \text{given}$$

is a unit root process, and its expected value is equal to $E(x_{t+1})=x_0,\;\;\; \forall t$, while

$$x_{t+1} = a +x_{t} + v_{t+1}, \;\;\;E(v_{t+1}) = 0,\;\;\; x_0 \;\; \text{given}$$

is also a unit-root process, but $E(x_{t+1}) = x_0 + a\cdot(t+1)$

which is very different compared to the previous case.


Is the arable land a mean of production? Wikipedia claims that "capitalism is an economic system and an ideology based on private ownership of the means of production and their operation for profit".

And then, the land used for agriculture is a mean of production? Are the farmers capitalists?

Yes.

Anyone who utilizes their privately owned property or assets as a means of production for the sake of profit is a capitalist.

In this case the farmer's capital  is the land which they use for agricultural production.


Government debt constraint I am reading Some Unpleasant Monetarist Arithmetic (Sargent and Wallace, 1981) and I had some questions about a claim made by the authors. They say:

  The public's demand for interest-bearing government
  debt constrains the government of a monetarist economy in at least two ways. One way the public's demand for bonds
  constrains the government is by setting an upper limit on
  the real stock of government bonds relative to the size of
  the economy. Another way is by affecting the interest rate
  the government must pay on bonds.

First of all, are we assuming that the government borrows from the private sector and spends it on something that improves productivity? For example, the government could borrow from the private sector and spend it on a road (something that increases productivity) or they could spend it on unemployment benefits (beneficial, but not productive). I think "real stock of government bonds" is what is confusing me. So the way I understand the first reason is that if government debt becomes too high and the interest payments exceed the growth rate of the economy, this will not be sustainable because the government will have to pay more to the private sector than is produced by the private sector.

For example, consider a extremely simplified economy where corn is the only thing produced and the agents are: (i) the government (ii) the private sector. So the government borrows 1 ton of corn from the private sector and promises to pay back 2 tons next year. They use that corn to improve corn producing ability of the private sector. However, the private sector was only able to produce 1.5 tons of corn the following year. Hence the real government debt is too high relative to the real size of the economy. Is this what Sargent and Wallace are referring to?

The second reason sounds very logical but I just want to ensure I understand it correctly. Is it simply saying that if the interest payments on government debt becomes too high, they will have to raise taxes to a level that is not optimal?

However, the second reason appears to be very similar to my corn example so it feels like I am not understanding the authors reasoning very well. If anyone could explain or refer me to a source, I would greatly appreciate it.

The government just consumes within this model, as is similar to other standard DSGE models. Therefore, its consumption (G) never has an effect on productivity. Imagine a wartime situation where the government is buying goods that are used to provision the army; the goods are consumed, but will not help develop the domestic economy. If you wanted to simulate government infrastructure spending raising productivity within these models, the government infrastructure build would have to be added to business investment (raising the capital stock).

The "real government debt" constraint says that although the nominal level of debt is fixed, if future taxation policy is expected to be "too low" relative to the nominal stock of debt, the price level will rise now. This the Fiscal Theory of the Price Level. The governmental budget constraint is used to determine the formal relationship between the expected primary surpluses and the real value of current government debt (effectively, the current price level, since the initial nominal debt level is fixed).

With regards to your examples, even if debt due was greater than GDP, the situation can be sustained. (We have seen debt-GDP ratios greater than 100% in a number of countries, including Japan at present.) Most of the debt will be rolled over into new debt. That is, in year 2 of your example, the government could just borrow the nominal amount equivalent to two tons of corn, and roll over the debt from year one. (This is possible since these are models of monetary economies, in which nominal claims - money and bonds - are used in exchange, and not just goods themselves, see below.) The issue with sustainability is whether the debt/GDP ratio will tend to infinity.

If transactions were barter transactions with real goods, you could then have "real debts" which are payable by goods (corn, say). What the limits are for paying back debt depends upon your assumptions about the payment system. Normally these models assume simultaneously clearing of all transactions in a period. However, if we assume that there are multiple transactions possible within a period (and we are only simulating the aggregate), the government in your example could borrow corn from some members of the private sector, and then use that to pay off other lenders, and then repeat the process until the entire debt stock is rolled over. If that is assumed not be posisble, the government would have to lengthen maturities, so that only part of its debt stock needs to be rolled over, and the previously described procedure is again possible. Having debt with multiple maturities is avoided in DSGE models due to complexity concerns, but it would be necessary if the payments system was restricted like this.


HARA preferences details I am searching for some exntensive details about HARA preferences.  Where could I find some extensive details for HARA preferences? Something like a textbook or notes

The paper Optimum consumption and portfolio rules in a continuous-time model (Merton (1971)) presents (as far as I know, the initial presentation.
[
Next we turn to a paper that discusses the importance of the HARA utility.
The Fundamental Nature of HARA Utility (Perets and Yashiv (2013))

Many models in Economics assume a utility function belonging to the
HARA family. This paper shows that HARA utility is fundamental to
economic analysis. The HARA functional form is the unique form which
satisfies basic economic principles in an optimization context. Using
HARA is not just a matter of convenience or tractability but rather an
essential restriction....

This notable paper has a multi page exploration of the HARA utility family.
Implications of Constant Risk Aversion (Bamberg and Spremann (1981))

The assumption of constant risk aversion often leads to a considerable
simplification of decision theoretic analyses. It is shown that this
restriction on constant risk aversion permits the description of a
wide range of risk averse patterns between the extreme cases of risk
neutrality and the exclusive orientation on the pessimistic maxmin
criterion. In particular, a new axiomatic foundation of the constant
risk aversion is given and a series of properties for the certainty
equivalent are derived. Possible applications are shown by the
treatment of risk premiums, values of information, portfolio
selection, capital market theory and syndicates.

There is a book that I can't vouch for but may be useful:
Hyperbolic absolute risk aversion: Second Edition


What measure of unemployment is used by central banks to find out whether the rate of unemployment is below the natural rate of unemployment? Having an unemployment rate below the natural rate of unemployment (NRU) leads to wage inflation and a reduction in productivity. Seeing the consequences of that, and knowing that one of the roles of a central bank is to control unemployment and inflation, central banks must accurately determine what the unemployment is currently at and see whether it is above or below the NRU.
I ask this because after looking at the Bureau of Labor Statistics' data on U-3 and U-6 (seasonally-adjusted) between the years 2010 and 2020, the lowest U-3 got was 3.5% in 2019Q4, whereas U-6 was 6.5%. However, the NRU in 2019Q4 4.45%
So, what measurement is used by central banks and what would be the best way to measure unemployment so that it can best be compared to the NRU?

The phrase “natural rate of unemployment” has been largely replaced by NAIRU or similar concepts. Each country has its own definition of the unemployment rate, the U.S. “headline” measure is U-3.
Nobody has created an estimate for NAIRU that is based on a function of other variables, instead it is estimated based on the behaviour of the economy and the chosen unemployment rate measure. This implies that a NAIRU estimate is defined relative to the unemployment rate used in the estimation procedure. In the United States, most researchers would run their estimation versus U-3, but one might need to validate this.


Workforce productivity If I would like to say, in a technical way, that the problem of a place is its lazy people, then I could say that its workforce productivity is low. However, "workforce productivity" is composed by these elements:

Physical-organic, location, and technological factors;
Cultural belief-value and individual attitudinal, motivational
and behavioural factors;
International influences – e.g. levels of innovativeness and
efficiency on the part of the owners and managers of inward
investing foreign companies;
Managerial-organizational and wider economic and political-legal
environments;
Levels of flexibility in internal labour markets and the
organization of work activities – e.g. the presence or absence of
traditional craft demarcation lines and barriers to occupational
entry; and
Individual rewards and payment systems, and the effectiveness of
personnel managers and others in recruiting, training, communicating
with, and performance-motivating employees on the basis of pay and
other incentives.

In that sense, saying that the problem of a place is lazyness, some advocates would ask: How do you measure it? The answer would be: With workforce productivity. However, those advocates of lazy people could argue that workforce productivity is low because it is affected by any components from 1 to 6.

Is there any technical term to refer lazyness?

The terms of art here for laziness like concepts are "shirking" and "effort", particularly  "endogenous effort" or "variable effort". You should also look into "efficiency wages". "Free riding" sometimes appears in this literature but because it is used heavily in the public goods literature it will have more false positives.

This paper may also be of interest:

  Using a sample of male and female workers from the 1992 Employment in
  Britain survey we estimate a model of employees’ self-reported effort
  levels. Effort is modelled as a function of wages, the perceived
  monitoring and supervision environment in the individual's workplace,
  labour-leisure preferences, local unemployment rates and unionisation.
  Using a two-step estimation strategy to account for the endogeneity of
  the wage, we find that effort levels are increasing in wages and in
  preferences for work over leisure. While the extent of monitoring
  seems not to affect workers’ effort levels the ease with which they
  can be dismissed is a motivating factor. Unionisation reduces
  self-reported effort levels which may reflect the outcome of an
  effort-bargain and, in contrast to the efficiency wage shirking story,
  local unemployment rates do not affect effort. Finally, in spite of
  being paid more than women, men report exerting less effort at work.

The Determinants of Work Effort: Evidence from the Employment in Britain Survey
(Clark and Tomlinson (2001))


Reason behind the decomposition of price effect into substitution and income effects I was studying the decomposition of price effect into substitution and income effects. I am finding it a bit complicated.

This is what I have understood:

(0) Let us assume that there are two commodities. We have a budget line and an indifference map. The budget line is tangent to one of the indifference curves. This point of tangency is the initial equilibrium point.

(1) Due to the change in price of a commodity, the budget line rotates to a new position and we obtain a new equilibrium point. This change in position of the equilibrium point is known as the price effect.

(2) Due to price change, the relative price of the commodity as well as the real income of the consumer changes. Due to change in relative price of the commodity, the consumer will substitute the relatively less expensive commodity for the relatively more expensive commodity and we get a new equilibrium point. This change in equilibrium point is the substitution effect. Due to change in real income, the consumer will change his consumption of the two commodities depending on whether they are normal or inferior commodities and we get a new equilibrium point. This change in equilibrium point is the income effect. Hence we can say that the price effect is the resultant of the substitution effect and the income effect.

(3) To segregate the two effects we draw a hypothetical budget line by shifting the rotated budget line to compensate for the change in real income and the magnitude of the shift varies according to the approach of compensation followed (Hick's approach or Slutsky's approach).

(4) The budget line thus obtained as a result of rotation and shift starting from the original budget line shows the substitution effect.

(5) The remaining part shows the income effect.

(6) Thus we get the substitution effect by rotating and shifting the budget line and then the price effect can be viewed as the combination of substitution and income effects.

Have it grasped it correctly? I am finding all this a little twisted and kind of a reversed logic. First we rotate the budget line to get the price effect and then shift the budget line to obtain the substitution effect or segregate the substitution and income effects. Finally to get to the price effect, we first get to the substitution effect and then the income effect.

I do not understand the rationale behind the decomposition of price effect. Why are we decomposing the effect of a change in price of one commodity into all these effects which are (as I have understood), all hypothetical. Is there any particular advantage of this decomposition? Also I don't exactly understand the meaning of real income. Does it mean the quantity that we can buy given the income and price? If someone could explain it with an example I would be very grateful. Also in substitution effect, why do we substitute the relatively less expensive commodity for the relatively more expensive commodity? Why not the reverse? Also what is the significance of the compensated demand curve? Why do we need two demand curves.

Why are we decomposing the effect of a change in price of one commodity into all these effects which are (as I have understood), all hypothetical.

They're hypothetical, but they are nevertheless meaningful.  We can easily imagine what it would be like if an agent had a larger budget while prices remain unchanged; we can also imagine what it would be like if, under diminishing marginal utility assumptions, the relative prices of goods were to change.

One reason we do this is that it helps develop intuition and show why naive assumptions don't necessarily hold.  For example, if we have goods $x$ and $y$, prices $p_x$ and $p_y$ with budget $B$ in an initial equilibrium, we might naively think that setting $p_x^{'} = 0.5p_x$ means that we consume twice as much of $x$, when this is not the case for most utility functions.

  Also in substitution effect, why do we substitute the relatively less expensive commodity for the relatively more expensive commodity? Is there any particular advantage of this decomposition?

The answer to the second question is that the Slutsky decomposition allows us to tell a story that answers the first question - when the price of $x$ falls, we may buy more of $x$ (an income effect), but we will also buy more of $y$ because diminishing marginal utilities implies that after using the price-savings to buy some number of additional units of $x$, we get more "bang for the buck" by purchasing an additional unit of $y$ instead.  This is the substitution effect.

  Also I don't exactly understand the meaning of real income.

Real income is income adjusted for inflation from a base year, so that it reflects real purchasing power. In the context of these Econ 101 budget-line models, it's implied that the budget is in real units for pedagogical reasons. There's no base year, but the point is to ensure that any price-changes contemplated are "real", and to get you to think of consumption as the basic economic unit, rather than money per se. Often you'll see simplifications where one of the goods is priced at $1/unit, and referred to as the "numeraire".


Why are imports subtracted from GDP? GDP is a measure of a country's production.

$$GDP = C + I + G + X_n$$

$C$ = Consumer Consumption
$I$ = Gross Investment
$G$ = Government Expenditures
$X_n$ = Exports - Imports

Exports are what we produce and make a profit from by selling to buyers outside our country.  Imports are not produced by our country, so it shouldn't be included in the GDP, so it makes sense to exclude it from the calculation; ie. there should be no "- imports" in the calculation.

However, the calculation subtracts imports from the GDP.  Imports somehow take away from what we produced?  That seems to say, calculate how much I have produced, X, and then don't count some of it because I imported Y.  Which doesn't make sense given that importing doesn't remove goods and services that have already been produced!

For example, let's say I can take apples and make pies... I produced value in the form of the "pie" quality.  Importing the "pie" quality and tacking it on an apple creates an apple pie.  However, I didn't make that "pie" so I can understand how it doesn't get included in the GDP: the value of the "pie" quality was not produced in this country, so it isn't included in the GDP.

Let's also say my GDP = "made a cat meow" + "turned a tree into a fountain".  Somehow, by importing the "pie" quality, I am to ignore some of the value of making a cat meow?

When we import something, we consume it. So when calculating consumption we are bound to count import as a positive component of GDP. Since it is not (we did not produce imports domestically), we subtract it to make it neutral.


Asymmetric (in sign) cross-price derivatives in consumer-theory problem I'm puzzled why, in the following optimal-choice problem, good $x$ depends on price $p_y$ but the opposite is not true. Should not the sign of $\frac{\partial x}{\partial p_y}$ be the same of $\frac{\partial y}{\partial p_x}$?

Optimal-choice problem: given prices $p_x$ and $p_y$ and income $m$ find the optimal demand function for $x$ and for $y$:
\begin{equation}
\max_{x,y} \{x\cdot(y+6)\} \qquad \text{s.t. } p_x x+p_y y \leq m \tag{1}
\end{equation}
after imposing $MRS_{xy}=p_x/p_y$ and substituting back in the budget constraint I find:
\begin{equation}
x = \frac{m + 6p_y}{2p_x} \qquad\qquad y = \frac{m}{2p_y}-3 \tag{2}
\end{equation}
so that $sign\left(\frac{\partial x}{\partial p_y}\right) = sign\left(  \frac{6}{2p_x}\right)\neq sign\left(\frac{\partial y}{\partial p_x}\right) = 0$.

What I would like to understand better:

How can this happen? I remember having read somewhere in MWG that the  price-derivative matrix should be (even!) symmetric. Can you provide me with some explanation and/or some reference? Alternatively, is there any mistake in the calculations?
Provided the situation described above can happen [i.e. $sign\left(\frac{\partial x}{\partial p_y}\right)\neq sign\left(\frac{\partial y}{\partial p_x}\right)$], I would be very happy if you can come up with some "real world" examples of that.

MWG proposition 3.G.2 is the one you’re thinking of, but that applies to Hicksian demand’s hessian (constant utility). What you solved for is the Walrasian demand, so we want to look at the Slutsky matrix.
$$S_{lk}(p,w) = \partial x_l(p,w) / \partial p_k + \partial x_l(p,w)/ \partial w * x_k(p,w)$$
First term: uncompensated change in demand of good l due to a change in $p_k$ (when multiplied by $\partial p_k$)
Second term: effect of wealth change on demand of good l (when
multiplied by $\partial p_k$) [https://scholar.harvard.edu/files/basilico/files/mwg_flashcards.pdf]
If you check the symmetry of this matrix (in our case l and k are x and y), I believe it should work out.


When to prefer maximisation of surplus and when instead to prefer minimising differences in price and q to find market equilibrium? Two alternative approaches to compute a market equilibrium (in static analysis) are either to minimize the differences (either using abs() or a quadratic diff) between supply-demand quantities and prices in a given market or maximise the total surplus.

Which are the advantages of these two approaches and when to prefer one over the other?

I noticed that many partial equilibrium models (e.g. 1, 2 (p 42)) use the max surplus method, but I wonder why.

Market Equilibrium occurs when the difference between demand and supply is minimized. Equilibrium price and quantity is determined by solving this problem.

Surplus Maximization (or efficiency) is a property that we would want equilibrium to have. First Welfare Theorem says that in competitive markets (in the absence of externalities) market equilibrium is surplus maximizing. In standard demand-supply framework, solving for equilibrium and efficiency yields identical outcomes, and that is why these methods are used interchangeably.


Oligopolistic producers and retail price wars Consider an industry with few producers selling differentiated products. The products must be sold through retailers of whom also there are a few and who therefore possess some degree of market power. Each retailer sells the products of all producers.

  What might be the reasons for the producers to dislike a price war
  among the retailers?

With just one producer my guess would have been that the producer would always like a retail price war since a more competitive retail sector would reduce the double-marginalization problem and hence allow the producer to capture more profits. Is this intuition right? And how does moving from monopoly to oligopoly in production change things?

This question comes from a real-world observation. This Diwali (which is to Indian retailers what Christmas is to western ones) there was an intense price war among online retailers in India. In response to this price war, many producers of consumer durables like TVs and cameras made public statements against this price war and actively discouraged consumers from buying from these online retailers by measures such as offering longer warranties for products bought from brick-and-mortar stores.

A simple explanation for this behavior is that this was just to appease the brick-and-mortar stores which still dominate Indian retail.

But could there be a deeper explanation?

One story I could think of was as follows: suppose that the price charged by producers to retailers is not directly observed. Then a retailer price war can make it harder to detect a cut in the producer-to-retailer price. This can cause any implicit price collusion between the producers to break down, something which none of the producers would like to happen.

But I'm sure this is not the only possible explanation.

A producer won't always want the retail outlets to compete on price. This is the reason for minimum resale price maintenance. By competing on price, it may be that the retailers competition amounts to something closer to a zero-sum game. Supposing there are some consumers who value something like service, it might be better for joint profits to provide good service and thus bring in new consumers. You might imagine two stores selling electronics. The stores might find it best to cut price to pull the customers away from the other. The producer would rather there be good service, display models, helpful employees, etc to bring in new customers.

Reference: Winter (1993)


Questions regarding foreign exchange online trading I am currently studying economics in college and taking course Macroeconomics and International Finance which covers foreign exchange market topic. The class is very crowded since there are more than 500 students taking this course and I find myself as the youngest in the class so psychologically it's not easy for me to ask a question when I don't understand certain topics. Here are my complete questions regarding this topic:

How does 'taking sell position' in foreign exchange trading work? How come a trader takes sell position despite not owning currency pairs?
How come when a trader takes sell position his transaction is immediately executed without waiting? Does it mean when he takes that position there is another trader who takes buy position at the same price?
Is  it possible there is imbalance transaction between buy and sell  position? I mean there are more traders who taking sell position (in  term of volume transaction/ lots) than those who taking buy position or  vice versa?
Is one person’s profit meaning another person’s loss?

Those questions are not my homework but they arise due to lack of my understanding in this topic and my fear of asking those questions in my class. I apologize in advance for asking too many questions. Any help would be greatly appreciated. Thanks.

"Short selling" is a method of trading that includes selling a security (in this case currency) that the trader doesn't own, by borrowing it from a broker.
Prices on forex trading websites are quoted at the current market price, meaning that people around the world are buying and selling at that price at that time. Brokers buy for slightly under market price and sell for slightly over, and they are the ones who actually trade with the average currency trader.
In the scenario where there are more sellers than buyers at a current price, all buyers at that price level will make their purchases and then the price will drop so the market includes more buyers. Demand < Supply so price falls.
People trade currencies for many reasons. Forex trading as an investment does not make up the majority of currency exchange. Businesses that are involved in international trade need different currencies to pay for operations in other countries, to import goods from other countries, etc. and visitors to foreign countries have to buy the currency of those countries. Therefore price changes are not primarily affected by investor activity and many people/businesses do not win or lose on purchasing a currency because they do not hold it as an investment but just spend it.

Hope this helps.

http://www.dailyfx.com/forex/education/trading_tips/trend_of_the_day/2012/02/07/Short_Sell_Basics.html

http://www.econedlink.org/lessons/index.php?lid=342&type=student


Mankiw's version of the Cagan model - need help interpreting it To keep the math as simple as possible, we posit a money demand function that is linear in the natural logarithms of all the variables. The money demand function is
$$m_t - p_t = -\gamma(p_{t+1}-p_{t})$$
where mt is the log of the quantity of money at time t, pt is the log of the price level at time t, and γ is a parameter that governs the sensitivity of money demand to the rate of inflation. By the property of logarithms, mt−pt is the log of real money balances, and pt+1−pt is the inflation rate between period t and period t+1. This equation states that if inflation goes up by 1 percentage point, real money balances fall by γ percent.

From Mankiw's Macroeconomics Textbook (Appendix, chapter 4).

I'm struggling to understand how this expression leads to the interpretation in bold. Applying some of the results from this answer to the same question (Need a math help for the Cagan's model in macroeconomics):
$$\ln\left(\frac{m_t}{p_t}\right)=-\gamma \ln\left(\frac{p_{t+1}}{p_t}\right)$$ (re-writing the expression to include logs)
$$RHS = -\gamma \ln\left(1+\frac{\Delta p_{t+1}}{p_t}\right) \approx -\gamma \frac{p_{t+1}-p_t}{p_t} $$
$$\text{(using } \ln(1+x) \approx x)$$
Now sub this back to the first expression:
$$\ln\left(\frac{m_t}{p_t}\right) \approx \gamma \frac{p_{t+1}-p_t}{p_t}  \approx \ln\left(1-\gamma \frac{p_{t+1}-p_t}{p_t}\right) $$
$$ \text{using } \gamma x \approx \ln(1+ \gamma x) $$
$$\frac{m_t}{p_t} \approx 1 - \gamma \frac{p_{t+1}-p_t}{p_t}$$
Am I correct and/or on the right lines? Not sure how to go about it from here.

I think that you are unnecessarily overthinking it. For any relationship of the form:
$$\ln y = \beta \ln x  $$
the interpretation of beta coefficient is that $1\%$ increase in $x$ leads to $\beta$ $\%$ increase in $y$. The mathematical reason why this relationship holds was already explored at cross-validated stack exchange and you can see it here, or on this website or in virtually any econometric textbook since the log-log form is important, so I wont be unnecessarily restating it.
Mankiw defines real money balances as $M/P$ or in logs $m-p$, hence the left hand side of your equation is by definition the real money balance term expressed in logs $\ln (M_t/P_t)$. The inflation is by definition change in price level again in your case expressed in logs $\ln(P_{t+1}/P_t)$. So you can directly apply the interpretation from previous paragraph as Mankiw does.
Furthermore, you can actually derive it also with your calculations. To be more specific. Growth rate $g$ for variable $x$ is given as $g_x= \frac{x_{t+1}-x_t}{x_t}$. Then we know that:
$$\ln x_{t+1} = \ln ((1+g_x)x_t) \implies \ln x_{t+1} = \ln (1+g_x)+ \ln x_t  $$
Then since $\ln (1+g_x) \approx g_x$ we have:
$$\ln x_{t+1} = g_x  + \ln x_t \implies \ln x_{t+1} -\ln x_t =g_x $$
as a consequence you can actually directly say that:
$$\ln(M_t/P_t)=-\gamma \ln(P_{t+1}/P_t) \approx \ln(M_t/P_t)=-\gamma \left( \frac{P_{t+1}-P_t}{P_t} \right)$$
that 1 in your final expression should not be there. In this case the LHS gives you percentage in the real money balances and LHS percentage change in price level (inflation).


Can the demand curve be a rectangular hyperbola, but $E_D \neq 1$? So, I am given the next table:

I am asked to find $Q_D$.
So the prerequisites to find $Q_D$ is that the price must change, and all other factors of demand must be steady. So, I can find the $Q_D$ between A and C. Our professor stated that, as $P_A Q_A= P_C Q_C =20000$ , the demand curve is a rectangular hyperbola and $Q_D = \frac{20.000}{P}$. However, in the rectangular hyperbola, $E_D=-1$ in every point of the demand curve, but here we have that $E_{D}=-0,8$. Is there something I am missing? Does $E_D=-0.8  \neq -1$ imply that the curve is a line or not? Thanks!

Let's try a linear demand function, so $Q=a-bP$. Then $\epsilon_A=\frac{\partial Q}{\partial P}\frac{P_A}{Q_A}=-b\frac{P_A}{Q_A}$, so $b=-\epsilon_A\frac{Q_A}{P_A}=0.8\frac{500}{40}=10$. Then $a=Q_A+bP_A=500+10\cdot 40=900$. Thus, your table is compatible with the demand function $Q_D=900-10P$.


Quasilinear Preference and MRS Do quasi-linear indifference curves have MRS's that depend only on the nonlinear variable?  For example, for a U(x) = √(x) + y, I calculated that the y would not be in the MRS.  Does that mean that a consumer does not factor the consumption of a "linear" good y into their utility maximization?

If this is the case, can someone explain to me, practically, what it means for a good to be "linear" and for an MRS to exclude one variable?

The MRS is a function of $x$ and $y$. The fact that $y$ doesn't appear in the formula simply means that this function is constant in $y$.

The linearity does not imply indifference. It means that an additional value of $y$ is valued equally by the agent irrespective of his baseline consumption. In your example, this contrasts with the marginal utility of consuming $x$ which is decreasing with the baseline consumption since the function $u$ is concave in $x$.


How can a one currency gain against the other if it is pegged aginst it? I have been reading about when the Swiss national Bank decided it would no longer peg its currency against the euro and this caused massive turmoil in the markets.

But my question was before this the Swiss Franc was pegged against the euro. So how is it the you could have place a bet the euro would rise against the swiss franc when the Swiss Franc was pegged against the euro . Surely they would rise by the same amout.

Strictly speaking it was not a peg but a cap: the Swiss National Bank said it would sell unlimited Swiss Francs at the rate of 1.2 CHF : 1 EUR.

You could have bet that the Euro would rise against the Swiss franc by borrowing some Swiss Francs and selling them for Euros, and then taking any profit or loss by unwinding the transaction.

If for example you had bought Euros with Swiss Francs in May 2012 and sold back in May 2013, this might have been profitable (at least before transaction costs), but if you had held past 15 January 2015 you would have made a loss when the cap was withdrawn.


Buyer's efficiency in auctions first and foremost, I'm not an economist, probably a scientist though.
In my country the most popular way to buy and appartment or a house is by first-price-auctions (the highest bid takes it all).
Rules are simple : bids ends up at a specific time, you can only bid online, and each bid has generally a 30min validity (meaning if no one bids higher than you in these 30min, and if you are the highest, you get it.)
We also don't know who's bidding, if there's 2,3,4,x people bidding on the same good.

Each appartment has a "showing price", and from my experience, bids starts at -10%. Nevertheless the market is pretty down these last weeks/months, and only very good value appartments are sold, often higher than the showing price.

My question is simple : I tried to look in scientific reviews, what are the strategies to bid better as a buyer (i.e. lowering the final price as much as you can), but still it is hard for me to get into general applicable strategies.

For instance, is bidding systematically the minimum bid over another offer a good strategy to limit final price? (if I bid +100 USD each time to another bid, will it statistically at the end make me win with a lower price?)
Or, if I wait until the last minute to bid, is it a better strategy than bidding asap ?
Do the trick with uneven number work to lower the final price? (offer of 12458$ for instance, instead of 12500USD)

I have been looking into bibliography for a while, but I haven't found any solid argument.

Maybe you guys know a bit more than I do? :)

Cheers !

Interesting question,
It can be dealt with with two models: economic theory and game theory (which, in turn, is the base for modern economic theory)

Game theory should be the most practical.
To start if we simplify, we can assume that "everybody else" is one player
In a turn based game, each provides his own minimal bid as long its the highest bid,
That means that the response of each player, will be higher bid, until the maximal value will be reach, for the player with a maximal rate

So the end-game for each player, will the other's maximal bid + delta

Notice that the optimum has to arrive by playing and responding
With an endless amount of players, endless amount of games,
The market price will be the market price: The maximal price will be reached, based on the available supply.
Once that sets, market price is a given known number, based on which a consumer will decide whether to buy or not = economic equilibrium...

So, to answer your question: you can and should play and respond to others' prices, but close enough to market prices (and of course, based on the unique parameters for each flat), simply to save the time and trouble

hope that helps,
Guy

Game theory game tree


Why in most macro models technology is labor-augmenting? Take Romer's advanced macro book as reference. In it the Solow model,the Ramsey model and the Diamond OLG all contain the fundamental $A_t$  variable representing technological progress.
In all these models, technology affects only labor, that is:
$Y_t = F(K_t,A_t L_t)$

Now my question is why is such assumption so prevalent in these models. It seems to me that when we imagine technology as affecting output we think of the Northrop loom, the Bessemer steel, the container, the railroad. You know, stuff. All these seem to me to be mostly capital-augmenting technologies.
So why do we tend to assume labor-augmenting technology instead?

The mathematical reason, is that this happens in order for the model to have a steady-state in terms of growth rates: variables like Consumption, Capital, Income, grow at the steady-state, but grow at the same rate, so their ratios remain constant (and it is in this sense that this situation represents a "steady"-state). If they were to grow at different rates, their ratios would tend to either zero or infinity which is not very realistic, since it would imply that the economy tends towards one or the other "corner" situation.

The mathematical proof can be found in Barro & Sala-i-Martin book (2nd ed) , section 1.5.3, pp 78-80. Relevant and useful is also the discussion in section 1.2.12, pp 51-53.

For functional forms like (generalized, even) Cobb-Douglas, it is really indistinguishable (not separately identifiable), especially since we predominantly use the exponential function:

$$Y_t = A\cdot \left (K_te^{zt}\right)^\alpha \left (L_te^{vt}\right)^\beta = A\cdot K_t^{\alpha}\left (L_te^{(v+\frac {\alpha}{\beta}z)t}\right)^\beta = A\cdot K_t^{\alpha}\left (L_te^{wt}\right)^\beta$$

So strictly speaking in such a functional setup we can say that technology is also capital augmenting.

But since for other functional forms, the above does not hold, and so we must explicitly assume that technology is "labor-augmenting" for the reason stated previously, authors settled in labeling it as such in order to cover all cases, and when they want to keep the functional form unspecified.

Regarding the conceptual issue the OP poses, which is insightful, a conceptual way out is to think of "Technology" more like "Knowledge". So "Knowledge" that goes into the machines, is part of the Investment that augments capital, while the other knowledge turns raw labor $L$ into human capital: essentially a production function with "exogenous labor-augmenting technology", is equivalent to a formulation that includes Human Capital instead of labor but where the investment in Human Capital is not subject to optimizing behavior but "automatic" (which points to Arrow's "Learning-by-Doing" concept of human capital accumulation).


Why does borrowability of shares inversely correlate with probability of assignment or exercise? I transcribe 5:26 of this video. I don't know that YouTuber's credentials.

So looking back here, what could possibly
cause you to get assigned early? If we
look right here, AMD shares are listed as easy to borrow.
That's really important to know,
and it means that the risk of early
assignment is almost non-existent.

If we put something like Tesla in,
they're listed as hard to borrow
and that slightly elevates your risk. If
shares are harder to borrow, calls are
more likely to get exercised, which puts you in a position where you
could be hitting max loss early on account of early assignment like we
just talked about. And there's some
smaller OTC stocks things like this [the YouTuber is pointing to ticker symbol TSOI] that
are less not available to borrow. These, pretty much the second that
they're in the money, are going to be
exercised so that's the risk that you
earn right there.

I disagree with the author's premise. The primary reason that options are exercised early is because of discount arbitrage (an ITM option trades below its intrinsic value) or there is a dividend arbitrage in an ITM put (the time premium is less than the dividend, NOT the call).
No one with a lick of sense would exercise an option that has time premium remaining because that would be throwing away the time premium and incurring more transactional costs (B/A spread and commissions if you're still paying them).
I listened to another minute of the video and I think that the author really has no clue. He talks about the possibility of an OTM short option being assigned early because of a dividend. Now who wouldn't want that to happen to them? If the stock is \$102 and I'm short the \$105 call, please, make me sell the stock to you for \$105! It makes no sense at all.
He continues his errors with another example. A stock is \$101 and you are short a \$100 call that's worth \$2. The company announces a \$2 dividend and the call owner exercises and you are assigned. Why in the world would he do that? He could sell the call for \$2 and buy the stock for \$101. Exercising throws a dollar of time premium away.


Monetary Approach to a depreciating currency I am currently doing some research on the monetary approach to the effects of currency fluctuations on trade balance. It's been a while since I took an int econ class back in the undergrad, so I hope I can glean some understanding from the gods of macroecon. I have a good understanding of the overall assertion being made by this approach (trade balance change dissapates in the LR), but am a bit confused by the details and how equilibria are reached. One of my old textbooks summarizes it as such: when the currency depreciates, money demand shifts up, and rates rise, trade balance improves. In the LR, investors will flock towards the higher rates, and the money supply shifts right, where equilibrium will return to the initial interest rate. This doesn't really make sense to me....

What is causing the currency to depreciate here? When I think of a devalued currency, I think of an expansionary policy/decrease in rates. But here, rates increase due to the depreciation
Where is the deviation from the net zero trade balance and where does it return in terms of the process of the money market changes?
How do foreign investors affect the supply of the currency? I thought that when higher rates existed, that the demand of the currency increased (which would explain why contractionary policy leads to currency appreciation)
More as a question about the theory in general, is there empirical evidence of this? The US has had a trade deficit for a very long time. Does this approach suggest that our net exports should be zero?

Thanks!

Let us call the country with the trade deficit, country A, which is our domestic country. If a country builds up a trade deficit, it is selling less goods to other countries than it buys from them. To do so, A must exchange its currency for foreign currency. This means more demand for the foreign currency and more supply for the domestic currency. More supply reduces the price of domestic currency relative to other currencies. More demand for foreign currency increases their price relaive to domestic currency. All this causes a depreciation of the domestic currency. For more detail on this see, for example, the answer to this question.
Currency values are fundamentally determined by supply and demand for currency (see answer above). Both of those are driven by both the goods and financial markets. So trade deficits have an effect here, as well as investors flocking to higher rates.
Foreign investors both affect and are affected by the exchange rates. If these investors want to invest in a foreign country with higher interest rates, they need the currency of that country in one way or another. So they sell their currency to buy the foreign currency, which like in the answer to 1) will have an effect on the value. Even if foreign investors have the foreign currency to invest, they will need to exchange it at some point in order to consume their earnings at home.
Solid empirical evidence is rather difficult when it comes to long term effects. It is true that the US has had a trade deficit for a long time. However, it is unclear how long a time is a long-run. Furthermore, before having a deficit, the US has had a surplus for a very long time, so it is natural it would eventually have a deficit. Whether this deficit has exceeded past built up surpluses is not necessarily clear.


Will money still have any value in the fully automated world? Moved from the personal finance & money SE:

The following question is somewhat of an existential nature and may not necessarily be related to finance or economics in the strict sense.

Reading various articles about professions, or things in general, that are progressively being automated (and it's not just about work in factories but doctors, brokers, lawyers, artists (sic!) and heck! even programmers themselves...), the development of medicine and biology (let's just grab CRISPR for example) I often imagine a world in which literally everything is automated: from agricultural production through everyday things (maybe even maid robots) to high-end jobs. Since in such a world literally everything is done for people, what is the meaning of work and money? When there is no work that people can do, I imagine that there are no costs associated with it, and consequently, everything is free for everyone. We live in times when people could completely give up using physical money (and some countries have already done so, I guess Sweden have forbidden using physical money and left only cards). Hence I can not fight the feeling that in today's world money is such a virtual thing, something that has no "real" value: it's just printed pieces of paper or stamped metal pieces, and people have agreed on how much they are worth, and that whole economy has been built on top of these ephemeral, imaginary things, and the finances basically come down to the database entry and the fact that someone could just type in the UPDATE TABLE query with the new amount of money that is in the account (of course, I know that it is impossible that there is inflation, etc.).

Summing up:
there is certainly a lot of mistakes or misunderstandings in my thinking, but I wonder what role the money will have (or any other means of payment) in the world at the moment when there will be no more jobs for humans on the planet? Is it possible that the money will still exist at all? I know that there is a fairly fierce debate on this subject and that different approaches to the topic, such as universal basic income, are invented, but again I have the impression that it comes down to the thing above, that is subtracting the amount in one cell and adding in the other.

Your argument is built on this assumption:

  When there is no work that people can do, I imagine that there are no costs associated with it, and consequently, everything is free for everyone

That assumption is not true, and so your conclusion does not stand.

We usually classify production factors into labour, land, capital, enterprise. As you can see, labour is only one of the four factors. But all four factors incur costs: land still needs rent, enterprise still needs profit, capital still needs investment.

Another way of looking at it, is that even if the supply of labour is effectively unlimited (because so little of it is needed to produce anything), the supply of other things is still limited, i.e. there is still some scarcity. There is still a limited amount of iron in the world, or copper, or cabbages. And money is part of markets, which are the main mechanism for managing those limited supplies.


DMP Search Model - Terminology In the most basic Diamond-Mortensen-Pissarides (DMP) model we have the variable $V$ which represents the present discounted value of expected profits from a vacant job. The corresponding Bellman equation is

$rV = -pc + q(\theta)(J-V)$

Where $pc$ is the cost of a vacant job per unit of time, $q(\theta)$ is the rate at which vacancies are filled and $J$ is the present discounted value of expected profits from an occupied job. If I think of a vacancy as an asset for the firm the Bellman equation makes sense but how can a vacancy be an asset?

What I don't understand is the intuitive meaning of $V$. How can a vacant job result in profits for the hiring firm? Furthermore, my textbook says

  In equilibrium all profit opportunities from new jobs are exploited, driving rents from vacant jobs to zero. Therefore the equilibrium condition for the supply of vacant jobs is $V=0$

Again, how are there 'rents' from having a vacant job?

A vacant job is an asset if we consider that the firm can match with a worker and get a positive expected profit. Firms post vacancies up to a point where $V=0$. If $V$ were positive, more firms would enter, would post additional vacancies, and would get a `rent' (by matching with worker).


Stationarity of cyclical economic data I'm having trouble understanding how macroeconomic or industry data could be made stationary if there's only a limited length of time series available (e.g. 2012-2019) and I have a time series that first goes up during e.g. 2012-2015 and then goes down 2016-2019 i.e. we have just one longer economic cycle in the data. This data would not be stationary even though we take log or change percentage since first the growth is positive and then negative. How do people typically tackle these situations, do you split the time series into the different periods to get a consistent slope? Many thanks for help!

First of all, just because there is an economic cycle in a data that does not imply that data is non-stationary. For example, consider the completely stationary process simulated in R below, which is based on $x_t = \phi x_{t-1} +e_t$ with $\phi=0.9$ which is stationary by construction yet it exhibits something like economic cycle.

So the first thing you should do is to make sure there actually is non-stationarity in your data and not just assume that because data exhibit some sort of cycle. Either look in the literature on the given aggregate whether in general it is considered to be integrated of some order or perform your own unit root tests (assuming there is enough observations to carry them out - you dont mention if your data is on monthly, quarterly or yearly frequency. Depending on frequency there might be plenty of data points to carry out these tests even within the given years).
Second, taking logs  is not a solution for non-stationarity even if you have long time series (and I am not even sure what you mean by change percentages). The way how you solve non-stationarity is by taking differences of your data.
For example, a simple non-stationary process is given by
$$x_t= x_{t-1} + e_t$$
The process is non stationary because $\phi=1$  which implies that present variables are fully determined by initial conditions of the system and sum of shocks. If that is the case just taking logs of variables $\ln x_t = \ln x_{t-1} +e_t$ does not solve the unit root problem as you will have the same dependence and it does not matter how long your time series is. Taking logs of your variables can be desirable for many different reasons but not related to non-stationarity per se.
What actually solves the non-stationarity/unit-root problem is to take first differences. For example, in the example above we could transform data as:
$x_t -x_{t-1}= e_t$
Which would become stationary series. You can apply the same procedure to $\ln x_t$ but what ultimately gets rid of the non-stationarity is the differencing. In a worse case scenario you could have series that is integrated of order 2 in which case you would have to make one more second difference. However, eventually taking difference of the series will always produce stationary series. According to Verbeek (2008) guide to modern macroeconomics most economic series that are non-stationary are I(1) and in some rare cases I(2), so even with extremely short time series you should be able to make it stationary.


How to find the cost function for perfect complements Imagine I got a production function like it :
$$
\min\{x_1, x_2\}
$$
How can I find the cost function?

Hint: Think how many units of $x_1$ and $x_2$ are needed to produce $q=1$ in order to minimize the cost. What about producing $q=2$? Can you generalize it?
In order to minimize the total cost, you want to use as few units of either input as possible. Imagine you wanted to produce $q$ units. You would need at least $x_1=q$ and $x_2=q$ (otherwise you wouldn't be able to produce $q$). Therefore, to produce $q$, you choose precisely $x_1(q)=q$ and $x_2(q)=q$. These are the derived factor demand functions. You only need to plug them in the cost identity
\begin{align}
TC(q)&=w_1 x_1(q)+w_1 x_2(q)\\
&=w_1 q +w_2 q\\
&=(w_1+w_2)q
\end{align}


If banks started simply depositing money with each other, then what else? [Source:] If banks started simply depositing money with each other, all else aside, then what would happen? Keep in mind that the interest rate is basically the price of money. Supply-and-demand would dictate that ... ♦ a huge inflow of capital => you can lower the interest rate paid on that capital ♦. Banks don't pay high interest (and certainly wouldn't do so to each other) because of their intristic good will; they pay high interest because they cannot secure capital funding at lower rates. This is a large reason why the large banks will generally pay much lower interest rates than smaller niche banks; the larger banks are seen as more reliable in the bond market, so are able to get funding more cheaply by issuing bonds.

I understand (and so ask NOT about:) that interest rate = the price of money = opportunity cost of money, and also the implication that I surrounded with ♦ (a lozenge). What else would result? Please differentiate and segregate the positive and negative effects.

The purpose of paying interest is to get people to lend you their money (by depositing it) so you can lend it out at a higher rate of interest. The argument here is that if the deposits outstrip the bank's ability to invest/lend, they don't need to offer as much interest to get those deposits. However, given current banking practice i don't think there is ever going to be more deposited funds than the bank can find profitable uses for, so the thought experiment sorta falls apart.


Boundary solutions in the Utility Maximization Problem I'm trying to find boundary solutions for the following utility maximization problem, but i'm unsure on how to proceed. Here is the problem and what I got so far:
$ \max x_1^\alpha + x_2 \qquad \text{s.t.}\ x_1 \geq 0,\ x_2 \geq 0,\ p_1x_1 + p_2x_2 \leq w$
where $\alpha \in [0,1]$. The Kuhn-Tucker conditions are
$\begin{equation}
\dfrac{\partial \mathcal{L}}{\partial x_1} = \alpha x_1 ^{\alpha -1} - \lambda p_1 + \mu_1=0,\\
\dfrac{\partial \mathcal{L}}{\partial x_2} = 1 - \lambda p_2 + \mu_2 =0,\\
p_1x_1 + p_2x_2 \leq w,\\
x_1\geq 0,\\
x_2 \geq 0,\\
\lambda(p_1x_1 + p_2x_2-w)=0,\\
\mu_1x_1 = 0,\\
\mu_2x_2=0,\\
\lambda \geq 0, \quad \mu_1 \geq 0, \quad \mu_2 \geq 0.\\
\end{equation}$
If I consider boundary solutions with $x_1=0$ and $x_2>0$, then by the complementary slackness condition we have $\mu_1 \geq 0$ and $\mu_2=0$.
Since $\nabla u(x_1,x_2) \gg 0$ and $p_1,p_2 > 0$, $\lambda > 0$. The constraint on the budget set is binding (Walras' law holds). My candidate for the optimum therefore is $x_2=w/p_2$.
The Kuhn-Tucker necessary (and in this case also sufficient) conditions for $x_2=w/p_2$ being optimal restrict to
$\begin{equation}
 \alpha x_1 ^{\alpha -1} \leq \lambda p_1 ,\\
 1 = \lambda p_2,\\
x_1 = 0,\\
x_2 \geq 0.
\end{equation}$
By dividing the first condition by the second we obtain
$MRS_{1,2}(x_1,x_2)= \alpha x_1 ^{\alpha -1} \leq \dfrac{p_1}{p_2}$
but then I do not know how to proceed.

Except for the extreme cases $\alpha=0$ and $\alpha=1$, there is no boundary solution with $x_1=0$. Note that the marginal utility of good 2 is constant, while the limiting marginal utility for $x_1\to 0$ is infinite. So the consumer will always consume a bit of $x_1$.


Depreciation and second-hand markets for bicycles Probably the answer to this question is "business as usual", but I've observed of late that the market for bicycles is pretty weird.

You can buy a brand new factory-produced bicycle in the US (I'm really only talking about the US here) for anywhere from \$50 (when not on sale) to maybe \$10,000 (depending on where you want to draw the line between "production" and "custom" bikes).  Some of this difference is due to actual quantifiable value -- the more expensive bikes generally are lighter, handle better, have advanced features, and are marginally more durable (though the cheap bikes are remarkably durable).  However, much of the difference is clearly "glitz" -- the latest features, fancy (though oddly impractical) arrangements of spokes in the wheels, etc.

More to my point, however, is what happens to the value of a bike once you "drive it off the lot".  A "moderately priced" bike (say \$500-1000) will lose (very rough figures -- I've not done any rigorous research) maybe 50% of its value each year, such that it's market value (if in perfect condition) is less than \$50 after 5 years.  The net result is that lower-end bikes are not deemed worth selling when unused, and they tend to accumulate (even worse than other possessions) in basements, garages, and backyard sheds.

I became involved in this "market" because I work with a small group which reconditions used bikes and distributes them to various charities (primarily Christmas Anonymous).  Our small group, consisting of about 8 active members working two afternoons a week 8 months out of the year, manages to rehabilitate 200-300 bikes a year.  But we get donations of at least twice that amount, with the surplus being sold for scrap.  Currently we have so many bikes that many must be stored outside, and it is somewhat disheartening to see, say, a very nice looking bike in good condition, which sold originally for maybe $800, standing in a field of weeds, rusting away.

So I get to thinking that there must be some economic principle at work here, beyond simple supply-and-demand, to cause such a skewed market.  Why can something of such inherent value (and so highly valued by the purchaser when new) become valueless so rapidly?  But I admit that not only do I not have a clue what it might be, but I find myself failing to even describe my perplexity adequately.

What principles are at work here?  Is there anything "interesting" or instructive in the scenario?

(I'm guessing that many will instantly shout "Technology!" -- that technology makes last year's bike much less valuable -- question answered!.  But I've observed that "technology" is the last (or is it first?) refuge of scoundrel economists -- technology hardly ever has the economic effect claimed.)

Interesting observation. Perhaps a part of the answer lies in Akerlof's lemons' problem?

Admittedly judging the quality of a 2nd hand bike is easier than that of a car, but from what you're describing in the US there doesn't seem to be a well functioning market for 2nd hand bikes in the US. Moreover, bikes are becoming more and more like cars in that respect with all the gadgets and technology that one cannot fix in their own shed or backyard.

Perhaps it also plays a role that US citizens are not used to bikes and therefore have a harder time judging their quality (just guessing here, and perhaps stereotyping too much). Here in the Netherlands we seem to have a well-functioning market for them that serve all segments (including, I might add, a high theft rate), but everyone rides a bike here, so we should be better at judging their quality.


Non-constant returns to scale and competitive factor markets I am having difficulties to understand the conclusion in bold below, taken from Frankel (1962):

  A  second  limitation  of  the  Cobb-Douglas  function  appears  when  it  is  fitted  to  historical  data.  All  improved  fit  generally  is  obtainable  if  the  exponents:  and  a  are  allowed  to  vary  freely  instead  of  being  constrained  to  equal  unity.  With  some  sets  of  data,  the  resulting  sum  of  the  exponents  has  differed  significantly  from  unity,  an  outcome  that  opens  the  door  to  economies  and  diseconomies  of  scale  and  that  leads  to  abandonment  of  the  convenient  assumption  that  factors  are  paid  their  marginal  products.

As I understand things, returns to scale is a technical issue, which might be independent on market conditions. Albeit not a reliable source, the same appears in the Wikipedia entry.

One interesting answer to this might come from the first answer here. However, the author is interested in competition among producers, in terms of the final goods price. Basically, that a natural monopoly (where IRS hold), has an average cost always below the marginal cost, so competitive market produces loses. But what prevents a natural monopoly to pay its factors their marginal products? You can think of a natural monopoly, or any other example of firms with DRS or IRS, in which they operate amid competitive capital and labour markets. I see no a priori reason why market forces would not lead these firms to pay the factors their marginal product.

To sum up: why IRS or DRS mean we should abandon competitive assumptions in the factor markets?

Frankel examines the use of the Cobb-Douglas formulation in aggregate data, where as a matter of macroeconomic(and essentially logical) identity output is exhausted in paying the factors of production.

So the macroeconomic identity states, for any aggregate production function

$$Q=F(K,L) \equiv rK + wL$$

where $r,w$ are ex post average unit rewards for the factors of production (hence the identity character).

The only way to equate $r$ and $w$ with marginal product is to have a function homogeneous of degree one ("constant returns to scale") because it is only then that we have

$$F(K,L) = F_K\cdot K + F_L\cdot L$$

and we can map $r=F_K,\; w=F_L$.

If the function is homogeneous but not of degree one but of a degree $k\neq 1$, then we have

$$F(K,L) = \frac 1k(F_K\cdot K + F_L\cdot L)$$

which leads to $r=(1/k)F_K,\;\; w=(1/k)F_L$

If $k>1$ we have Increasing returns to scale and factors are paid less than their marginal product (again, on average and on aggregate), while if $k<1$ we have Decreasing returns to scale and factors are paid more than their marginal product.

We then run into trouble regarding the behavior and structure assumptions at the micro level that lead to such a result at the macro-level.


What does 'establishment' mean in real estate industry? I read data on real estate industry and there is a table titled "establishments". The title of it is "number of establishments in real estate for all establishment sizes". Is 'establishment' a terminology for real estate industry? Does 'establishment' here means construction sites? Thank you.

Establishments are business locations (source). The real estate industry does not include construction (under either NAICS or SIC). It’s not really possible to tell what exactly would be included without more detail on the specific industry group you are looking at; it could be anything from realtors’ offices to apartment rental buildings, or both+other types of establishments. A summary of the NAICS groups can be found here.


What does 'currency convertibility' mean? As a student with almost zero background in economics, I've been struggling to comprehend the notion of the currency convertibility. Most of the definitons I've found online talk about the ease with which a country's currency can be converted into another currency. But what exactly is meant by the ease? Does it mean both currencies should be equal, or close to being equal, in their value or is it something else?

To provide context, I'm attaching the part of an article from nationalarchives.gov.uk talking about the American financial aid to Britain during and after the WWII. Also, as I'm not able to figure out the meaning of the word, I don't understand the following (the last) sentence of the extract either.

  The economic circumstances of the late 1940s tested relations between
  the unions and the Labour Party. Financial assistance through the
  American lend-lease system ended in the autumn of 1945. Although a
  further loan was negotiated in 1945, it was apparent that a great
  increase in production and exports would be necessary to prevent a
  balance of payments deficit. In the winter of 1947, a coal shortage
  produced an energy crisis, which threatened to undermine production.

  In July 1947, the Chancellor, Hugh Dalton, returned the pound to
  convertibility against the dollar (as required by the terms of the
  American loan). However, as dollar reserves rapidly flowed out of the
  country, a full-blown economic crisis followed and in August of the
  same year Dalton was forced to suspend the move.

Thank you in advance for the response, I'd very much appreciate it.

This definition of a freely convertible currency may be clearer to you:

  Freely convertible currencies (also called as fully convertible or permitted currencies) are those that anyone can convert into another foreign currency without restrictions or interventions by government of the original country.

It makes clear that the "ease" you refer to typically refers to the lack of government restrictions.

The stereotypical case of a non-convertible currency is one for which the government maintains a fixed exchange rate.  Imagine the UK pegs £1 to be worth \$2, although the market value (i.e. the equilibrium if restrictions were lifted and the goverment didn't intervene) is only \$1.80, say.  In order to maintain this exchange rate, the UK government has to be willing to buy sterling for a price of \$2 from anybody that wants to sell it.

Often this leads fairly quickly to the UK government running short of dollars, at which point the temptation is to try to bring in some sort of restrictions on who can buy dollars, in what circumstances, how long they have to wait for them to be delivered, etc. -- in order to slow the outflow of foreign exchange.  They may also introduce laws that say that when British firms sell goods abroad, they have to convert the dollars they earn to sterling through the central bank, to provide a bigger source of foreign exchange.  They may also introduce laws banning the conversion of pounds by banks, street traders, etc.

By this point the "ease" with which sterling can be converted is pretty low; it has low convertability.

In the example you mention, the UK suddenly removes restrictions, returns the pound to full convertability, and buys dollars from anybody that wants to sell.  In this situation, you'd expect all sorts of people to rush to buy dollars from the UK government at the favourable rate before they run out and are forced to reintroduce restrictions.


Why a non-autonomous increase in aggregate demand will not trigger muliplier effect? I understand a non-autonomous increase in AD as an increase in AD caused by an increase in income (please correct me if I am wrong). However, I do not understand why the multiplier effect must be triggered by an increase in autonomous AD.

I suppose that an increase in income will increase household's purchasing power thus consumption. This will in turn encourage the firms to increase output and hire more factors of production, thus increasing the national income, which will further increase expenditure? Is this not the multiplier effect's working?

Because if the increase doesn't come from an autonomous component, it already amounts to the non-autonomous demand increase + multiplier.


Producer's cost for buying full solution vs. buying parts This may be a very basic question.

From a producer's standpoint, what are the theoretical or empirical results on the comparison of cost between buying assembled or full solutions from suppliers vs. buying individual parts from suppliers?

For example, hypothetically speaking, a car manufacturer may choose between multiple assembled braking systems from different suppliers, or, may decide to assemble the system itself and choose between multiple suppliers for each component of the system.

Intuition suggests that buying individual parts and assemble itself has lower cost than buying the full solution even if there are multiple solution providers, as long as the manufacturer has sufficient capacity in assembling. But I wonder if that is the case in every scenario, e.g. in the car manufacturing example above.

Some economists (Oliver Hart and John Moore are among the most prominent) have developed a "theory of the firm" which could help address some of the issues involved. One of the considerations in that theory is that the different parties involved in production can 'hold-up' each other. For example, in this case, the brake manufacturer or the auto manufacturer can suddenly threaten to cancel the relationship with the other party, unless the contract is improved.  This, in turn, means they don;t invest much in each other and production is inefficient.

Under that scenario, the optimal solution is for a single party to be the owner of all crucial processes.

This relates to your question in the sense that, from this perspective, the manufacturer is better off buying the individual parts because then it's much harder for anybody to hold it up. Put simply, it has more negotiating power. It will want to in-house processes that are simple, but which could hold it up.

alternatively, it will want to have some serious lawyer power writing the contracts with all its suppliers so that they can't come up with any surprises. That's hard to do. The principle that this is hard to do is called the 'incomplete contracts' principle.

(edits in response to comments:)
Other key authors in the theory of the firm are Ronald Coase, Oliver Williamson and Sandy Grossman. For Coase, as long as property rights are well-defined,  market allocation would be efficient regardless of who owns what. However, there are transaction costs in markets, maybe you can think of them as contracting or negotiating costs). The firm overcomes the costs of transactions by creating non-market relationships within itself. The boss does not negotiate with the worker every day. This can be more efficient than having all activity being performed in the marketplace.


Characterising utilitarianism and altruism in economics This question is a quantitative analogy to this question on philosophy.SE.  Within the framework of economic decision-theory using utility functions, how do you characterise the moral principles of utilitarianism and altruism, and how do they relate?  (Please ignore uncertainty in the outcome of actions, since I don't want to complicate the question unnecessarily.)

Descriptive Framework: Consider a society composed of $n$ individuals, and consider a person in this society who is faced with a decision problem where he has to choose an action $a \in \mathscr{A}$.  For simplicity, we will presume that the marginal utility from this action for each individual is known to the decision-maker, and is given by the function $\Delta U_i : \mathscr{A} \rightarrow \mathbb{R}$ for person $i$.  A positive value of a marginal utility function means that there is a gain from the chosen action to that individual, and a negative value means there is a loss.  Note that utility is interpreted here in the cardinal sense, so it is not merely an ordinal measure (i.e., it can be aggregated by summation).
The vector function of all the marginal utility functions is $\boldsymbol{\Delta U} = (\Delta U_1, ..., \Delta U_n): \mathscr{A} \rightarrow \mathbb{R}^n$, and this gives the total change in utility from the action, for all individuals in society.  We can represent an ethical system dependent on these utilities as an ordinal ranking $\succeq$ over $\mathscr{A}$ that depends on $\boldsymbol{\Delta U}$.  This ranking describes which actions are more or less good under the ethical systems, based on the vector of marginal utilities in the society.

How to describe utilitarianism and altruism: Both of these ethical systems involve judging the goodness of an action by the benefit to oneself and others, which we will take to be a judgement in relation to some aggregation of the marginal utilities of the action.  We characterise these two ethical systems with the following rankings.

Utilitarianism: This ethical system holds that a person should act to maximise the aggregate benefit of their action to the whole of society.  This is represented by the ranking $\succeq_{\text{U}}$ given by:
$$a \succeq_{\text{U}} a' \quad \quad \iff \quad \quad \sum_{i} \Delta U_i (a) \geqslant \sum_{i} \Delta U_i (a').$$

Altruism: This ethical system holds that a person should act to sacrifice his own welfare to others, to the greatest degree.  For each person $k$ in the society, this is represented by the ranking $\succeq_{\text{A},k}$ (each individual has a different ethical ranking) given by:
$$a \succeq_{\text{A},k} a' \quad \quad \iff \quad \quad \sum_{i \neq k} \Delta U_i (a) - \Delta U_k (a) \geqslant \sum_{i \neq k} \Delta U_i (a') - \Delta U_k (a').$$

Both of these rankings involve an inequality on sums of marginal utilities, but they differ in terms of the signs applied to the parts of the aggregation.  Both can be written in the general form:
$$a \succeq_{\mathbf{w}} a' \quad \quad \iff \quad \quad \sum_{i} w_i \Delta U_i (a) \geqslant \sum_{i} w_i \Delta U_i (a'),$$
for some specified vector of weights $\mathbf{w} = (w_1, ..., w_n)$.  In the case of utilitarianism we have weights $w_i = 1$, so that each individual contributes their utility equally to the aggregation.  In the case of altruism we have $w_i = \mathbb{I}(i \neq k) - \mathbb{I}(i=k)$ so that the decision-maker contributes his marginal utility negatively to the aggregation (i.e., self-sacrifice is considered good).


Macroeconomics textbook suggestion I'm looking for a book to refresh my macroeconomics and also continue studying the topics that I did not have. My math background is solid. Can anyone suggest a macro book that takes it from the beginning to advanced and covers hopefully most macroeconomics? if there is no such a book and a few books should be read, please also let me know your suggestions.

Obstfeld and Rogoff (Foundations of International Macroeconomics) or Romer (Advanced Macroeconomics) both cover a lot and present all the math.


Is the steady state of $k$ enough to show $Y$ grows at the rate $n+g$? To provide some context for the question: I was approached by a student needing help for a an empirical thesis based on Solow-Swan model. She had trouble solving the theoretical model she wanted to showcase in her work. She already put a lot of efforts and had a problem just with last steps of derivations so I helped her to solve simplified version of Solow-Swan model where:

$$ k^*= \left( \frac{s}{d+ n + g} \right)^{\frac{1}{1-\gamma}}$$

where $k$ is the capital per effective labor, $n$ population growth and $g$ technology growth and $d$ depreciation, and told her that this results implies that $K$ is growing at the rate $n+g$ which implies due to the assumption of constant returns that $Y$ grows at the same rate. Since $g$ and $n$ are exogenous the growth must be exogenous as well.

But her supervisor told her that the above is not enough to show that economic growth is driven by exogenous factors and she has to expand her model.

Hence my question is: was my statement incorrect or is her supervisor making mistake? If my advice was incorrect whats the missing link that unambiguously shows that economic growth depends on $n+g$?

Based on the steady state your production function is Cobb-Douglas.Taking logs and derivatives wrt time of $Y$, $\frac{Y}{L}$ and $\frac{Y}{AL}$ in the steady state yields the desired result: $K$ grows with $n+g$ on the BGP.

It would be interesting to know what the supervisor's objection was.


What institutions are examples of "shadow banking"? I often hear the term shadow banking tossed around when discussing the United States and Chinese economies. What exactly is shadow banking and could you give examples of some specific companies that act as "shadow banks"? I have been told that in China, shadow banking refers to informal loans that are not written up in any documentation. Is this correct?

While whomever told you about "shadow banking" in China is correct that in an international context, the term can often refer to informal banking arrangements (the earliest use of the term); however, these days, it is usually used in the sense first coined by Paul McCulley in a speech he delivered ("Teton Reflections") at the 2007 Jackson Hole conference. He described them as:

[T]he whole alphabet soup of levered up non-bank investment conduits, vehicles, and structures...
Unlike regulated real banks, who fund themselves with insured deposits, backstopped by access to the Fed’s discount window, unregulated shadow banks fund themselves with un-insured commercial paper, which may or may not be backstopped by liquidity lines from real banks.

Structured investment vehicles, as noted by Kitsune, are certainly one type of shadow bank, but nonbank broker-dealers, certain real estate investment trusts, and particular hedge funds can be viewed as types of shadow bank. The question to ask in determining whether an entity is a "shadow bank" is twofold— do they:

perform credit, liquidity, or maturity transformation; and
fund themselves through uninsured wholesale deposits (without recourse to liquidity facilities)?

As a direct answer to your question, Pozsar, Adrian, Ashcraft, and Boesky (2010) say:

Examples of shadow banks include finance companies, asset-backed commercial paper (ABCP) conduits, structured investment
vehicles (SIVs), credit hedge funds, money market mutual funds, securities lenders, limited-purpose finance companies (LPFCs), and the government-sponsored enterprises (GSEs).

I strongly recommend clicking on that link and taking your time to browse the map on page 2.
It's worth noting both that many of these entities have existed for long periods of time without incident, and that due to choices in how banking is regulated, shadow banks are often the result of a desire to both limit the scope of regulation and to limit the risk of failure within the scope of regulation— which has the effect of pushing intermediation activities outside the regulated sphere.


Specification bias - estimated variance is biased estimator of true variance of error term Consider the two models $ (a)  y = X\beta + u $ where $X$ is $n \times K$ and (b) $y = Z\gamma + \omega $ where $Z$ is $n \times r$.
Under classical assumptions (and $Z$ and $X$ are non-stochastic) if model (a), that is $y = X\beta + u$ is the true model, show that $E(\sigma^{2}_{\omega}) \geq \sigma^2_u$ and explain the implication of your result.

I can do it in two cases when $r>k$ (overfitting) or when $r<k$ (underfitting).

Is there any short way of doing this, without cases (because for both overfitting and underfitting variance is biased)? So, what I am asking is that can they be clubbed so that result doesn't depend on relationship between $r$ and $k$?

If the model $ (a)  y = X\beta + u $ is true, then $\omega = u + X\beta - Z\gamma $ in $(b)$, and the claim follows.


Teaching ethics and its Economic value Is there any literature that considers the benefits of ethical behaviour or teachings in Economics in terms of its value added to human capital?

If there is no difference in value added, then is there any economic value contributed by humanities faculty in a given university to the labour market? If so, is such an education a waste in terms of the labour market?

You ask:

  Is there any economic value contributed by humanities faculty?

A response from Neo-classical economics:

If there are for-profit companies hiring graduates from these faculties, then yes, they do produce value. The sum of their wages is their contribution in terms of value-added to GDP.

Same applies to economists. If they are hired by companies, then their production is valuable. I see no particular difference between economists and any other degree, and I do not see why you make such an a-priori distinction, other than an implicit view of economists as superior (widespread in the field, btw).

Now, the argument about the value of graduates that is allocated to non-profit organisations, including the state, universities, NGOs, and etc, goes exactly in the same way. Consider Greenpeace. If donors of Greenpeace consider it's activity as valuable, and Greenpeace wants to hire economists and artists, then their production has value, because some people benefit from Greenpeace activities. As such, there is no reason why you would not value the contribution of all these careers. Again, the argument applies to both economists and non-economists.

The only situation where you could argue that there is no value produced is when a degree is producing graduates which are then hired to run those same degrees, in a perpetual circle. I am afraid that economics is just as likely to suffer from this than any other discipline.


Game theory software I was wondering what software/libraries everyone uses to simulate games? For instance finding the Nash Equilibrium. I see that Gambit is a popular one, but I was wondering if there are any other good ones? (good=robust, reliable and not slow)

I have used gambit (python) in the past and could recommend it. It also includes a small GUI which makes things very intuitive.

R also has GameTheory if you prefer this platform instead


risk aversion and convexity of indifference curve This is a question from the CFA exam. With respect to utility theory, the most risk-averse investor will have an indifference curve with : (a) greatest slope coefficient (b) most convexity The answer is A but I think B is also correct. The utility function is described by $U=E(r)-\frac{1}{2}A\sigma^2$ where A is the measure of risk aversion. I want to understand this mathematically. How should we measure convexity? Is this just the second derivative or the curvature? And why is B incorrect?

It would seem that both options are correct given the specific mean-variance utility function.
Use $\mu$ to denote the expected value. In the $(\sigma,\mu)$-plain, an indifference curve representing a particular utility level $\overline U$ is given by
\begin{equation}
\overline U=\mu-\frac12 A\sigma^2.
\end{equation}
Applying implicit differentiation, we can obtain the slope of the indifference curve to be
\begin{equation}
\frac{\partial \mu}{\partial \sigma}=A\sigma,
\end{equation}
which is increasing in $A$, the parameter of absolute risk aversion. This shows that option (a) is correct.
Moreover, if we measure the degree of convexity of the indifference curve by the value of its second derivative, we'd get
\begin{equation}
\frac{\partial^2\mu}{\partial \sigma^2}=A,
\end{equation}
which is again increasing in $A$. This suggests that option (b) is also correct.
This conclusion seems consistent with the graph you show: within risk aversion, the indifference curves with higher curvature are also the ones with steeper slopes.


Competitive vs complete and non-competitive vs incomplete marekts The very insightful questions that arise, when someone studies micro foundation are the following: What is the difference between competitive and complete marekts? When we refer to the first is it equivalent as to refer in the latter? Also, when we speak about non-competitive markets, can we also refer to them as incomplete markets? In addition to this, complete or incomplete markets have always the so-called Arrow-Debreu sense of complete/incomplete markets?

Complete market is a market where every possible asset or good can be assigned a price and where you have perfect information, can make perfect contracts and zero transaction costs. Any market can be complete regardless of its market structure. So you can have complete market dominated by monopoly, or oligopoly or monopolistic competition etc.

Perfectly competitive market is a market where there are so many buyers and seller that firms become price takers and when the products are identical so there is a little scope for differentiation.

You can’t just call non-competitive market incomplete. For example, in standard undergrad treatment of monopoly you still assume complete markets, yet the market structure is non-competitive.

Yes when people talk about complete markets they do it in a pretty much same sense as Arrow-Debreu


Running ols when dependent variable is correlation coefficient I am new to this form. I am going to run an OLS regression with dependent variable as a correlation coefficient (between -1 and 1). I am aware that this dependent variable may be problematic in the OLS regression. But what can I do in order to implement the regression? Thanks!

Welcome. Many things can be done. Some simple ones are:

Option 1: Do not care and just do OLS.

Option 2: Do some transformation such as $\ln (1+y) - \ln (1-y)$, logit of $\frac12 (y+1)$, to change the range from $(-1,1)$ to $(-\infty, \infty)$ and do OLS. I assumed that there are no $\pm 1$.

Option 3: Change your model. Let $y_{1,ij}$ and $y_{2,ij}$ be the firm-level ($j$=firm) variables from which you obtain the correlation coefficient $y_i$. As $y_i$ is also obtained by regressing $y_{1,ij}$ on $y_{2,ij}$ (up to a scaling factor), you might want to regress $y_{1,ij}$ on $y_{2,ij}$ including other industry-level variables $x_i$ as regressors. But in that case you need to think about which one of $y_{1,ij}$ and $y_{2,ij}$ to use as the dependent variable. If you are worried about endogeneity, you can also consider instrumental variable estimation, but that's a different story.

I would choose Option 1 unless many correlation coefficients in the sample are very close to $\pm 1$. Note that interpretation changes in Option 2.