Optimal consumtion bundle of lemons and sugar Alex consumes only lemons and sugar. For each lemon he requires exactly 2 spoons of sugar. He doesn't like more sugar on his lemons, and he won't eat lemons with less sugar. What is Alex's optimal consumption bundle?Write down the precise quantities of each good.(Assume that the price of each lemon is 20 and the price of a spoon of sugar is 1. Alex has 44 to spend on lemons and sugar)

Alex's preferences of sugar and lemons can be expressed in form of a utility function as:

$U(x,y)=min(x/2,y) $

where $x$ is sugar and $y$ is lemons.This function tells us we need at least 2 spoons of sugar to consume 1 lemon.

we need a minimum of 2 sugars initally so we can say $x=2$ for 1 lemon so $y=1$

Plugging those values into our  budget constraint:

$44=20x+y$

$44=20(2)+(1)$

$44>41$

Notice how we end up having 3 left over, however with the budget constraint and preferences provided our consumption bundle will be 2 sugars and 1 lemon.


Practice question on Correspondences and maximization We're learning about Theory of the Maximum. I tend to struggle with correspondences in this context, so I'm trying to work through some practice questions. I will start with some general notation of a canonical maximation problem (which can be found from Rajiv Sethi's lecture here, but reposted below so you don't have to go look).
Parameter set: $\Theta$
Choice set: $X$
Objective function: $f: X \times \Theta \to \mathbb{R}$
Constraint correspondence: $\Gamma: \Theta \rightrightarrows  X$
Solution Correspondence: $\Gamma^*(\theta):= argmax_{x \in \Gamma(\theta)} f(x,\theta)$
The maximized value of the objective function: $f^*(x, \theta) = \max_{x \in \Gamma(\theta)} f(x,\theta)$
phew.
Ok, now consider the following maximization problem parametrized by $p \in [0,1]$:
$\max_{(x_1, x_2) \in \mathbb{R}_+^2} x_1 + 5x_2 $
s.t. $px_1 + x_2 \leq 1$
I know that we can write this in the form: $f(x,p) = x_1 + 5x_2$ and $\Gamma(p) = \{(x_1,x_2) \in \mathbb{R}^2_+: px_1 + x_2 \leq 1 \}$. I also know that at $\Gamma(0) = \{(x_1,x_2) \in \mathbb{R}^2_+: x_2 \leq 1 \}$ is not compact-valued, and thus we cannot apply the theorem of the maximum.
In the solution to this question, I see that the optimal policy correspondence is
$\Gamma^*(p) = \begin{cases}
\emptyset & \text{if} \: p = 0 \\
\{(1/p,0)\} & \text{if} \: p = (0, 0.2) \\
\{ (x_1, x_2) \in \mathbb{R}_+^2: 0.2x_1 + x_2 = 1 \} & \text{if} \: p = 0.2 \\
\{(0,1)\} & \text{if} \: p = (0.2, 1]
\end{cases}$
At $p = 0$, $\Gamma^*$ is empty-valued. For $p>0$ it is compact-valued and upper hemicontinuous. It fails to be lower hemicontinuous at $p=0.2$. Substituting $\Gamma^*(p)$ into the objective function, the value function is $f^*(p) = \max \{1/p , 5 \}$.
I'm not sure how, mechanically, to get to the optimal policy correspondence, as we didn't do anything like this in class, and I'm finding reading materials scarce. I would really appreciate if someone could walk me through the steps as if I'm a 5 year old.

I think the easiest way is to notice that since the problem is increasing in both arguments, we can assume $px_1 + x_2 = 1$ the budget binds (at least for $p \not =0$).
Substituting our constraint into the objective function, we have:
$$
\max_{x_1} x_1 + 5(1 - p x_1) = x_1(1 - 5p) + 5
$$
If $1 - 5p<0$, we choose the smallest possible $x_1$, so $x_1 = 0$ and thus $x_2 = 1$.
If $1 - 5p = 0$, any $x_1$ would maximise the above.
If $1 - 5 p > 0$, you choose the biggest $x_1$ possible, so $x_2 = 0$ and $x_1 = \frac{1}{p}$.
If $p = 0$, there is no constraint on $x_1$, and your objective function is unbounded in $x_1$, so you would choose $x_1 = \infty$, so no solution exists.


Guvenen et al: Earnings Guvenen et al look at earnings shocks over time, and try to argue whether these are compatible with standard career-ladder models with normal shocks.

However, their data is no real shocks, it is time differences in labor earnings. We do not know which part of these were expected. What are things to consider if one tries to take into account for the fact that these income changes are - to some extent - expected ex ante?

My first guess would be that since people expect future rise in income, correcting the "shocks" for that would mean that the unexpected part of the shocks is to the left of their yearly changes in wage income. That is, there are more shocks downwards than upwards.

If I understand correctly we have observed earnings first-differences that we decompose into an "expected" part and an "unexpected" part. But f they are unexpected, it means something like

$$y_{t+1} -y_t = h(I_t) + u_{t+1} , \;\;E(u_{t+1}\mid I_t)=0$$

where $I_t$ is the "information set" (in the broad sense) at time $t$. So by construction, the unexpected part will have conditional mean zero. But , this does not imply necessarily that $u_{t+1}$ will also have a symmetric distribution around zero. If as you conjecture, there are "more shocks downwards (negative) rather than downwards", the distribution will have more probability mass in the negative. Then, in order to maintain a zero-mean the distribution will have to have higher values on the positive: more and smaller negative shocks, fewer and higher positive shocks.  Something like a shifted to the left gamma distribution, so as to have zero-mean,

Is this close to what you have in mind?


Demand function for partially subsumable products I am struggling with this question that should be simple for economists (I am not an economist at all):
There is a market with a limited number of (heterogenous) consumers with two firms, each offering a product. The two products are ‘partially’ substitutable. I am looking for demand functions to show how the two products interplay in terms of price and demand.
I remember there were some traditional models in microeconomics showing something like this:
d1= a1 – b1.p1 + c1.p2
d2= a2 + b2.p1 – c2.p2
where d and d2 show the demands and p1 and p2 denote prices of products 1 and 2 respectively.
The issues with these functions are that:

They include many unknown parameters (i.e., a1, b1, c1, a2, b2, c2);
They do not directly consider ‘partial’ substitutability;
They include prices identified by the firms, but ideally, I would also like to include ‘values’ of products (v1 and v2) identified by consumers regardless of their prices (perhaps, this is similar to what utility functions consider).

Is there any way to solve these issues by using stronger functions?
Thank you

In general, a demand function (for a certain good) gives the demanded quantity as a function of the price of the good and a set of other variables. These other variables include things like prices of the other goods, income, weather, etc.
If we consider a framework of two goods and if we excluding all other variables, except for the prices this gives two demand equations:
$$
q_1 = d_1(p_1, p_2),\\
q_2 = d_2(p_1, p_2).
$$
Usually, it is assumed that the law of demand holds, which means that demand is decreasing in own prices. If so, $\frac{\partial q_1}{\partial p_1} < 0$ and $\frac{\partial q_2}{\partial p_2} < 0$.
An interesting question is how the demand for good 1 changes if the price of good 2 changes. In a first setting, it might be that the two goods are subsitutes (e.g. apples and pears), in this case, we should have that $$
\frac{\partial q_1}{\partial p_2} > 0.
$$
the reasoning is the following. If the price of good 2 increases, its demand decreases and, in turn, the demand for good 1 increases. The idea is that consumers will buy less of the more expensive good and will (at least partially) compensate this by buying more of good 1.
A second setting is where the two goods are complements (i.e. consumed together like coffee and milk). In this case, one can expect that $\frac{\partial q_1}{\partial p_2} < 0$. If good $2$ becomes more expensive then the consumer will not only buy less of good 2 (due to its higher price) but also less of good 1.
One particular specification that is frequently used (for example in theoretical work) is the linear specification:
$$
q_1 = a_1 + b_1 p_1 + c_1 p_2\\
q_2 = a_2 + b_2 p_1 + c_2 p_2.
$$
If $b_1 < 0, c_1 > 0, b_2 > 0$ and $c_2 < 0$, this gives the correct signs to have substitutes:
$$
\frac{\partial q_1}{\partial p_1} = b_1 < 0 \text{ and }\frac{\partial q_1}{\partial p_2} = c_1 > 0\\
\frac{\partial q_2}{\partial p_1} = b_2 > 0 \text{ and } \frac{\partial q_2}{\partial p_2}  = c_2 < 0
$$

In practice we are not really interested in the exact values of the parameters $a_1, a_2, b_1, b_2, c_1$ and $c_2$, but only their signs, because this determines whether the law of demand holds and whether the goods are substitutes or complements. You can think of the values of $|c_1|$ and $|b_2|$ as the degree of substitutability (of complementarity)
Demand functions do not include something like the value of the good. You are correct that "the value of the good" is usually captured by the utility of the consumer (from buying the good). The amount of goods that gives the highest utility for the give prices is what determines the demand. So the values determine the demand, but they are not an argument of the demand functions themselves.


Decision over "max" production function: I've been presented with the following problem:

$$y=3(x_3)^{\frac13}(\max\{x_1,8x_2\})^{\frac13}$$

And the objective is to both maximize profit and minimize cost. First of all, if the problems are dual, does that mean the result will be the same in variables such as demands?

STILL, MY BIGGEST ISSUE IS THIS: When you get rid of the max, this becomes a Cobb Douglas piece of cake. But I just don't understand how to do that. So far, all I've got is that this function allows corner solutions, so it's not solved just as a Leontieff function. How would you go about choosing each good? I'm also sure it has to do with input prices $w_1$ and $w_2$

Hint

For profit maximization, either $x_1$ or $x_2$ (but not both) must be zero. If not, say $x_1^*>x_2^*>0$ at the optimum, then one could increase profit by lowering cost by reducing $x_2^*$ without affecting output and thus revenue.

Let $z=\max\{x_1,8x_2\}$. The profit function can be written as
\begin{equation}
p[3(x_3)^{1/3}(z)^{1/3}]-w_3x_3-c_zz,\tag1
\end{equation}
where
\begin{equation}
c_z=
\begin{cases}
w_1&\text{if }x_1>8x_2\\
w_2/8&\text{if }x_1<8x_2\\
\min\{w_1,w_2/8\}&\text{if }x_1=8x_2
\end{cases}
\end{equation}

Solve $(1)$ for the condition determining the optimal level of $z$, and compare the costs of achieving this level using either $x_1$ or $x_2$. Use the one that entails the lower cost.


What were the factors that caused the Philips curve to stop working during the 1970s? Philips curve says that inflation and unemployment were inversely correlated. In the 1970s, stagflation happened. If Philips curve hold true, stagflation is impossible.

What were the factors that caused the Philips curve to stop working during the 1970s when the economy was hit by stagflation?

The general way people figured the Phillips curve worked was that a shock in aggregate demand or fiscal stimulus would cause labor demand to increase as government spending generated growth, which makes labor more scarce and causes firms to compete for workers by raising nominal wages. Wage costs then rise, and the firm passes on some of the cost to the consumer by raising the prices of their products.

So in this way, unemployment and inflation become tradeoffs. The problem is then this can be easily exploited, but also easily noticed. Lucas's critique states that people's expectations of inflation--and future inflations--will affect price levels as well. So if a policy maker tried to create inflation all the time to lower unemployment, what would happen is that the Phillips curve would actually shift around, so the tradeoff would hold, but you would be getting worse tradeoffs as people's expectations shifted.

By raising inflation constantly by the central bank and by politicians, you'd fall into a liquidity trap (when raising inflation fails to decrease interest rates and stimulate and economy). The reason why is because if everyone expected the rise in inflation, there'd be no reason to hire more workers, since real demand is staying the same. So instead of a short run rise in output, firms just went straight to raising prices instead of hiring more people.

That said, today, Lucas's critique has its limitations. Even transparent policies that are fully known to increase inflation by firms can still boost output in the short run. This is probably because after the 1970s in America, the new head of the Federal Reserve, Paul Volcker, decided that the central bank should commit more heavily to a set inflation rate in the long run, so that their policies would be more credible.

We can set up a game-theoretic model for optimal monetary policy, as such:

$$\max_{u, \pi} V(u, \pi) = -(u^2 + \pi^2)$$

The central bank wants to minimize a combination of unemployment and inflation. Their constraint is a simple Phillips curve:

$$u = u^* - k(\pi - \pi^e)$$

Where $k > 0$ is some weight for the degree of the tradeoff ($-k$ is the slope of the Phillips curve). $u^*$ is the natural rate of unemployment and fixed, while $\pi^e$ is the expected inflation.

Comparing the Ramsey and Nash equilibria of this game, where consumers and firms set expectations of inflation and the central bank tries to game that, we'll find that if firms trust the central bank to be honest about what inflation they are targeting, the central bank will always have the incentive to lie, if only acting for one period.

Substitute the Phillips curve into the central bank's maximization problem:

$$\begin{align}
& V = [u^* - k(\pi_t - \pi^e)]^2 + \pi^2 \\
& \frac{\partial V}{\partial\pi} = -2[u^* - k(\pi_t - \pi^e)]k + 2\pi = 0\\
& \implies \pi_{\text{opt}} = \frac{k}{1+k^2}(u^* + k\pi^e)\\
& u_{\text{opt}} = u^* - k(\pi - \pi^e) \\
& \implies u_{\text{opt}} = \frac{1}{1+k^2}u^* +  \frac{k}{1+k^2}\pi^e \\
\end{align}$$

Now assume the private sector knows the Fed's optimal monetary policy problem, and set $\pi^e = \pi_{\text{opt}}$. Say the Fed is credible.

$$\pi_{\text{opt}} = \pi^e = \frac{k}{1+k^2}(u^* + k\pi^e)$$
$$\boxed{\pi^e = ku^*}$$

$$u_{\text{opt}} = \frac{1}{1+k^2}u^* +  \frac{k}{1+k^2}\pi^e$$
$$= \frac{1}{1+k^2}u^* +  \frac{k}{1+k^2}ku^*$$
$$\boxed{u = u^*}$$

These are the best responses for the Fed...if they are worried about telling the truth. Investigating Ramsey's time inconsistency problem, the Fed can technically do better. Suppose it announces $\pi = 0$ as a target.

$$\pi_{\text{opt}} = \frac{k}{1+k^2}u^*$$
$$u_{\text{opt}} = \frac{1}{1+k^2}u^*$$

You can verify that the Fed has an incentive to deviate in a one-period game.


Are CPI stats weighed based on population size Generally inflation and CPI are reported on a national level. If a country for example has 10 cities, after surveying prices in each individual city, how is the total CPI number determined for the national level? The cities may have very different living costs and population sizes, how is this taken into account when aggregating to a single CPI value?

Yes, the data is weighted based on the population size of the area from which it came. The survey designers employ a method called stratified random sampling, which ensures that the prices of goods selected for the sample are distributed across all areas (rather than by chance landing up concentrated in a few areas). Then, the prices in each stratum are assigned a sampling weight, the ratio of size of the population in that stratum to the number of prices collected in that stratum. Those weights are used when calculating the mean price for that item (i.e. multiply each observation by its weight, divide by the sum of the sampling weights).

Further, a representative basket of goods and services is used (which was found through household surveys, again with random sampling), and the estimated mean prices of goods are plugged in to that basket to get an overall index of price. The basket should thus be the same across all years in order for the price index to be comparable across years (except when using a chained price index).


Is there a problem with Inflation-corrected real price? Consider CPI and PPI, Consumer Price Index and Producer Price Index respectively. Note that many book correct inflation using the above measures. However, I doubt inflation corrected by these values tells the true or whole story. Consider the following case. According to a microecon textbook I am reading, the real price of copper has been stable over the past decades despite the fact that demand soared over these decades. Let us assume that the real price is computed using PPI. If the PPI has increased siginificantly more than CPI in terms of percentage increase comparing to their common base year, then although PPI-corrected real price is stable for copper, it's relative price to basic commodities has soared. In this case, we note that PPI is not useful in assesing whether the real price of copper had risen. Rather, GDP deflator seems to be a better option. Am I correct? Any suggestion is helpful.

You are right that if the inflation rate is calcualted using PPI, then PPI-adjusted price for copper didn't not change, i.e. the real prie for copper did not change. However, we would also consider the real income and real prices of the necessities in determinging wether copper has increased in value reative to income and daily necessities. Since this time when we compute the real income, we would be using the PPI calculated inflation rate as well. If nomial income rose by $5\%$ by the end of the fifth year while the price of copper along with other PPI goods rose by $15\%$ at that time, we would get a real income that is lower than the real income five years ago, which then would be apparent that the value of copper, or the relative value of copper, has increased.


Examples of a good student's project with minimal economical knowlege I have to provide a theme for students for a project like a bachelor's thesis. Students know all the basic math like calculus, linear algebra, ODE etc, but nothing fancy like PDE and stochastic calculus. Plus they supposed to have some very basic courses in economy. What could the possible themes be?

From one hand it should be something  really of a serious project, so a student can make by himself one thing then another and so on, and from the other hand it probably should not require lots of purely economic concepts (preferably only  basic ones).

Could it be  (given the absence of deep economical training) something in mathematical modelling or analysis of some economical processes? I want to catch the gist of it, so the more examples the better. Please, if possible, not only a theme's name but a few words what a student is expected to do. Sorry if it's too broad a description, but I have a very vague idea that a good project of this sort would constitute.

This question is quite broad, but I'll give 3 ideas I would have liked to do, and is of appropriate difficulty, while in undergrad.

Review a seminal paper - Wikipedia has a list of important publications in economics.  They could write a 10-20 page paper and give a deep analysis of what the authors did and why.  I.e. if there is a derivation they could explain why it is solved that way, if it is the only way, or if there is another way and suggest these alternatives.
Construct a new policy function - Let them argue their intuition in constructing a new policy function (e.g. why do you take log consumption?) and solve for the constrained optimization problem.  They should know how to use the method of Lagrangian optimization, but the courageous student could set theirs up as a Bellman equation.
At my school it was perfectly acceptable for a Bachelor's thesis to do a real world project instead of write a paper.  They could make some kind of event, I had a classmate present on the UN Millennium Development Goals and had a video message from Jeffrey Sachs.  They could find somebody (or a few people) local to come and speak.  Also they may have access to a small budget from their school, or can elicit donations from local restaurants, and can provide food (college students love free food)!


How can two different utility functions represent the same preferences? I have this question for microecon that asks do the following utility functions represent the same preferences:

$u(x_1, x_2) = x1 \cdot x2, \; v(x_1, x_2) = \ln x_1 + \ln x_2$
$u(x_1, x_2) = x1 \cdot x2, \; v(x_1, x_2) = x_1 + x_2$

How do I go about approaching this problem since they are two different functions?

First of all, an utility function $u: X \rightarrow \mathbb{R}$ represents the preference relation $\succsim$ if: $$\forall a, b \in X, \; u(a) \geq u(b) \iff a \succsim b.$$

Well, if another function $v: X \rightarrow \mathbb{R}$ represents $\succsim$, then: $$\forall a, b \in X, \; v(a) \geq v(b) \iff a \succsim b.$$

But the above implies the following:

$$\forall a, b \in X, \; u(a) \geq u(b) \iff v(a) \geq v(b).$$

Which means that both functions preserves the order relation, just as Herr K. said it. Another important part of Wikipedia's article is this one. You see, any monotonically increasing (and it must be increasing, not nondecreasing) function preserves the preference relation.

So now I think you will be able to answer both questions. As a tip for the first one, think about the $\ln(x)$ function: is it a monotonic increasing function?


Which economic research articles or books use anthropological methods? Most of the social sciences and even disciplines have a stable relationship with economics. And rightly so because our world is so interconnected. But there are certain fields which remained separated from this interdisciplinary connection.

One of them is anthropology. Reading on the web there isn't much work done by both researchers in collaboration. What are some examples in the literature of this? And which papers would have benefited from an interdisciplinary approach but didn't take the chance to do so?

In economics, people usually use mathematics as an intermediary to understand some economic mechanisms that would be difficult to understand without maths.
Economists usually focus more on mechanisms in an analytic way than some historical facts in these mechanisms. That's a little bit what it is said "homo economicus"

Youtube Lecture Link

This link could be interesting for you but I don't know really (and don't think) some mainstream orthodox economists interested in the link between anthropology and economics.


Under what BLS line do "people who want a job but haven’t searched in the last 12 months" show up? I'm trying to understand how this CNN math was derived:

  This category — jobless people who “want a job now” but “did not search for work in the previous year” — has hovered around 3 million workers per month for most of the last decade, but it suddenly more than doubled to 6.9 million in April. Because these workers didn’t search for new jobs in the last 12 months, they were not counted in either the unemployment rate or the U6 underemployment rate.

But where are these 6.9 million reported by the BLS? I see BLS says "discouraged workers" are actually included in U6...

So where are these 6.9m "people who want a job but haven’t searched in the last 12 months" reported by the BLS?

That's reported in A-38 under "not in the labor force" but "want a job" and "did not search for work in the previous year". The line/figure doesn't have a U-style indicator.


Deadweight Loss Due to Taxes Represented on a Graph of the Market? Let's say a market is operating at equilibrium, with MSB=MSC, and a tax is imposed on the market. This would shift the supply curve to the left and cause a deadweight loss represented by the triangle on the graph. However, somewhere in a different market, the demand for a substitute good would increase and the surplus in that market will increase. Does that mean that some of the deadweight loss in the original market is canceled out by the increase in surplus in the new market?

I would say yes. In the extreme case: if there is a perfect substitute demand for the original good is perfectly elastic and its demand curve horizontal. That means that any tax imposed on the original market will lead to zero demand for the original good. All demand would move to the new market due to perfect substitutability. The entire surplus of the original market is deadweight loss. If both demand and supply moved to a new market they could replicate the original market there. The deadweight loss would be compensated completely by the surplus in the new market.

If the new market has preexisting demand not all additional demand from the original market could be satisfied at the same price point as in the original
market leading to a welfare loss. The demand curve in the new market would move to the right but not sufficiently to compensate the deadweight loss incurred in the original market.

Correspondingly, the less elastic the demand for the original good is, the less demand can move to the new market and the less deadweight loss can be cancelled out by the new or increased surplus in the new market.


Does consumer surplus over-weigh the interests of high-income consumers? An individual's willingness to pay for a good not only depends on how much they value that good, but also on their income level (at least under the conventional non-economics definition of the word 'value').

Consider the case with a single indivisible unit of a good and 2 consumers, a very wealthy consumer and a very poor consumer. Even if the poor consumer would benefit more from receiving the good than the wealthy consumer  (let's say the good is a drug that the poor consumer medically needs but the rich consumer wants to take recreationally), the 'efficiency-maximizing' free market will still give the good to the wealthy consumer under most conditions. The wealthier consumer has a higher willingness-to-pay not because the good is worth more to them, but because a single dollar of their wealth is worth less.

The normative idea that a good should always go to the individual with the highest willingness to pay is then surely flawed. The policy objective of maximizing surplus, which follows from this idea, must also be flawed. Given how glaring this problem is, I am surprised to see so many papers that still use WTP-derived consumer surplus in their normative analysis.

My questions are:

-What does the literature have to say about this issue?

-Have alternative measures of surplus been proposed?

-Is my reasoning flawed/is the measure of CS not as unfair as I am suggesting?

Partly inspired by some of the arguments in this thread:
What does economics say about "price gouging" during an emergency?

Consumer surplus in Microeconomics 101 is indeed often used in the way you describe and to illustrate a point about the allocation efficiency of a free market.

However, it is important to keep in mind the assumptions and limitations of the framework you describe.

First, the case you describe is a partial equilibrium case. This framework does not allow for such general statements as you are making about all goods always going to richer people. In partial equilibrium we look at one small market and forget about everything else. To use such a framework we must accept that it is reasonable for our question at hand to analyze one purchase in isolation. That assumption is clearly not reasonable for the question you have on all goods and as such the framework you describe cannot be used as it will lead to false conclusions.

With partial equilibrium we can look at this purchase in isolation from other markets. If income effects and the purchases in question are important then we cannot use the consumer surplus idea as done in Micro 101. Certainly this is an issue for the point you raise about all goods always going to a wealthier consumer. All goods cannot be analyzed with partial equilibrium.

The good allocation properties that economist often talk and that you mention about are based on general equilibrium and the proofs do not really involve the concept of consumer surplus.

To fully ensure avoidance of income issues, we often work with quasilinear utility functions when talking about consumer surplus and allocation, as you are doing. It is important, however, to keep in mind that these utility functions are special cases. They imply that income effects do not matter so they are widely used in Micro 101 for illustrative purposes.

Consumer surplus has a nice interpretation for quasilinear utility functions: it’s equal to the gain in utility. This makes quasilinear utility functions especially instructive. If everyone’s utility function has this form then the Pareto efficient allocations are exactly the allocations that maximize total consumer surplus (in the absence of production).

So when using consumer surplus to talk about efficient allocation you need to accept the assumptions that go along with quasilinear utility. However, such utility function are only realistic for certain goods and certainly not for all goods.

Luckily, what you learned about free markets achieving allocation efficiency is still true even when considering more complex cases. However, these results are then true for different reasons and under different assumptions than what is taught through consumer surplus in introductory lessons.


Why could China, much poorer than US, lend so much money to US? The GDP per capita of China is only a fifth of that of US.
But China has lent more than a trillion dollars to US.

How could the much poorer China lend so much money?
Where did those money come from?

You don't have to be richer than someone to lend them money. You only need to have money to lend. China has a lot of money to lend because it has a high savings rate. In the past, it preferred to lend the money to the US, because that would allow the US to buy more goods from China. However, the situation is now changing.


Could a Cap-and-Trade and a Carbon Tax both work together as a system to reduce carbon emissions? For example, the European Union currently has a Carbon Emissions Trading Scheme in progress the ETS which acts to cap the amount of carbon dioxide released by large corporations. However, let us imagine, for example that the UK implements a carbon tax, which taxes fossil fuels as they enter the UK (at well, mine or port of entry) based on the amout of CO2 they will emit (at an escalating cost per ton of CO2).

Could these two systems feasibly act and coexist together, or would it simply be double taxing?

The combination of the two policies could work and would have some advantages over either alone, and for a given reduction in emissions the overall cost burden on industry and consumers would not be doubled.  However, the cap on emissions would weaken the effect of gradual escalation of the tax rate.

The model represented in the following diagram is a simplification in several respects (which will be considered below) but is a helpful starting-point.  It assumes a single homogeneous fossil fuel, with emissions depending solely on the quantity of fossil fuel consumed.  Hence the horizontal axis represents quantity of fossil fuel and quantity of emissions.

Supply is shown as highly elastic (nearly horizontal) because the UK buys large amounts of its fossil fuels, especially coal, on competitive international markets.  In the absence of policy intervention, equilibrium is at point A with consumption and production (assuming no change in stocks) at $Q_A$, which also represents emissions.  Note however that while consumption and emissions relate to the UK, production includes amounts produced elsewhere and imported to the UK.

The effect of the carbon tax is to raise the supply curve vertically by the amount of the tax. In the absence of other measures, the new equilibrium is at B.  Production, consumption and emissions fall to $Q_B$.  The cost burden of the tax is mainly shared between users of fossil fuels and consumers of goods produced using fossil fuels, the shares depending on elasticities in particular markets. A share of the burden would also take the form of a fall in the price received by fossil fuel producers, but this would be small given the elastic supply curve.  The tax revenue could be used by the government in various ways with various distributional effects.

The effect of adding cap-and-trade, assuming an effectively enforced cap at $Q_C$ below $Q_B$, is to limit consumption, production and emissions to $Q_C$.  Thus the part of the demand curve to the right of $Q_C$ becomes redundant.  Equilibrium is brought about via the market for emissions permits, which will determine a permit price such that supply (post-tax) and constrained demand are in equilibrium at C.  Distributional effects depend heavily on the mechanism for the initial allocation of permits.   The ‘corporate welfare’ point in BKay’s answer relates most clearly to the case of free allocation.  This can be avoided if allocation is by auction, with the revenue accruing to the government with, again, distributional consequences depending on how it is used.

Within this model we can infer the following:

The tax and the cap both reduce production of fossil fuel and emissions.  It is not a case of separate policies to achieve separate objectives.
The cap provides certainty that emissions will not exceed a pre-determined level (whereas a carbon tax alone cannot give this certainty because its effect depends on the position of the demand curve which cannot be known with certainty).  The tax provides certainty that there will be some reduction in emissions, as compared with their level in the absence of policy (whereas cap-and-trade alone cannot give certainty in this respect because of the risk that poor forecasting or industry lobbying will result in the cap being set at too high a level, ie above $Q_A$).  In this respect the combination of policies overcomes limitations of either policy alone.
If a firm has to buy its permits at the market price, as well as bear a share of the burden of the tax, it might be perceived that it is subject to double taxation.  However, the effects of the tax and the permit price are additive, so that the total cost to the firm, for a given reduction in emissions, is no more than the cost under either policy alone.
With a fixed cap in place, gradual escalation of the tax rate will not normally produce further reductions in production or emissions.  It will move $Q_B$ gradually towards $Q_C$, increasing the share of emissions reduction due to the tax and reducing the share due to cap-and-trade, but will not shift $Q_C$.  Only if the tax rate were so high, or the cap so lenient, that $Q_B$ were below $Q_C$ (in which case the cap would have no effect) would escalation reduce production and emissions.  To achieve further progressive reductions in emissions within this policy framework, it would be essential gradually to reduce the cap.

Let’s now consider some ways in which the above conclusions need to be modified because of departures from the model’s assumptions.  Firstly, cap-and trade, because it depends on measurement of actual emissions, is for practical reasons normally limited to large users or specific industrial sectors, certainly excluding household use. By contrast, a carbon tax levied at point of entry on the carbon content of the fuel is a simple and effective way of bringing all consumption of fossil fuels within the scope of policy.   In practice, therefore, users within the scope of cap-and-trade would be at (their individual equivalent of) $Q_C$, while those outside its scope would be at $Q_B$.  This difference in coverage could result in emissions reduction not being achieved in the most efficient way, eg by creating a greater incentive for expensive measures by large firms than for simple measures in the home.  In this respect the combined policy would be inferior to a carbon tax alone, but superior to cap-and-trade alone.  A further consequence is that escalation of the tax will always reduce emissions by users outside the scope of cap-and-trade.

Secondly, fossil fuels are not homogeneous.  For example, emissions can be reduced by switching from coal to natural gas in electricity generation.  The combined policy (like either policy alone) would not only reduce production of fossils fuels but also encourage this type of switching.

Thirdly, the assumption that emissions depend solely on consumption of fossil fuel, though currently fairly accurate, may become less so in future.  Currently the main ways in which carbon emissions can be reduced are improved fuel-efficiency, switching to alternative energy sources, and energy-saving measures such as improved insulation.  However, the implementation of carbon capture and storage (see here) may be beginning to weaken the link between consumption and emissions. It is desirable therefore that policy should include an element based on actual measured emissions.  In this respect either the combined policy or cap-and-trade alone are superior to a carbon tax based solely on carbon content.


Data Set/Database listing NAICS codes for U.S. firms? I need access to a dataset that matches firms to their NAICS codes so that I can fill in some missing data in a data set I have for some research.

I was wondering if anyone on here might know of such a database or dataset I could explore?

If NAICS are not provided in the dataset, you need a second variable, related to NAICS, to do the match. Two options are ISIC and SIC, related to industry classification. You can find the official link between these two and NAICS here. These are Excel files with the concordances, which will not be perfect (sometimes you have m-to-1 or 1-to-m matches). There are more crosswalks between classifications here, here, and here.

In terms of Stata files (if you need that), check file [C1] here. There is also this very good NBER crosswalks (under Concordances heading), where you get SIC-NAICS crosswalks in Stata, SAS, Excel and CSV formats.

For reference, here you can find a mapping between SOC (occupations) and NAICS, but I am do not sure how it works, as I cannot see a 1-to-1 mapping between occupation and industry.

Finally, here there is a document describing some technical aspects of the crosswalks.


What are the fundamental economic proofs We had a question on this site for  Fundamental equations in economics. What I'd like to know is what are the most important proofs needed in economics?

I would say the following four:

Nash Equilibrium via Fixed Point (either Kakutani, Brouwer or Tarski, depending on the problem);
Welfare theorems via Hanh-Banach theory (mainly the separating hyperplane theorem);
Utility and Profit Optimization via Weierstrass Theorem, Kuhn-Tucker conditions, and existence of a Lagrangian;
Minimization of Least Squares;


Macroeconomics for Mathematicians I'm coming from a math background (so my mind is set up for Definitions-Observation-Lemma-Proof frameworks) and looking for recommendations of a Macroeconomics textbook mainly devoted to growth models and foreign exchange rates.

Any recommendations?

I really think a great place to start in general is Olivier Blanchard's "Macroeconomics". However, this is an economics undergraduate text and may not be optimal for a mathematician, especially given the structure you expect.

More to your taste may be the following standard texts:

"Introduction to modern economic growth" by Daron Acemoglu.

"Recursive Macroeconomic Theory" by Lars Ljungqvist and Thomas J. Sargent

"Recursive Methods in Economic Dynamics" by Nancy L. Stokey, Robert E. Lucas and Edward C. Prescott

"Foundations of international macroeconomics" by Maurice Obstfeld and Kenneth Rogoff. A bit old by now, but a classic and a good place to start for international economic topics. Alternatively, try:

"Open Economy Macroeconomics" by Martín Uribe and Stephanie Schmitt-Grohé.


Chicago Fed National Activity Index: underlying data download Is there quick way to download the 85 time series (already transformed, i.e., seasonally adjusted and stationarized, if necessary) that are used to construct the Chicago Fed National Activity Index (CFNAI)?

https://www.chicagofed.org/publications/cfnai/index

Friend.   Yes there is.   You can use the St. Louis Federal Reserve Economic Data download website (FRED)     https://fred.stlouisfed.org/series/CFNAI

Not sure about seasonal adjustment.  For seasonal adjustment you may need a statistical computing software to do that and you would have to choice your parameters.


Understanding this particular criticism of RCTs by Deaton and Cartwright Deaton and Cartwright make several criticisms of randomized controlled trials (RCTs).
My question is about this one in particular from a 2016 VoxEU piece:

Well-conducted RCTs could provide unbiased estimates of the average treatment effect (ATE) in the study population, provided no relevant differences between treatment and control are introduced post randomisation, which blinding of subjects, investigators, data collectors, and analysts serves to diminish. Unbiasedness says that, if we were to repeat the trial many times, we would be right on average. Yet we are almost never in such a situation, and with only one trial (as is virtually always the case) unbiasedness does nothing to prevent our single estimate from being very far away from the truth. If, as if often believed, randomisation were to guarantee that the treatment and control groups are identical except for the treatment, then indeed, we would have a precise – indeed exact – estimate of the ATE. But randomisation does nothing of the kind, even at baseline; in any given RCT, nothing ensures that other causal factors are balanced across the groups at the point of randomisation.

Similarly, in their accompanying 2018 publication, they write:

It is common to treat the ATE from an RCT as if it were the truth, not just in the trial sample but more generally. ...
the RCT strategy is only successful if we are happy with estimates that are arbitrarily far from the truth, just so long as the errors cancel out over a series of imaginary experiments ...
More fundamentally, we strongly contest the often-expressed idea that the ATE calculated from an RCT is automatically reliable, that randomization automatically controls for unobservables, or worst of all, that the calculated ATE is true. If, by chance, it is close to the truth, the truth we are referring to is the truth in the trial sample only.

I am having trouble understanding or appreciating the significance of the above criticism. It seems to me that the criticism here is analogous to the criticism that can be made of any estimate from a single random sample:

Suppose we get a random sample of a population, measure their heights, and compute a sample average height. Then Deaton and Cartwright's criticism or objection is simply that this sample average height estimate may not be generally true of the population as a whole; that we should be happy with this single estimate only if "we are happy with estimates that are arbitrarily far from the truth, just so long as the errors cancel out over a series of imaginary [samples]".

Does the above analogy describe all there is to Deaton and Cartwright's criticism? Or is there something deeper and bigger that I'm missing?

Without having read the full piece I'd say you are mostly spot on, but for a subtle difference. The objection runs a bit deeper than your rephrasing of it, where you refer to single estimate. The thing is that there are way more than a single estimate this applies to, and therefore you are more likely to be off.

The point is that for RCT to establish causality both groups have to be equal on all other characteristics except for the treatment. By doing assignment randomly one can expect that in a large number of potential samples for all these aspects the independent samples' averages will be close to the population means for these characteristics.

The problem is, as you rightly point out, one may be unlucky and have samples where the sample averages are not actually close to the population means. The additional problem is that sample averages have to be close to the population means for all variables that matter, but 1) you don't always know which variables matter and 2) given the large number of variables that do matter you'll always have one or two where you are "unlucky" in terms of the sample averages not being close to the population mean.


GNP v. GDP as a true measure of national vibrancy Is the GNP a more realistic number or measure of national economic vitality regarding its citizenry/residents of the nation in question versus the GDP?

What used to be called GNP is now called Gross National Income (GNI) as being more descriptive of what it is measuring.

So GDP measures what is produced in a year while GNI measures incomes in a year, with the difference being some cross-border flows of money unrelated to exports and imports of goods and services.

Personally I prefer GDP as it reflects what is happening in a country, but it depends on what you regard as vitality.


Why doesn't government work more like a company when it comes to taxes? In government, the revenue is fixed (most of the time); you don't have to anything extra to get money from your "investors", i.e citizens. Similarly, from a citizens' perspective, whether the government reduces the cost of doing business will not have a direct effect on the taxes they will be paying (more of less). Plus, they probably wouldn't even know how cost-effective the government is and wouldn't change who they vote for.
So, overall, the government doesn't have any real incentive to operate in a cost-effective manner.
But, let's consider this. The government & parliment (as usual) outline what they what they will fund in the next year, and outlines the overall cost. Then, the percentage of taxes (income, wealth, capital gain) are determined [with a fixed proportion; cost = (%a of income tax) + (%b of wealth tax) + ..., where a,b,.. are fixed] according to that cost.
This way, for a citizen, how cost-effective the government would have a direct consequence on their own personal economy, so they would vote for government who could/do work cost-effectively. They would vote for representatives who pushes for cost-effective reforms.
Question:
Have there been such governments in the history? What would be the downsides of such a scheme?

Getting the facts straight
First before addressing the question, lets get the facts straight as arguing based on incorrect premises is not good and in this case this is also relevant to the answer.

In government, the revenue is fixed (most of the time)

This is completely incorrect. In fact government revenue varies quite significantly most of the time.
According to OECD data on government revenue the tax revenue varies a lot as you can see in the graph I made in R below. Even the countries for whom the lines look flat they look that only because of the scale but if you would 'zoom'in you would see quite a large variation in government revenue.

Second, it is also not true that government has no incentive to operate efficiently. There is already an incentive for government to be cost-efficient as in the long run government must balance its budget. That is in the long-run all taxes $T$ must be equal to all government expenditure $G$.
A less cost effective government will have to ultimately impose higher taxes than more efficient government. Since people dislike paying taxes government officials already have some incentive to be cost effective. Arguably this incentive is not strong due to all political and public choice considerations. See for example Public Choice III by Dennis Mueller which provides wide overview of literature on public choice which also discusses why inefficiencies arise in government provision of public goods and redistribution.

Addressing the question
There would be several downsides to such a proposal. You state that:

The government & parliment (as usual) outline what they what they will fund in the next year, and outlines the overall cost. Then, the percentage of taxes (income, wealth, capital gain) are determined ... according to that cost.

This is terrible idea as it does not allow government government to have counter-cyclical tax policy which is undesirable and destabilizing for economy.
The standard textbook policy advice (see for example Blanchard et al. Macroeconomics: an European Perspective)  for a government when it comes to spending ($G$) and taxes ($T$), over business cycle is that government should run deficits during recessions $G>T$ and surpluses during expansions $G<T$ in order to help smooth the business cycle. Yet at a core of your proposal is that in short run $G=T$ which would prevent government to fiscally respond to recession. Now, as discussed before in long-run $G=T$ as government has to ultimately respect its intertemporal budget constraint, but this should be done by balancing deficits and surpluses over business cycles not every year.
Moreover, you make your tax proposal too vague to make any historical comparisons. On the balanced budget part there were historically countries that run or tried to run balanced budget. A recent example would be Germany, but such proposals are usually always abandoned during the recessions for the aforementioned reasons.


How is money destroyed when banks issue debt? Bank of England (2014):

Money can also be destroyed through the issuance of long-term debt and equity instruments by banks.

How is money destroyed when banks issue debt?
Say Bank X issues a £100 10-year bond that Person Y buys with £100 cash. Then

X has assets +£100 (cash) and liabilities +£100 (10-year bond); and
Y has assets +£100 (10-year bond) and assets -£100 (cash).

How is any money destroyed?

Generally, people do not pay for bonds with currency (e.g. pound notes). They pay with bank deposits. This means that Y has lost a deposit.

If the deposit was with X, the deposit is just destroyed; X does not hold deposits against itself.
If the deposit was with another bank Z, bank Z loses the deposit, and it has to transfer the 100 pounds to X via the payments system. X will not hold a deposit at Z.

In either case, bank deposits are destroyed, and they are a component of the money supply.


Was the gold standard a monetary union? In the previous question here, one comment said:

"Currency unions to work properly need either perfect mobility of all factors of production (i.e. free migration/capital flows etc) or fiscal union".

However, I remember our professor at university once mentioning that gold standard worked like a monetary union. In past countries did not had fiscal unions and people could not move around as easily as today. How come that the gold standard was able to exist? Or was gold standard not monetary union?

tl;dr:
That quote refers to conditions for currency area/monetary union to work optimally. Even sub-optimal monetary union can exist. Furthermore, the gold standard existed in era of relative stability, low government spending and actually in era where movement of labor and capital was virtually unrestricted. As soon as that era ended gold standard collapsed. So it was able to exist because at the time conditions were favorable for it.
Full Answer:

was gold standard not monetary union?

Technically they are not completely equivalent, but they are both very similar as they represent an extreme regime of fixed exchange rate. Consequently, many economists draw parallels between gold standard and monetary union. For example, Eichengreen & Temin (2010) in their paper Fetters of gold and paper also argue that gold standard and European Monetary Union (EMU) were virtually equivalent, so your professor is not wrong.

How come that the gold standard was able to exist?

Well first lets correct some incorrect premises. You write:

In past countries did not had fiscal unions and could not move around as easily as today.

The first part is generally correct, however the second part (where I assume the moving refers to movement of different factors such as labor/capital) is not correct. In fact prior to WWI people could move around the world relatively more freely than today. Most countries did not even have passports for their citizens. When it comes to capital arguably there were also less barriers to capital flows. For example, Keynes, who lived in the era of gold standard, argues in his book economic consequences of peace that:

“What an extraordinary episode in the economic progress of man that age was which came to an end in August 1914!
...
The inhabitant of London could order by telephone, sipping his morning tea in bed, the various products of the whole earth, in such quantity as he might see fit, and reasonably expect their early delivery upon his doorstep; he could at the same moment and by the same means adventure his wealth in the natural resources and new enterprises of any quarter of the world, and share, without exertion or even trouble, in their prospective fruits and advantages; or he could decide to couple the security of his fortunes with the good faith of the townspeople of any substantial municipality in any continent that fancy or information might recommend.
He could secure forthwith, if he wished it, cheap and comfortable means of transit to any country or climate without passport or other formality, could despatch his servant to the neighbouring office of a bank for such supply of the precious metals as might seem convenient, and could then proceed abroad to foreign quarters, without knowledge of their religion, language, or customs, bearing coined wealth upon his person, and would consider himself greatly aggrieved and much surprised at the least interference.
But, most important of all, he regarded this state of affairs as normal, certain, and permanent, except in the direction of further improvement, and any deviation from it as aberrant, scandalous, and avoidable.
The projects and politics of militarism and imperialism, of racial and cultural rivalries, of monopolies, restrictions, and exclusion, which were to play the serpent to this paradise, were little more than the amusements of his daily newspaper, and appeared to exercise almost no influence at all on the ordinary course of social and economic life, the internationalisation of which was nearly complete in practice.”

Furthermore, also empirical research shows that in the pre WW1 era there were large capital flows between poor and rich countries (see the sources provided in this answer). So the premise that factors could not move easily in the era of gold standard is false.
Next, the comment you quote was actually mine and note I was specifically talking about conditions for currency unions to work 'properly' i.e. to be optimal (sorry if that was not clear). A monetary/currency union does not need to be optimal to exist.
This being said note that gold standard did actually broke down because gold standard tended to exaggerate asymmetric macroeconomic shocks (see the previously cited Eichengreen & Temin) and it did broke down after WW2 where the kind of globalization and international mobility (which could mitigate the above mentioned shocks) was all but lost.   In fact as measured by value of exported goods as share of GDP, the world only as late as in early 1980s reached the same level of globalization as in 1914 and when it comes to international mobility arguably there are still more restrictions on it than in 1914.  Although in form of  Bretton Woods system Gold Standard technically lasted till 1970s, Eichengreen and Temin argue this was largely due to  ideological reasons, and generally the system was not considered successful.

Furthermore, one of the reasons why gold standard also broke down was that as government spending  and government debt increased after WWI and WW2. This put pressure on governments to monetize their debt and finance portion of their spending through seigniorage. The pre-WW1 gold standard era was also an era of relative stability (macro-economically speaking) as argued by Eichengreen & Temin and sources cited therein. In contrast the interwar and post WWII period was from macroeconomic perspective much more turbulent (Great Depression, Oil Shocks, recent Great Recession etc.). When times are ‘good’ it is much easier to sustain suboptimal monetary union then when economy is expecting macroeconomic shocks, especially asymmetric ones, as smoothing out asymmetric shocks requires countries to adopt different monetary policies or some sort of fiscal transfers (See DeGrauwe Economics of monetary union).


What does "steep incentive contract" mean in the context of adverse selection? This term was mentioned in a slide and when I looked online, the only thing which I could find talking about this is this paper.

For example,in the cost-plus-incentive contract

$$x(T, c) = a(T) - a'(T) × (T-c)$$

where $x$ is the contractor's fee, $T$ is the cost target, $c$ is a verifiable cost; $a(T)$ is decreasing and convex.

I was told that with smaller $T$ and hence higher $a(T)$ and $-a'(T)$, the incentive contract is steeper. Is the steepness represented by $-a'(T)$? What exactly is the interpretation of steepness of incentive contract? Does it mean more risk for the contractor? If this is the case, am I correct that the decreasing $a(T)$ motivates the contractor to take a smaller T? How is it translated to incentive constraint? That high-cost contractor would not recklessly take a small T?

"Steep incentives schemes" are synonymous with "high-powered incentives". A steep incentive scheme is thus one in which there is a large or high-powered performance incentive. This can take either the form of a small fixed payment and a (potentially) large bonus, or it can be a large fixed payment and a (potentially) large penalty for deviation.

Normally we think about using steep incentive schemes when we wish to have a separating equilibrium in which high-skilled (or risk-seeking) workers choose steep incentive schemes and low-skilled (or risk-averse) workers choose flatter incentive schemes. Here is one paper I'm aware of that discusses this. You will find more examples if you look at optimal contracts under risk-aversion. https://www.econstor.eu/bitstream/10419/30169/1/620692227.pdf

In your example, I believe the decreasing nature of $a(T)$ is capturing the movement from a low-cost (less risky) project to a high-cost (more risky) project. As the cost (risk) for the project increases, the principal will want a steep incentive scheme to ensure that only a high-skilled contractor will choose to perform the task. This is because we are shifting the weight away from $a(T)$ (the fixed payment) and towards $a'(T) \times (T-C)$ (the bonus/penalty) as $T$ increases. Moving the other direction, as the cost (risk) for the project decreases, $a(T)$ increases and the incentives have less power.


Marginal Product and Average product So I've seen in my textbooks and many places online that when marginal product is more than average product average product is increasing, when average product is falling average product is greater than the marginal product. I get the economic intuition behind all this but I was wondering how can one show this mathematically.

Here is a simple explanation for a single input and output technology represented by a production function $f:\mathbb{R} \to \mathbb{R}$.

Note that Average Product (AP) is defined as
$$
AP(x) = \frac{f(x)}{x}
$$
, and Marginal Product (MP) is defined as
$$
MP(x) = \frac{\partial f(x)}{\partial x} = f'(x)
$$

Now, we take the derivative of the function $AP(x)$, and then we have
$$
\frac{\partial AP(x)}{\partial x} = \frac{f'(x)x-f(x)}{x^2}
\\
= \frac{1}{x}\bigg[f'(x)-\frac{f(x)}{x}\bigg]
\\
= \frac{1}{x}[MP(x)-AP(x)]
$$

Since $x$ indicates the level of the input, $x>0$, and thus we have,
$$
\frac{\partial AP(x)}{\partial x} > 0 \iff MP(x)>AP(x)
$$
, or
$$
\frac{\partial AP(x)}{\partial x} < 0 \iff MP(x)<AP(x)
$$


Optimizing Lagrangian Function Subject to 4 Input/Output Constraints: The objective function:

$$\text{utility}=U\left(x_{c}, y_{c}\right)$$

subject to,

$x_{o}=f\left(y_{i}\right)$
$y_{o}=g\left(x_{i}, x_{o}\right)$
$x_{c}+x_{i}=x_{o}+x^{*}$
$y_{c}+y_{i}=y_{o}+y^{*}$

where o represents output, i is inputs, c is consumed, and * represents initial quantity stocks. Lagrangian is combined and the first-order conditions are as follows:
$$
\begin{array}{l}{\partial \mathscr{L} / \partial x_{c}=U_{1}+\lambda_{3}=0} \\ {\partial \mathscr{L} / \partial y_{c}=U_{2}+\lambda_{4}=0} \\ {\partial \mathscr{L} / \partial x_{i}=\lambda_{2} g_{1}+\lambda_{3}=0} \\ {\partial \mathscr{L} / \partial y_{i}=\lambda_{1} f_{y}+\lambda_{4}=0} \\ {\partial \mathscr{L} / \partial x_{o}=-\lambda_{1}+\lambda_{2} g_{2}-\lambda_{3}=0} \\ {\partial \mathscr{L} / \partial y_{o}=-\lambda_{2}-\lambda_{4}=0}\end{array}
$$

Simplification leads to the following expressions:
$$
M R S=\frac{U_{1}}{U_{2}}=\frac{\lambda_{3}}{\lambda_{4}}
$$
$$
M R S=\frac{\lambda_{3}}{\lambda_{4}}=\frac{\lambda_{2} g_{1}}{\lambda_{2}}=g_{1}
$$
$$
M R S=\frac{\lambda_{3}}{\lambda_{4}}=\frac{-\lambda_{1}+\lambda_{2} g_{2}}{\lambda_{4}}=\frac{-\lambda_{1}}{\lambda_{4}}+\frac{\lambda_{2} g_{2}}{\lambda_{4}}
$$
$$
=\frac{1}{f_{y}}-g_{2}
$$

Q: The text states that optimality in y production requires the individual's MRS in consumption equal the marginal productivity of x in the production of y. I do not understand this statement. We are optimizing utility not the production function?

I think what it’s referring to optimal $y$ (i.e. what would be normally in calculus denoted as $y^*$- but you already use that for the initial stock).

It makes sense that to maximize the utility MRS should be equal to marginal productivity since MRS should be equal to ratio of prices and in case like this where the person produces goods for themselves the prices will equal to the marginal costs of production which in turn will also equal to the marginal product (essentially producing for yourself is like being in a perfectly competitive market). The intuition is that person will produce good only to the extent the marginal utility of consumption becomes equal to marginal disutility of production, as if you are producing less you can increase utility by producing more and if you are producing more than that you can increase utility by producing less. At least that’s my understanding of the intuition behind this kind of model.


Contradictory FOC and maximizing solution I have to maximize the following function -
$\max_{x \in (0,1)} (((p_1x)^{2r} + (p_2(1-x))^{2r})/2)^{1/r}$
where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered to be given for this maximization problem.
FOC are given as -
$\frac x {1-x}$ = ${(p_2/p_1) }^{2r/{2r-1}}$
My problem is -
Whenever $p_1$ > $p_2$, FOC argues that value of x should be < 1/2 but this doesn't maximize the function. Rather solution should be x>1/2. Why the FOC solution is not maximizing the objective function. What have I done wrong?

As alluded to by Bertrand in his +1 comments this is because FOCs do not tell you where maximum or minimum occurs. This is common misconception among some students but it simply does not hold.
FOCs give you location of stationary points. They give you points where $df(x,y)/dx = df(x,y)/dy= 0$.
A maximum or minimum will occur at points where $df(x,y)/dx = df(x,y)/dy= 0$, but so will saddle points. FOCs cannot distinguish between whether point is maximum, minimum or saddle point, it can just tell you that you found points at which slope is zero.
What even more a function can have multiple local maxima/minima and saddle points. In optimization you will generally want want to find the global maximum not just a local maximum. You can see this visualized at a figure below taken from EMEA by Sydsæter, Hammond & StrØm.

If you want to know whether the point is maximum or minimum you need to examine second order conditions (SOCs) which tells you whether the function is concave or convex (or some people like to call it concave down) then based on the concavity of the function you can infer if it is a local maximum, minimum or saddle point. For non-constrained (e.g. Lagrangian SOCs are different) multivariable optimization SOCs are given by:
A function will be concave (implying local maximum) if the conditions for $C^2$ function in $\mathbb{R}^2$ are satisfied:
$$f_{11}''(x, y) \leq 0, f_{22}''(x, y) \leq 0, \text{ and } f_{11}''(x, y)f_{22}''(x, y) −
(f_{12}''(x, y))^2
\geq 0$$
A function will be convex (implying local maximum) if the conditions for $C^2$ function in $\mathbb{R}^2$ are satisfied:
$$f_{11}''(x, y) \geq 0, f_{22}''(x, y) \geq 0, \text{ and } f_{11}''(x, y)f_{22}''(x, y) −
(f_{12}''(x, y))^2
\geq 0$$
However, the conditions above only tell you if you found local minimum or maximum. In order to find global maximum/minimum, you have to examine all maximums or minimums as well as the boundaries of your function (e.g. maximum could occur at some endpoints for example $y=x+10$ defined on interval $x\in[0,10]$ will have maximum at the upper boundary $x=10$ even if FOC does not find any stationary point at $X=10$) and check which of their output value is highest or lowest (although most introductory problems will typically be set in a way there is only one max or min - this is likely why some students confuse FOCs as conditions for max or min rather than just conditions for stationary points).


EMH: Difference between market price and fundamental value? I am confused by the relation between stocks market prices and fundamental (or intrinsic) values stated by Efficient Market Hypothesis. How these deviates regarding to efficient market theory or are these the same according to EMH?

Why I am asking this is because among the literature, there can be found two kind of statements.

This is the very general statement that can be found from here and there:

  Investopedia: This principle is called the Efficient Market Hypothesis (EMH), which asserts that the market is able to correctly price securities in a timely manner based on the latest information available. Based on this principle, there are no undervalued stocks to be had, since every stock is always trading at a price equal to its intrinsic value
  **.

The another one what can be found from academic literature and books, states:

  Fama (1965) In  other words,  in  an  efficient  market  at  any  point
  in   time   the   actual   price   of   a   security   will   be
  a good estimate of its intrinsic value.

and line with previous, other source states :

  Market efficiency
  does not require that the market price be equal
  to true value
   at every point in time. All it requires is that errors in the
  market price be unbiased,
  i.e.,
  that
  prices
  can
  be
  greater
  than
  or
  less
  than true value, as long as these deviations are random

I also saw algebraig illustration where it was shown that the market price estimates the fundamental value of security better any individual trader can estimate it. (with certain assumptions)

So the question is, why here and these is stated, that in efficient market, the market price of stock is trading at a price equal to fundamental (or intrinsic) value? Which is right?

And if the market price is at the best good estimate of intrinsic value, how can it be stated that in efficient market there are not under- or overvalued stocks, if the market price is only best estimate of instrinsic value?

I am not very familiar with algebraig definitions, but some kind of clarification behind this issue would be appreciated.

Thank you for clarification.

The fundamental value of an asset over an infinite horizon is the sum of dividends discounted over time.

You are stumbling into the literature on rational and irrational bubbles. In general, the difference between the fundamental value of an asset and its market price constitutes, to some degree, bubble behavior.

Edit — I can probably expand this for clarity.  Each of those definitions tries to get at the same thing — there is no room for systematic bias in the prices of assets traded on the market. Markets, more or less, are powerful because they aggregate massive amounts of information. They incorporate ever trader’s wants, fears, expectations, etc. and distill it all into a single thing — a price. And markets do this very quickly. We can see this, for example, when markets adjust to incorporate information shocks that occur around FOMC statements. Because of this, it should be true that prices do not deviate systematically from fundamentals. The argument boils down to one of arbitrage opportunities, I suppose.

However, many economists (many people, really) openly discuss bubbles. A bubble, rather loosely stated, exists if prices deviate systematically from fundamentals. The common theme of each definition above is that we should see systematic deviations on prices away from fundamentals. They just vary a bit in how emphatically they say this. Nevertheless, we all talk about bubbles.

Also — how do we know if prices have deviated from fundamentals? Well, there is a nice literature built around this idea, but I am not convinced this is possible to do with empirical data. However, economists have used the laboratory to show that this happens in markets. In fact, generating bubbles in an asset market is probably among the most reproducible laboratory phenomena I can think of.


Unable to determine price ratio for a pure exchange economy The problem is simple. However, I'm having trouble deriving the price vector for the system. What exactly am I doing wrong/missing out?

Two consumers.

$$
U_A = \min(x,y), \hskip 20pt U_B = x+y.
$$

Initial endowments
$$
(x_A,y_A)=(100,100), \hskip 20pt (x_B,y_B)=(50,0).
$$

Putting A on the bottom left, the contract curve will be a line with slope 1 from A, from point (0,0) to (100,100), A's endowment point. [Seen from A's perspective.] All points on this contract curve are points of 'tangency' between A's kinked indifference curves, and B's linear indifference map.

$x_A= 100(p_x+p_y)/p_x $

$x_B = 0$  (if  $p_x>p_y$)

$x_B = 50$  (if  $p_x<p_y$)

A cannot benefit from more than (100,100), while B will benefit from as much of either good as she can get: i.e. endowment point lies on contract. Thus, the endowment point can be the competitive equilibrium allocation.

The question is, what will be the equilibrium price vector.

If we keep the price vector as (1,1), X can sell and buy back endowment, and so can B. So, (1,1) makes the endowment point affordable. However, so does any price vector where $p_x<p_y$ (ensuring 0 demand for Y from B.)

Does a unique price vector (ratio) exist for this system? How do we derive it? And what am I doing wrong?

Any help (resources on CE problems of this kind) will be wonderful. Thanks.

Your analysis seems to be spot on, except for some minor typos:
$$
x_A^* = 100 \frac{p_x + p_y}{p_x + p_y} = 100,
$$
because the value of A's endowment is $100 \cdot (p_x + p_y)$. And you could include the case of
$$
x_B^* \in [0,50]  \mbox{ if } p_x = p_y.
$$

As you state at the end the equilibrium price vector is not unique, there is equilibrium for all $\frac{p_x}{p_y} < 1$, because with this price vector we have
$$
(x_A^*,y_A^*) = (100,100), \hskip 20pt (x_B^*,y_B^*) = (50,0)
$$
and the market is then indeed in equilibrium as
$$
x_A^* + x_B^* = x_A + x_B, \hskip 20pt y_A^* + y_B^* = y_A + y_B.
$$
The price ratio $\frac{p_x}{p_y} = 1$ also results in equilibrium, because one of the optimal consumptions of B is still $(x_B^*,y_B^*) = (50,0)$.


Prove that a preference is linear Given the following two conditions:

$x\succ y$ implies $x+a\succsim y+a$,

And,

$x\prec y$ implies  $x+a\precsim y+a$

We want to prove that $\succsim$ is a linear preference.

One of the definition of linear preference is that:
$x\succsim y \Leftrightarrow x+a\succsim y+a$

So I am trying to do this:

Since $x\succsim y$ means that $x\succ y$ or $x\sim y$

We already know that $x\succ y$ implies $x+a\succsim y+a$,

all things left is to prove that $x\sim y$ also implies that $x+a\succsim y+a$.

You cannot prove this. It is wrong.

Define $u(x)=\min{\{x,0\}}$. Let $\succsim$ be the preference relation represented by $u$. This preference relation satisfies $x\succ y \Longrightarrow x+a\succsim y+a$ for all $x,y,a\in\mathbb R$. But let $x=0$, $y=1$, and $a=-1$. Then $x\sim y$, but $y+a=0\succ -1=x+a$, thus $x+a\not\succsim y+a$ and $\succsim$ is not linear.


What is the difference between a transitory and a permanent shock? In my study of time series regression models in econometrics, we are discussing basic time series regressions and interpreting the effects of shocks in finite distributed lag models. I was wondering what the difference is, in intuitive terms, between a transitory and a permanent shock. According to my understanding at the moment, every shock would be permanent because you cannot undo the past. Wouldn't saying that an effect is transitory be like completely erasing its effect from existence and never accounting for it? I think I am wrong, but I don't know why.

"Permanent shock" is a shock whose effects on current values of a variable never die out in absolute terms. "Transitory shock" is a shock whose effects gradually die out. Consider the simplest one-lag model

$$y_t = \beta y_{t-1} + u_t, \;\;\; y_0 = 0$$

By direct substitution one gets that

$$y_T = \sum_{t=0}^{T-1}\beta^t u_{T-t} = u_T + \beta u_{T-1} + \beta^2u_{T-2} +...+\beta^{T-1}u_1$$

If $|\beta| <1$ the absolute effect of say shock $u_1$ on $y_T$ diminishes as time passes, $T \uparrow$. While mathematically it doesn't die off completely except at infinity, its absolute contribution decays exponentially.

On the other hand, if $\beta =1$ (a "unit root" model) then

$$y_T = \sum_{t=0}^{T-1}u_{T-t}=u_T + u_{T-1} + u_{T-2} +...+u_1$$

and no matter how far we move into the future the shock at period $1$ will fully contribute to the value of $y_T$.

Of course, if autocorrelation is strong (high $\beta$) then a "transitory" shock will influence visibly many periods in the future, so it may be "ignored" when examining "long-term" outcomes, but not when one deals with mid-term effects and policy.


Swaps and systemic risk I understand the systemic risk that can be associated with the trading of credit default swaps, but is it the same with interest rate swaps? What was the "default rate" on interest rate swaps during the 2007-2008 crisis compared to CDS for instance?

A standard ("vanilla") interest rate swap is a contract in which one party pays a fixed rate of interest, and the other pays a floating rate (typically LiBOR, but it depends upon the market convention in the currency). (There are a lot of interest rates that deviate from this formula, but they have the same "system risk" characteristics as standard swaps.)

As a simplification, assume that the floating rate of interest is paid annually.

If you receive fixed, each year, you would net receive:

Net receipt = (contracted rate of interest - the "swap rate") - (latest 1-year floating rate).

There is no notion of "default" in the contractual payments, unlike a credit default swap.

From a risk perspective, this can be viewed as owning a fixed rate bond, and borrowing 100% against it at the floating rate. There is obviously leverage, which poses risks (see below).

The only way a default can affect you is if your counterparty fails. All that you lose is:

whatever value of future payments you would have received (the Net Present Value), that is not covered by collateral.
You lost the interest rate risk exposure that the swap provided. If that swap was a required hedge, you need to find a new hedge.

The normal procedure is that the net NPV exposure is covered by collateral; an entity would have have to be in a weak bargaining positiom (or badly informed) to enter into derivatives trading without a collateral agreement.

During the Financial Crisis of 2007-2008, I believe that it is safe to say that there was very little NPV losses that were incurred by inadequate collateral. That is, losses due to "defaults" was a very small number (compared to the other types of losses). The losses that were associated with interest rate swap trading was the result of needing to replace hedges that were lost when Lehman (and others) defaulted. (Not all of the problems that occurred during the Financial Crisis were documented, but I am unaware of issues in the interest rates swap market being a trigger. Once the crisis was underway, the swaps markets were dislocated, like most other ones.)

Otherwise, the movements in interest rates were not enough to trigger a crisis in 2007-2008. The source of the crisis was funding/credit risks.

You would need to go back to the 1994 bond bear market, or the LTCM Crisis of 1998 to have a historical event where interest rate swaps were a factor in the crisis.

In the case of 1994, there were very large movements in interest rates, coupled with risk management systems that did not really know how to measure interest rate risk. Since 1994, interest rate risk measurement is much better understood at any credibly managed investment firm or bank. (The comments about risk management are based on my knowledge of interest rate risk management that I gained from working in fixed income from 1998-2013. They are the result of my discussions with market participants who were involved with investment management during 1994. You would need to track down a paper on the evolution of interest rate risk management to get a formal reference.)

Whether a situation similar to 1998 or 1994 could happen again is an open question that could not expected to be answered here. Regulators are certainly aware of what happened then, so they could be expected to take actions that would prevent an exact repeat.


Government spending and revenue statistics I am looking for thorough statistics of budgetary spending and revenues by category for approx all oecd countries. If not for all oecd i will be happy to have data only for Switzerland. I am interested in time period from 1995 to 2013. Unfortunately i am not able to find comprehensive source for those data. Could you give me some hints with regard to possible source of such data?

EDIT: Precisely i am looking for something ( http://en.wikipedia.org/wiki/Federal_budget_of_Switzerland ) like 4.1.  i.e. this table (but for both expenditures and revenues) with example budget but i want to have this year by year.

As you want data for OECD countries have a look at the OECD's Statistics portal. You will find the data in the "National Accounts" as section as well as in the "Public Sector, Taxation and Market Regulation"

As an alternative or as a complement you can also have a look at the Eurostat database on Government Statistics. They do have data for Switzerland as well as for many OECD countries.

Finally, as you seem to be focussed on Switzerland, you can also try to find the data via the Federal Statistical Office.

You can obtain time series by following the links in the "additional information" column.


Is non-monotonic local non-satiation supported by consumer theory in economics? In general (Walrasian) equilibrium, local non-satiation is one of the assumptions that guarantee existence of equilibrium. Question is, is non-monotonic local non-satiation preference supported by rational consumer theory in economics?

Suppose we're talking about some bundle of consumables, $x$. If preferences are monotone, either weakly or strongly, the general idea is that more is better. With local non-satiation the idea is that, no matter what $x$ you have, there is always some small change in $x$ that would make you better off.

Is your question, does there exist rational preferences where:

More is better does not hold.
You can always make a tiny change that leads to a preferable bundle.

Imagine a consumption set on the surface of an infinite dimensional unit sphere, where the dimensions are indexed by the counting numbers and represent different varieties of goods.  The consumer prefers goods found in higher dimensions.  So the 1 unit of good on the second dimension is preferred to the 1 unit of good on the first dimension.

Thus, the consumer is never satiated because they would always prefer one unit of a good found in a higher dimension, and there are infinitely many dimensions.  But these preferences do not satisfy monotonicity, because you must always give up a little bit of at least one good to acquire more of another.

Hence, these preferences are rational, because you can rank all pairs on the surface of the sphere, and transitivity holds trivially.


Is there autocorrelation in stock prices? I've heard that stock prices are random. But I know if the price is 15 at one tick, the next price has a range that hovers around 15 because it won't randomly hit 15,000,000 in the next tick.

Fist, how could I go about finding the answer to that question myself? I was thinking of downloading historical tick data on Apple Inc. and running this regression in Stata

reg price time

then doing a newey test. Would I need to include volume? And what lag is normally used for this?

Second, to find an answer about stocks in general, would I have to look at  every stock? Or is a random sample good enough?

I looked at some research from the top google results of "is there autocorrelation in stock prices". But it was a little over my head. What I managed to gather is that at least for stock returns yes, there is, in large diversified portfolios. Any further light and knowledge is appreciated.

Stock prices follow a random walk process, usually we include a drift term to account for the somewhat prolonged upward/downward drifts. This is basically an AR(p) process, p being the lag order. For instance AR(1) with drift is $X_t=\delta+\beta X_{t-1}+u_t$ where $\beta = 1$. Try testing this model for unit root using ADF test in stata. One lag is enough. You should fail to reject the unit root for an evidence of autocorrelation in the prices. Stock returns are not autocorrelated, they usually follow a stationary process if you take sufficiently long sample.


Showing utility function gives preferences that are rational and convex Consider a consumer with preferences relation $\succsim$ over non-negative commodities $x_1$ and $x_2$ such that their utility U = $x_1$ + $\ln(x_2)$
Are these preferences rational and are they convex/strictly-convex?
I'm a bit confused on how to do this.  So first, I know preferences need to be complete and transitive to be rational, but for a utility function, it just needs to be continuous right?  Is there another property it needs?  With that said, how would I mathematically prove this function is actually continuous?  If I graph it, it's continuous, but is there a mathematical proof for this?
For the second part, if preferences are (strictly) convex, then the preferences must be (strictly) quasi-concave right?  How would I mathematically prove that this function above is quasi-concave?
Online, it says a function is quasi-concave if $f(\lambda x+(1-\lambda )y)\geq \min {\big \{}f(x),f(y){\big \}}$, but I'm having a tough time understanding this in relation to a utility that has both an $x_1$ and an $x_2$ value.  When I'm looking at the above function, I only understand it for like $f(a) = a^2$ and there's not a second variable in there.
Thanks!

I'll give a few hints to get you started. First, note that since the preference $\succsim$ is represented by the utility function $U(x_1,x_2)=x_1+\ln x_2$, it follows that
\begin{equation}
(x_1,x_2)\succsim (x_1',x_2')\quad\Leftrightarrow\quad U(x_1,x_2)\ge U(x_1',x_2') \tag{1}
\end{equation}
Keeping this equivalence in mind, consider:

Completeness: $\succsim$ is complete if for all $(x_1,x_2),(x_1',x_2')\in\mathbb R_+^2$,
\begin{equation}
\text{either }(x_1,x_2)\succsim (x_1',x_2'),
\quad\text{or }(x_1',x_2')\succsim(x_1,x_2). \tag{2}
\end{equation}
Using $(1)$, we can rewrite $(2)$ as
\begin{equation}
\text{either }U(x_1,x_2)\ge U(x_1',x_2'),
\quad\text{or }U(x_1',x_2')\ge U(x_1,x_2). \tag{2*}
\end{equation}
Now $(2^*)$ should be easy to prove using the property that $\mathbb R$ is an ordered field.

Transitivity: Use the same trick to translate preference ordering into ordering of real numbers.

Convexity: Start from the definition that $\succsim$ is convex if for any $\alpha\in[0,1]$,
\begin{multline}
(x_1,x_2)\succsim(x_1'',x_2'') \text{ and } (x_1',x_2')\succsim (x_1'',x_2'')
\\\Rightarrow \quad
\alpha(x_1,x_2)+(1-\alpha)(x_1',x_2')\succsim(x_1'',x_2'')
\end{multline}
Again, translate the preference ordering into ordering of real numbers to prove the implication. Since $U$ is quasi-linear, this way will save you some trouble of dealing with Hessians and so on.


How to find the Utility Possibility Frontier when there are Perfect Substitutes? I am trying to derive the Utility Possibility Frontier (UPF) when both utility functions display perfect substitutes (in an Edgeworth economy with to consumers and two goods).
The specific problem:

$u_A = 2x_{1A}+x_{2A}$

$u_B = x_{1B}+2x_{2B}$

The total endowments being five of each good. Thus:

$x_{1A}+x_{1B}=5$

$x_{2A}+x_{2B}=5$

We are given the hint that "the Utility Possibility Set can be described as the set of
$(u_A, u_B)$ in the non-negative orthant of $R^2$ satisfying: $u_A ≥ 0, u_B ≥ 0$".

I keep trying different approaches, but always end up with imposible conditions. When following the suggestions from this another post (How to derive utility possibility frontier?), I keep getting weird first order conditions such as "1=0".

Once the UPF is found, we are asked to maximize social welfare through the following Social Welfare Function (SWF):

$W(u_A,u_B) = 3u_A + u_b$

Thank you in advance.

In addition to the solution worked out in the comments, there's also a faster way to find the welfare maximizing distribution:

Note that social welfare can also be written in terms of $x_{1A}$ and $x_{2A}$ as $W(x_{1A},x_{2A})=15+5x_{1A}+x_{2A}$, which is maximized in the Edgeworth box at $(x_{1A},x_{2A})=(5,5)$. As long as utilities are increasing in the quantities of both goods, this point is always on the contract curve and is therefore the maximizer of social welfare independently of the specific forms of the individuals' preferences.


Forecasting with game theory? Im familiar with sequential games in game theory. Specifically Im interested in if one can forecast using such a method?

what specific models I should know about if I can forecast using game theory?

As @denesp has pointed out making real precise predictions with game theory is difficult because it is hard to gather data on payoffs and behavior under uncertainty, not to mention the fact that game theory typically assumes individual rationality (although the behavioral game theory referenced by @HerrK above loosens some of those requirements)
Of course that has never stopped people from trying. At least in environmental and resource economics there are plenty of papers looking into dynamic games that are calibrated to make some general (but perhaps not very accurate) predictions. This overview paper from Hannesson includes a lot of references to such papers in fisheries, a similar but older overview paper on transboundary polution was written by Finus.
Given what you're interested in, I'd look into repeated games with sequential moves. In a very simple set-up it could work out like this: each period the employers make an offer, and the unions then decide to either go on strike (hurting the employers and employees and moving to another round) or accept (which ends the game). As said, I don't think it will give you an accurate prediction, but it would perhaps give you some insights in the motives at work.
The problem with such a game set-up is that

I'd expect both the employers and unions to fall for sunk cost arguments (can't quit now, we've gone so far...), which a rational player wouldn't do
Repeated games in the presence of uncertainty often have multiple equilibria that can be supported by trigger strategies. Although these trigger strategies are subgame perfect, they are also non-renegotiation proof, and that is probably exactly what you're interested in.

Hope that helps.


best books about GDP i would appreciate titles on GDP--academic and lay.

ty

I can recommend "GDP: A Brief but Affectionate History" by Dianne Coyle as a non-technical background on GDP for a wide audience.

Why did the size of the U.S. economy increase by 3 percent on one day in mid-2013—or Ghana's balloon by 60 percent overnight in 2010? Why did the U.K. financial industry show its fastest expansion ever at the end of 2008—just as the world’s financial system went into meltdown? And why was Greece’s chief statistician charged with treason in 2013 for apparently doing nothing more than trying to accurately report the size of his country’s economy? The answers to all these questions lie in the way we define and measure national economies around the world: Gross Domestic Product. This entertaining and informative book tells the story of GDP, making sense of a statistic that appears constantly in the news, business, and politics, and that seems to rule our lives—but that hardly anyone actually understands.
Diane Coyle traces the history of this artificial, abstract, complex, but exceedingly important statistic from its eighteenth- and nineteenth-century precursors through its invention in the 1940s and its postwar golden age, and then through the Great Crash up to today. The reader learns why this standard measure of the size of a country’s economy was invented, how it has changed over the decades, and what its strengths and weaknesses are. The book explains why even small changes in GDP can decide elections, influence major political decisions, and determine whether countries can keep borrowing or be thrown into recession. The book ends by making the case that GDP was a good measure for the twentieth century but is increasingly inappropriate for a twenty-first-century economy driven by innovation, services, and intangible goods.


Annual Fraud Recovery Over Time: Should I adjust for inflation? I have a dataset of the total amount the U.S. Department of Justice obtained annually in settlements/judgments of government fraud cases from fiscal years 1988-2019.  There's a lot of variation, but more recently the total settlements/judgments range from around 1 billion to 6 billion dollars.

We're trying to decide whether it makes sense to adjust the annual totals for inflation. Is there any reason not to? If we do, should we use CPI or GDP or something else?

You should definitely adjust for inflation, as you should with all monetary variables. I wouldn't worry using the CPI, you could use an alternative indicator as a robustness check to see whether the choice of indicator affects your main conclusions.


Why is Algeria the #2 milk powder importer in the world? Can anyone explain to me why Algeria, a country of 40 million people is importing almost half as much milk powder as China?

Turkey has 80 million people yet it apparently doesn't import milk powder, or very little. Likewise for Libya, which is right next to Algeria, although it has only 6 million people. Egypt has about 100 million people and is similar to Algeria in some respects, yet it imports no milk powder.

Four-fifths of Algeria is just desert --which leaves no room for agriculture.  The Algerian economy is mostly powered just by the oil industry, which contribute about ~70% of government revenues. Oil and oil related products constitute more than 80% of Algeria's exports.

For example, Turkey has twice the population of Algeria but it has more than 7.5 times the cattle Algeria has. (14.2 in Turkey vs 1.6 in Algeria). So the short answer is that Algeria isn't just suited for Agriculture.


How exactly did Venezuela's economy fail? Venezuela has unfortunately become the example of a first-world, wealthy democracy failing, and I'd like to make sure I understand why.

My understanding comes down to a few major steps, namely:

Venezuela has incredible stores of oil
In the late 90's and early 2000's, Hugo Chavez's government invested heavily in building up the oil sector, and redistributed most of the profits to the people in the form of social programs, and state-owned corporations filling most roles in the economy
The oil industry caused three major strains on private industry in other sectors of Venezuela's economy, causing private industry to begin to fail:

Spike in Venezuela's currency caused by oil exports ("Dutch disease")
Competition from state-owned competitors
Borrowing by the government to reinvest in the oil industry at high leverage

The drop of oil prices in 2007 to 2008 caused a gradual collapse of the one-product economy
Excess printing of money to try to combat the effects of the oil price drop caused hyperinflation and a loss in confidence in the currency
Hugo Chavez and Nicholás Maduro consolidated power in an attempt to more directly target economic issues and administer social programs (assuming good intentions, which may not be a good assumption)
Another drop in oil prices in 2014 caused additional damage to the economy
Protests against the drop in quality of life, and lack of popular support for Nicholás Maduro caused functional collapse of the government, as a government that people don't believe in is no government at all

Where are the holes in the above description, and where do I need to understand better?

I think you summarized most of it quite well. Few things that you missed:

There was a host of bad macro and microeconomic policies. For example, nationalization of many firms, price controls, subsidizing many uneconomical activities etc. Also actually the investments into oil industry and productivity declined in Venezuela after the industry got nationalized so that part was not fully correct, and Hugo Chavez was appointing people who were making it worse (see  thisforeign policy article).

Also when it comes to social policies, it’s definitely possible and legitimate to want to have Ralwsian welfare state - this is matter of philosophy and value judgements not economics. However, this does not mean that a country can just arbitrarily sets its social policies and ignore resource constraints. Venezuela was running large fiscal deficits even in their best times when oil prices were high save for few years with surpluses.

Moreover, one thing that many states that are running out of money resort to is printing more of them which causes inflation. Now moderate inflation is fine but if you are running large deficits that you can’t really hope to repay with future economic output you need to start printing so much that it will eventually lead to very large inflation which will in turn only accelerate collapse. Once money is worthless people start resorting to barter which is less efficient and just exacerbates the problems further.


How can China shield its public from the effects of a trade war? I found an interesting read in the NYTimes today. It read:

  The Chinese government also has much greater control over the economy, allowing it to shield the public from job cuts or factory closings by ordering banks to support industries suffering from American tariffs. It can spread the pain of a trade war while tolerating years of losses from state-run companies that dominate major sectors of the economy.

I could not understand what that meant. Could anybody explain it?

Barry Naughton is an authority on the Chinese economy. He offers evidence on China's government control over the economy in a nice paper called "Is China Socialist?"

China's government controls an unusually large proportion of national income flows. He argues that these income streams have grown dramatically as a share of GDP since the mid-1990s. He shows how the Chinese  government steers  the  economy  because it sees a strong economic performance as a core part of its political legitimacy. China's government has some tools to "shield the public from job cuts or factory closings" because of American tariffs.

Beyond the tools of funding direct government programs and ownership, the Chinese system has two distinctive mechanisms through which it attempts to foster development:

a set of bureaucratic incentives that reward officials for growth (of GDP and revenue);
planning that is centered on the national-level Five-Year Plans that propose a certain trajectory for growth.

Chinese Government's Control over National Income

The above Figure illustrates an expanded concept of government revenues that includes four main components:

budgetary revenues (not including social security);
social insurance  premiums;
land  revenues;
net  income from  state-owned enterprises.

These four components help Naughton providing an index of government control of resources, which tripled as a share of GDP between 1996 and 2013. This index gives an indication of the overall size of the Chinese government. For instance, all land in China is publicly owned: urban land is owned by the state, and housing is "privately owned" only in the sense that households hold long-term leases, typically of 50–70 years. The  financial system  in  particular is overwhelmingly dominated by the state-owned banks, which generate substantial profits.

Summing all four components, the Chinese government had direct or indirect control  of  38%  of  GDP  in  2015.  Overall,  the  Chinese  government  is  large,  well-resourced,  and  potentially  highly  intrusive.  This  is  both a  distinctive  feature  of the Chinese economy in comparative context, and a dramatic change from the China of 20 years ago.