Robust asymmetric information? Bergeman and Morris (2014) explain how the concept of Bayesian Correlated equilibrium contains all the robust predictions in games of incomplete information. In particular, their question is what are the possible Bayesian Nash equilibria of a game where we know each player has at least some information, but can potentially have more information.

Does anyone know of a useful reference to think of refinements of the set of BCE by imposing further assumptions? For example, what if we were willing to assume that one of the players has at least as much information as every other player? What kind of refinements can we expect to maintain the nice linear properties of BCE?

Any thoughts will be greatly appreciated.

It seems to me based on the 2019 JEL review of the same authors that they had published more-or-less what you ask about in a 2015 paper about monopolies and price discrimination (as an application of their BCE theory); see section 5 (and 5.1 in particular) in the 2019 paper. Here the relevant information is the monopolist's knowledge of the consumers valuation. Here are some snippets:

  The set of
  BCE is precisely the set of outcomes that can
  arise with additional information for a given
  basic game and prior information structure. If there are properties that hold for all
  BCE, we have identified predictions that are
  robust to the exact information structure.
  Identifying the best or worst outcome that
  can arise under some information structure
  according to some objective function as criterion is the same as solving an information
  design problem where the designer is maximizing or minimizing that criterion. In this
  section, we will review two such economic
  applications of information design. We will
  highlight the implications of this approach in
  the context of third-degree price discrimination.
  (Bergemann, Brooks, and Morris 2015) [...]

  A classic issue in the economic analysis
  of monopoly is the impact of discriminatory
  pricing on consumer and producer surplus.
  A monopolist engages in third-degree price
  discrimination if he uses additional information about consumer characteristics to offer
  different prices to different segments of the
  aggregate market. Bergemann, Brooks, and
  Morris (2015) characterize what could happen to consumer and producer surplus for all
  possible segmentations of the market.

  One can provide some elementary bounds
  on consumer and producer surplus in any
  market segmentation. First, consumer surplus must be nonnegative as a consequence
  of the participation constraint: a consumer
  will not buy the good at a price above his valuation. Second, the producer must get at least
  the surplus that he could get if there was no
  segmentation and he had no additional information beyond the prior distribution. In this case, an optimal policy is always to offer the
  product with probability one at a given price
  to all buyers. We therefore refer to it as uniform monopoly price, and correspondingly,
  uniform monopoly profit. Third, the sum
  of consumer and producer surplus cannot
  exceed the total social value that is generated by the good, which is willingness-to-pay
  minus unit cost of production. The shaded
  right-angled triangle in figure 5 illustrates
  these three bounds.

  The main result in Bergemann, Brooks,
  and Morris (2015) is that every welfare outcome satisfying these constraints is attainable by some market segmentation. This is
  the entire shaded triangle in figure 5. If the
  monopolist has no information beyond the
  prior distribution of valuations, there will
  be no segmentation. The producer charges
  the optimal monopoly price and gets the
  associated monopoly profit, and consumers
  receive a positive surplus; this is marked by
  point A in figure 5. If the monopolist has
  complete information, then he can charge
  each buyer his true valuation, i.e., engage in
  perfect or first-degree price discrimination;
  this is marked by point B. The point marked
  C is where consumer surplus is maximized;
  the outcome is efficient and the consumer
  gets all the surplus gains over the uniform
  monopoly profit. At the point marked D,
  social surplus is minimized by holding producer surplus down to uniform monopoly
  profits and holding consumer surplus down
  to zero.
  The main result states that we can make
  only very weak predictions about producer
  and consumer surplus. It can be understood
  as the outcome of a set of metaphorical
  information design problems. If an information designer wanted to maximize consumer surplus, she would choose point C.
  If she wanted minimize consumer surplus,
  or producer surplus, or any weighted combination of the two, she could choose point
  D. Any other point on the boundary of the
  triangle is the solution to some maximization
  problem of the information designer defined
  by some preferences over producer and consumer surplus.

  The information design problem has a
  very clear literal interpretation in the case
  where the monopolist knows the consumer’s
  valuation. She can then achieve perfect price
  discrimination at point B. However, giving a
  literal information design interpretation of
  point C is more subtle. We would need to
  identify an information designer who knew
  consumers’ valuations and committed to
  give partial information to the monopolist
  in order to maximize the sum of consumers’ welfare. Importantly, even though the
  disclosure rule is optimal for consumers as
  a group, individual consumers would not
  have an incentive to truthfully report their
  valuations to the information designer, given
  the designer’s disclosure rule, since they
  would want to report themselves to have low
  values.

  [...] One can show
  that any point where the monopolist is
  held down to his uniform monopoly profits with no information beyond the prior
  distribution—including outcomes A, C,
  and D in figure 5—can be achieved with
  the same segmentation. In this segmentation, consumer surplus varies because the
  monopolist is indifferent between charging
  different prices. [They then give a numerical example, which I omit here.]

  [...] Roesler and Szentes (2017) consider a
  related information design problem in which
  a single buyer can design her own information about her value before she is facing a
  monopolist seller. While the analysis of the
  third-degree price discrimination proceeds
  as a one-player application, the arguments
  extend to many-player settings. Bergemann,
  Brooks, and Morris (2017a) pursue the question of how private information may impact
  the pricing behavior in a many-buyer environment. There, we derive results about
  equilibrium behavior in the first-price auction that hold across all common-prior information structures. The results that we obtain
  can be used for a variety of applications, e.g.,
  to partially identify the value distribution in
  settings where the information structure is
  unknown and to make informationally robust
  comparisons of mechanisms.


Does the Samuelson condition assume all the prices for the private goods are the same? Suppose I have two agents with utility functions $U_i$ and $U_j$ and budgets $p_x x + p_g g = m_i$ and $p_y y + p_g g = m_j$.

If I solve a social planner UMP, I will get for my g FOC (after plugging in the other FOCs)

$$ p_x MRS_i + p_y MRS_j = p_g$$

If I assume $p_x = p_y$ then I have after rearrangement

$$MRS_i + MRS_j = MRTS =\frac{p_g}{p_x} $$

But suppose $p_x \neq p_y$. Does the Samuelson condition hold?

As I wrote the question, I noticed the following:

I can see one would write for $n$ agents

$$\sum_{i} p_{x_i}\frac{MU^i_g}{MU^i_{x_j}} = p_g$$

Now we can write that as

$$\frac{MU^i_g}{MU^i_{x_i}} + \sum_{j\neq i} \frac{p_{x_j}}{p_{x_i}} \frac{MU^j_g}{MU^j_{x_j}} = \frac{p_g}{p_{x_i}} $$

I thought it might be helpful to discuss the LS condition in general as it pertains to the LS equilibrium:

A Lind./Sam. equilibrium allows for a unique equilibrium price $q_i, \forall i \in {1,...,n} \equiv N$, the set of agents, for the public good. The clearing condition for the public good price vector, given by $\sum MRS=MRTS$  (as stated in another answer here) is an aggregate condition. Individuals value public goods differently, which is reflected by vector $q$.

To make it a bit more intuitive: If it were necessary that each individual contribute equally to a public good, then our idiosyncratic valuations would prevent some (or maybe many) of us from contributing to a public goods project (because the fixed contribution exceeds our individual, unique valuation for that public goods project). This could cause us to scrap projects that are actually socially desirable. And in easily conceivable circumstances, it can cause us to scrap projects that would be beneficial to every person in our society.

The price vector $q$ does not necessarily comprise distinct prices. However, the question is can it? The answer to that question is, clearly, yes.


Quarterly regression, year-fixed effects I am trying to inspect the heterogeneous effects of a USA-based shock on a panel of countries using quarterly panel data. My variables of interest are the USA-based shock (which has only temporal variation and is mildly serially correlated) and the interaction of this variable with another variable that has cross-sectional and temporal variation too. My question would be whether it makes sense to include year-fixed effects in this regression?
I mainly worry about something like controlling for a downstream variable (subtracting part of the effect of the US shock with the year-fixed effects).

I guess there's no easy answer. It depends on what you think the data generating process is.
Let $y$ be year, $q$ be the quarter and $c$ be the country.
Then $S_{y,q}$ is the USA shock at year $y$ and quarter $q$, $X_{c,y,q}$ is the observable covariates of country $c$, at year $y$ and quarter $q$ and let $Y_{c,y,q}$ be the variable of interest.
From reading your question, your basic regression looks like this:
$$
Y_{c,y,q} = \alpha_0 + \alpha_1 S_{y,q} + \alpha_2 X_{c,y,q} + \alpha_3 (X_{c,y,q} \times S_{y,q}) + \varepsilon_{c,y,q}.
$$
The underlying assumption is here that:
$$
\mathbb{E}(\varepsilon_{c,y,q}|S_{y,q}) = \mathbb{E}(\varepsilon_{c,y,q}|X_{c,y,q}) = 0
$$

A first thing you might be worried about is that $Y_{c,y,q}$ might be (systematically) different depending on the country in addition to what you observe in $X_{c,y,q}$. In this case, you should probably add country fixed effects.
If you think that $Y_{c,y,q}$ might differ according to the year $y$ in addition to what is explained by $S_{y,q}$ and $X_{c,y,q}$ then you should add year fixed effects.
If you think that $Y_{c,y,q}$ might change with $q$ (e.g. seasonality) in addition to $S_{y,q}$ and $X_{c,y,q}$ then you can add quarter fixed effects.
In principle you coud add country$\times$year fixed effects or country$\times$quarter fixed effects if you are worried about a combination of these problems. If you add year$\times$quarter fixed effects you loose identification for $S_{y,q}$.

Which of these options is best will depend on what exactly you are looking at (i.e. what is $Y_{c,y,q}$) and how you think this changes by factors not included in your regression.
If you decide to add year fe, then the identification of the coefficient on the shock $S_{y,q}$ (and the interaction) only relies on intra-year variation in $S_{y,q}$ and $Y_{c,y,q}$. So if you think there is a lot of yearly variation in $Y_{c,t,q}$ explained by $S_{y,q}$ then you will not be able to capture those when using year fixed effects.
There is also the (subtle) issue of how you define the year. For example, you could define a year from "Januari year $x$" to "December year $x$". An alternative could be, for example, to define the year from "April year $x$" to "March year $x +1$". Depending on this choice, your results might vary.


Rule for Number of Strategies in Bayesian Games Is there a general rule for finding the number of strategies (denote as $S$) for each player in a Bayesian game? I think it's related to the number of types (denote as $T$) and the number of actions (denote as $A$). From the few examples I've come across, I've noticed the following:

2 actions, 2 types, 4 strategies
2 actions, 1 type, 2 strategies
3 actions, 1 type, 3 strategies

This could mean that $S=T \times A$ but it could also be $S=A^{T}$.
Any clarification would be appreciated.

Consider a type space $\mathcal T=\{1,2,\dots,T\}$ and an action space $\mathcal A=\{1,\dots,A\}$. With $A=T=2$, you correctly found that there are $S=4$ different pure strategies mapping $\mathcal T \to \mathcal A$. Now fix $A$ and add one more type, so $T=3, A=2$. Type 1 and 2 still have the same number of different actions (4), and the strategy can be completed by two different actions by type 3. That is, $S= 4\cdot2=8$. If you added a fourth type, these $8$ combinations can again be completed to a full strategy with 2 different actions, i.e., $S=16$... and so on such that $S=2^T$.
Next, go back to $A=T=2$, fix $T$ and add actions. You see that type 1 has $A$ actions that can each be paired with $A$ actions by type 2, giving you $S=A^2$.
Combining your insights you find $S=A^T$. In simultaneous-move games, $\mathcal A$ is just the set of simultaneous actions. In more general games, $\mathcal A$ contains all complete plans of actions for each contingency in the game.


What does Eugene Fama mean "the amount of debt that's financed with equity isn't put aside"? I transcribed A Symposium with 2013 American Nobel Laureates at Embassy of Sweden, Washington - YouTube starting at 56:00.
The moderator, AAAS CEO Alan Leshner, claims

Locking up that kind of money would be hard for any

Eugene Fama cuts him off.

Wo Wo Wo. Now you're on weak grounds.

The moderator

In that case, I withdraw the offhand remark.

Fama explains

That's one of the worst fallacies in all this discussion actually.

Someone asks

Would you explain it?

Leshner attempts

Because it's expensive to use money?

Fama explains

It doesn't freeze...What determines the value of something is the assets out of the balance sheet. The amount of debt that's financed with equity, that's not put aside. That's financing assets on the other side. Then you have debt that's also financing assets on the other. So this statement that if they have more equity, they're going to put this aside. Nope. It doesn't happen that way. It gets invested in stuff.

Can someone pls elaborate Fama's answer?

Fama's idea is to look at the level of equity that would have been necessary in the last crisis and multiply by 1.1 and call that a starting point for a level of equity that makes the company safer from insolvency. He phrased it as adding 10 percent.
In Fama's view there will still be risk of insolvency. "You have to watch them because they are very clever at getting around these things."
The actual quote from the other person is "locking up that kind of money...".
Then Fama talks about the balance sheet but he's just making the point that even with regulation the assets as a whole still bear investment risk.  I would add, although he does not say it explicitly, "because they are very clever" he is suggesting it is not practical to consider assets as being locked up, frozen, or set aside.


Have I found the correct Emission Price Let's say that there is a hotel owner $(H)$ and a woodworker $(W)$ working in close proximity to one another.

The woodworker produces $x$ units to sell at market at $p_{x}=6,5$. From the woodworking activities, noise pollution is created that is measured by $a = \frac{1}{2}x$, and to protect workers' hearing $W$ incurs costs of $1$ unit of money per noise pollution unit $a$. Other costs of $W$ are at $\frac{1}{8}x^{2}$.

It follows that $\pi_{W}=6,5x-\frac{1}{8}x^{2}-\frac{1}{2}x$

and $\pi_{H}=7g-\frac{1}{4}g^2-2a$, where $g$ is the number of guests.

Now, I have calculated that the social optimum at which $H,W$ produce are $x = 20$ and $g = 14$

Question: The noise pollution will only be allowed if, for every noise pollution unit $a$ an emissions certificate at price $e$ is purchased. $H$ is given permission to sell these, under the premise that he will sell them at a welfare-maximzing price. Calculate $e$ and determine $\pi_{H}^{\operatorname{new}}$.

My idea:

Looking at $\pi_{W}=6,5x-\frac{1}{8}x^{2}-\frac{1}{2}x-e a=6,5x-\frac{1}{8}x^{2}-\frac{1}{2}x-e \frac{1}{2}x$

$\frac{\partial \pi_{W}}{\partial x}=6-\frac{1}{4}x-\frac{e}{2}=0$ and since social optimum is $x = 20$.

$\Rightarrow e = 2$

But in the solution set, it states $e=1$... What have I done wrong?

To calculate the socially optimal level of $e$, you should look at $\pi_W+\pi_H$ (presumably that's also how you come up with the socially optimal $x$). At $x=20$, $e=1$.

The intuition is that the woodworker's production creates an externality of $-2a=-x$ on the hotel. Since the hotel has to right to ban noise pollution, the woodworker would have to compensate the hotel for its cost from putting up with the noise. At social optimum, the marginal compensation ($e$) should exactly cover the marginal external cost ($-1$). Hence $e=1$ at the social optimum.


Controling the level of hours worked in the multiplicative formulation of KPR KPR preferences are generally given by

$$ \frac{c^{1-\sigma}}{1-\sigma} \cdot v(l)$$

with $l$ being leisure. Let's focus on the case where $\sigma \in (0, 1)$, where we know that $v(l)$ must be increasing and concave. Let total time be $T$, and denote $n$ by working hours. The standard problem then is

$$ \max_{n\in[0, T]} \frac{(wn)^{1-\sigma}}{1-\sigma} \cdot v(T-n) $$

An interior solution requires

$$ v(T-n) = v'(T-n)\frac{n}{1-\sigma} \tag 1$$

One increasing and concave function would be $v(x) = \frac{x^{1-\gamma}}{1-\gamma}$, $\gamma \in (0, 1)$. This yields

$$\frac{T-n}{1-\gamma} = \frac{n}{1-\sigma}$$

or

$$ n = (1-\sigma)\frac{T}{1 - \gamma + 1 - \sigma} $$

Now, generally, we should be able to pick the level of working hours - for each level of IES ($\sigma$). So let's fix $\sigma = 0$, the case of risk-neutrality, and we yield

$$ n = \frac{T}{2 - \gamma} \tag 2$$

As $\gamma \in (0, 1)$, that means that we have no fully control about the level of working hours: We cannot get that $n<0.5$ is an optimal choice with these preferences.

Note that a constant factor in $v(l)$ wouldn't help either, that would just drop out in (1). What am I missing - how can I control the level of working hours better in the multiplicative setup of KPR? That is, where $U = U(c, v(l))$ and not $U = \log c + g(v(l))$.

Continuing on my comment, if both parameters are set strictly higher than unity, then we can get all the range, indicatively:

This is why I asked how important for the work at hand is to constrain them in the $(0,1)$ interval instead.

This won't be the first time when a mathematical functional form has some inherent restrictions that do not allow it to reflect the whole spectrum of possible human behavior.


Is choosing an investment by a bank only due to its regulatory capital charge a form of moral hazard? The main shortcoming of the first Basel Accord (Basel I) was that its capital requirements did not reflect the actual risk of the bank assets.

One way this nonsense influenced the asset choice of banks was: risk being equal, they chose to reduce the availability of credit to some categories of borrowers shifting towards other categories with lower capital charge, at the expense of more socially preferable investments.

Now, suppose a bank has to choose between granting a loan to Company A and another investment, B, both equally risky.

Suppose that, due to the regulation rules, the bank has to put aside 150\$ of capital if it grants the loan to A or 100\$ if it invests in B. Hence, it will invest in B.

The same reasoning is valid for all the A-like companies and B-like investments, therefore it creates a credit crunch towards the former.

According to https://dictionary.cambridge.org/dictionary/english/credit-crunch, credit crunch is defined as:

  economic conditions that make financial
  organizations less willing to lend money,
  often causing serious economic problems

and this is bad for the regulator (which is the Central Bank or a similar State Agency).

Is this behavior by the bank (the agent) with respect to the regulator (the principal) a sort of moral hazard, taking into account that the actual riskiness of the companies is known by the bank but not by the regulator?

Wikipedia:

  In economics, moral hazard occurs when someone increases their exposure to risk when insured.

Investopedia:

  Moral hazard is idea that a party protected in some way from risk will act differently than if they didn't have that protection. We encounter moral hazard every day—tenured professors becoming indifferent lecturers, people with theft insurance being less vigilant about where they park, salaried salespeople taking long breaks, and so on.

Economics Help:

  Moral Hazard is the concept that individuals have incentives to alter their behaviour when their risk or bad-decision making is borne by others.

A moral hazard occurs when acting causes the behavior against which you are acting to increase.

For example, bailing out a bank due to risky loans that the bank took encourages future banks to make riskier loans.  If the loans pan out, they make a lot of money.  If the loans fail, they get a bailout.  A bailout is less harmful than a bankruptcy, so they view it as less of a risk.  The bailout avoids a bankruptcy today, but it puts more companies at risk of bankruptcy tomorrow.

In your example, you have two equally risky companies (or types of companies).  But the regulations regard one as riskier than the other.  So they encourage investment in one investment over the other.  That's the intended goal of the policy.  It's not a moral hazard if it is encouraging the intended behavior.

Now, it may be that the policy is misguided and distorts the market in ways that are not intended.  But that is not a moral hazard.  It would only be a moral hazard if the rule were intended to encourage increased investment in A but due to the way it changed the incentives, it actually increased investment in B.


Real life producer surplus I'd like to ask a question about  producer surplus. Basically I got the concept and how we calculate when a demand or price changes on a graph, but I cannot figure out how I should apply to real life.

I mean, let's say A = 10, B = 20 and Q = 5.

At first the producers accept to sell at the price $10. Is that right?

And the revenue they get would be  $10 \cdot 5 = 50 $   but the producers managed to sell at the price of 20 and the revenue they get is  $ 20 \cdot 5 = 100$.

And the difference between what the producers get and what the producers would ask for is $100 - 50 = 50$.

But when I calculate producer surplus using graphic (ABC), I get  $\frac{(20 -10 ) \cdot 5} { 2 } = 25 $

So I come to different conclusion in real life than when I calculate using graph. Why? Could anyone explain to me please?

I think you misunderstood what the supply line represents. The function takes as its argument the number of units sold. It then returns the lowest price which the supplier of the last unit requires such that he is willing to sell.

Thus, the profit would not be $10*5$. Instead, the last person willing to sell the good receives 0 profit as he is selling at the lowest price he is willing to accept. Counting in discrete units, we would have something like $10+7.5+5+2.5+0=25$ profit. Each additional seller of a unit makes less profit than the previous one.

The flaw in your logic was that the first seller can really only provide a single unit at price 10 and not 5 units. The next unit already costs a bit more in production all the way till the last unit makes its producer just break even.


On the Ms. Exponential vs Ms. Hyperbolic vignette I've come across this little parable purporting to show why exponential discounting is superior to hyperbolic discounting1:

  The greater bowing [of the hyperbolic discount curve] means that if a hyperbolic discounter engaged in trade with someone who used an exponential curve, she'd soon be relieved of her money.  Ms. Exponential could buy Ms. Hyperbolic's winter coat cheaply every spring, for instance, because the distance to the next winter would depress Ms. H's valuation of it more than Ms. E's.  Ms. E could then sell the coat back to Ms. H every fall when the approach of winter sent Ms. H's valuation of it into a high spike.

The figure that the excerpt refers to looks somewhat like the one shown below, the most notable difference being that I've added the legend to indicate which curve is which2, together with the analytical form of the actual discount functions used3.

But it seems to me that the argument, as presented above, is spurious.  It is clear that whose valuation would be more depressed, depends on the time.  Therefore, the exact same argument with the roles of Ms. E and Ms. H reversed, would work for any timepoint between the point at which the curves intersect and the vertical axis.

In fact, for certain choices of coefficients for the hyperbolic and exponential curves, the exponential curve is more depressed than the hyperbolic one for all time points.  For example:

It turns out that the green exponential curve above intersects the hyperbolic curve at only one value of $t$, namely $t = 0$ (i.e. at the time indicated by the vertical axis).  For all $t < 0$, the green exponential curve is strictly below the hyperbolic one.

This means that, if Ms. E's exponential discounting curve were the green one, then Ms. H would be able to quickly immiserate her by applying the strategy described in the excerpt, and this would be true irrespective of the length of the time interval between the buying and the selling back of the winter coat.

In summary, the excerpt's argument for the superiority of exponential discounting over hyperbolic discounting does not hold water, in my opinion.

Now, I realize that the excerpt is not being particularly rigorous, and that there may be a more convincing way to demonstrate the superiority of exponential discounting over hyperbolic discounting.  If so, what is it?  In particular, I want to know the following:

How can someone who uses exponential discounting take financial advantage unilaterally of someone who uses hyperbolic discounting?

(By unilaterally I mean that the strategy is available only to someone who uses exponential discounting vis-à-vis somoneone who uses hyperbolic discounting, and not viceversa.)

1 The reference I have for this passage is to Breakdown of will (2001) by George Ainslie (pp. 30-31).  I don't have the book, though.

2 I have added the labels "hyperbolic" and "exponential", according to my interpretation of what the author means by "greater bowing".  I'm not a native speaker of English, so please correct me if this interpretation is backwards.

3 Note that all these functions have $(-\infty, 0]$ as their domains.  This choice was required in order to match the appearance of the original curves.  Also, I should stress that the functional forms I used for all these curves are my own, chosen so as to approximate the appearance of the original curves.  The text of the excerpt does not give the functional form of the depicted curves.

I believe the money pump works like this:

At $T=0$ borrow a hundred dollars from Henry the hyperbolic discounter for the full time period $t$. The interest rate should be zero because their discount rate over loans of that period is $1$. For simplicity, make it a zero coupon loan, with the payment due at maturity and assume you both agree their is no credit risk. Now step forward one period to $T=\epsilon$. Offer to sell the loan back to Henry. His discount rate is now $\frac{1}{1-\epsilon} < 1$ so the interest rate is lower than what he would charge on a new loan so the price must be above par. Call the price $100 + \psi_1$. Do the sale, tear up the loan, and pocket $\psi_1$. Ask for a new loan of a hundred dollars, again at zero coupon, now at interest rate $\frac{1}{1-\epsilon}$ per period. Step forward another period to $T = 2 \epsilon$. Again, $\frac{1}{1-2\epsilon} < \frac{1}{1-\epsilon}$ so you can sell this obligation too for more than par ($1 + \psi_2$). Do the sale , tear up the loan, and pocket $\psi_2$. Rinse, lather, and repeat until they don't have a hundred bucks to lend you.

Update:
Hopefully this is a simpler example. What you do is in each period buy T (T$\geq$2) period a bond from Henry the Hyperbolic discounter. You also sell back to Henry the bond you purchased in the previous period. You will be willing to do this as long as the time period is short enough that the profit on the transaction is high enough to make up for your own discount rate.

Consider a 2 year bond with the preferences above. The 2 year discount rate is $\frac{1}{3}$ which is less than the 1 year discount rate $\frac{1}{2}$.

Eddy the exponential discounter is willing to lend the cash to Henry because is profits on that loan are high enough to compensate him, even though his rate of time preference for both 1 and 2 year loans is higher than Henry's.


Why do bonds pay back the entire principal at maturity instead of paying it off gradually? Bonds usually pay interest only and the entire principal is paid back at maturity. On the other hand fixed rate retail loans pay back both interest and principal such that at the end no debt is remaining.

To me, the latter seems to be more manageable. The borrower never need to pay back a lump sum of money at the same time.

Why do governments and companies prefer the first structure of payments when borrowing money instead of paying annuity?

They just issue new debt to roll over the principal anyway. Unlike individuals, they do not have a fixed life span.
Trading amortising bonds in the secondary market is a pain, since you then need to keep track of the amortising schedule when pricing them. (This point was discussed in comments. The calculations for amortising bonds in 2018 are straightforward, but not in the era before digital computers, and that is when bond market conventions were developed.) Vanilla bonds with the same maturity and coupon are effectively identical, but this is not true for two amortisers with different maturity dates. Although this does not appear to be an issue now; trading conventions were largely determined in the pre-digital computer age. For example, the principal amount on a bond is used in for default recovery purposes; that is equal to the face value of a bullet bond, but has to be determined for an amortising bond, which is an awkward calculation to be done on the fly without access to digital computing technology.
One added note is that straight amortising bonds have a very low duration relative to a bullet principal payment. Many investors want to get as much duration as possible for a given investment amount.


Fall in share due to litigation Recently, I read a news article stating

  Indiabulls Housing Finance shares plunges on reports of litigation against company

Why do shares plunge when company finds itself in a litigation process? How does litigation affect the profitability of a firm?

Litigation implies that the company may lose money if it loses the lawsuit. The expected loss decreases the expected profits of the firm, and thus negatively affects the share price.


Certainty equivalent and risk aversion parameter given utility function I know this is rather easy but I do not have any example or material to really work from that I could find online.

Consider an agent with a utility index over wealth given by $$v(w) = \frac{w^{1 - \gamma} - 1}{1 - \gamma}, \gamma > 0$$
Say the agent has $10$ dollars in wealth and also owns a lottery that pays $0$ dollars with probability $2/3$ and pays $12$ with probability $1/3$. What is the certainty equivalent value and risk compensation of this lottery to an agent with risk aversion parameter $\gamma = 2$?

So for $\gamma = 2$, we have $$v(w) = \frac{w-1}{w}$$ so the expectd value of the lottery is $4$ dollars. My question is how do we calculate the Certainty equivalent and risk premium. I could not find a good example anywhere. It seems like we get at undefined part in the equation when we calculate $E[v(L)]$ where $L$ is the lottery, thus I don't see how we can find the Certainty equivalent...

For the certainty equivalent and the "risk compensation" (which I am interpreting as probability premium because it's the only thing that intuitively makes sense in this context to me; feel free to correct me), think more intuitively about the concepts. The certainty equivalent is the amount of cold hard cash you'd be indifferent to taking in lieu of the uncertain outcome.

In the good outcome with $\frac{1}{3}$ probability, you'd end up with a wealth of $10 + 12$, and in the the bad state with probability $\frac{2}{3}$ where the lottery does not give you anything, you still end up with wealth of $10$. Thus, we are looking for wealth that I will denote $w^c$ where

$$v(w_c) = \mathbb{E}(v(w)) \implies \frac{w_c - 1}{w_c} = \left(\frac{22-1}{22}\right)\cdot \frac{1}{3} + \left(\frac{10-1}{10}\right) \cdot \frac{2}{3}$$

Solve for $w_c$ and that will be the certainty equivalent. You'll notice that trying to solve this out, we get:

$$\frac{w_c - 1}{w_c} = \frac{101}{110}$$
$$\implies \boxed{w_c = \frac{110}{9} \approx 12.2}$$

As for probability premium, it is the shift in probability towards the better lottery outcome that would be needed to make the expected utility of the new lottery equal to the utility of the expected value of the old lottery.

$$\mathbb{E}_{\text{new}}(v(w)) = v(\mathbb{E}_{\text{old}}(w))$$
$$\implies \left(\frac{1}{3} + \pi\right) \cdot \left(\frac{22-1}{22}\right) + \left(\frac{2}{3} - \pi\right) \cdot \left(\frac{10-1}{10}\right) = \left(\frac{22 \cdot \frac{1}{3} + 10 \cdot \frac{2}{3} -1}{22 \cdot \frac{1}{3} + 10 \cdot \frac{2}{3}}\right)$$
$$\implies \frac{101}{110} + \frac{6}{110} \pi = \frac{13}{14}$$
$$\implies \pi = \frac{8}{770} \approx 0.01$$

(assuming I calculated my fractions correctly)

Edit: I see that the question was asking for a risk premium, not probability premium. Notice that the expected wealth due to the lottery is 14, but the certainty equivalent is 12.222...

The difference between the two is the risk premium.


Is there empirical evidence on usability of Cobb-Douglas production function? I am trying to estimate a simple Cobb-Douglas production function $Y=AL^{\alpha}K^{\beta}$
on US data and get an unrealistic estimate of $\alpha$ and a high p-value for $\beta$.
Structure of regression is as follows:

$\frac 1 Y \frac{\mathrm dY}{\mathrm dt} = \frac 1 A \frac{\mathrm dA}{\mathrm dt} + \alpha \frac 1 L \frac{\mathrm dL}{\mathrm dt}
+ \beta \frac 1 K \frac{\mathrm dK}{\mathrm dt}$

and assuming technological growth constant:

$\text{growth}_Y = a_0 + \alpha\cdot \text{growth}_L + \beta\cdot \text{growth}_K$

I have the following output of linear regression in R:

\begin{array}{lllll}
 &\text{Estimate}\quad & \text{Std. error}\quad & \text{t value} & \mathrm{Pr}(>|t|) \\
\text{(Intercept)}\ & 0.008256 &   0.006070 &  1.360  &  0.186    \\
growth_L  &  1.388552  & 0.283867  & 4.892 & 5.47\mathrm e^{-05}\ ^{***} \\
growth_K   & 0.194165   & 0.255572  & 0.760  &  0.455 \\
\\
R^2 = 58\%
\end{array}

Estimate for the coefficient in front of $\text{growth}_L$ ($\hat\alpha$) seems unrealistically high (1.388552) and estimate for coefficient for $\text{growth}_K$ ($\hat \beta$) has high p-value (0.455).

Before running the regression I excluded outliers (observations outside 2.5% and 97.5% for growth_gdp, growth_L and growth_K).
I also checked correlation between growth_L and growth_K and it is 42% which is not that high to impact stability of coefficients of the regression that much.

Unfortunately I could not find a simple and reproducible analogue of the above analysis.

My questions are the following:

Is there an empirical analysis of simple Cobb-Douglas function producing realistic estimates of coefficients? So that I would understand my key mistakes
If not, what would be the simplest form of production function which could be supported by empirical analysis?

P.S. For the full reproducibility of the analysis below is more info on data and R code used in estimation of the coefficients.
I take data from OECD Economic outlook database

Variables used: GDPV – states for Real GDP, HRS states for hours worked per worker, LF – states for number of workers in Economy, KTPV states for productive capital stock. I calculated L as $LF*HRS$

Full R code and the input data set can be found at pastebin.

The simple answer to why the Cobb-Douglas functional form is used is because it is at least a log-linear approximation to some higher-order production function. That is, suppose you take a functional form that looks like this: $\log Y_t = f(A, K, L)$. Then a linear approximation would look like the Cobb-Douglas production function. (For a small $1\%$ increase in $K$, we get approximately an $\alpha \%$ increase in $Y$.)

One potential source of the strange estimation results you're getting is likely a bias due to the endogeneity of the regressors. Total factor productivity (TFP) in your notation is $A$. It is changing over time. In your regression, it shows up in the error term. Changes in productivity affect the composition of the inputs $L$ and $K$. Thus, $L$ and $K$ are correlated with error term. To see this, solve any typical cost minimization for a firm. $L$ and $K$ will depend on $A$. Also note that the behavior will be different in the short-run vs the long-run.

Hope this helps!

EDIT:

If you're interested, here is a problem set (no solutions available) that walks you through a demonstration of the bias described above. In the end, one potential improvement to the estimation procedure is explored via Monte Carlo simulation. This improvement relies on the availability of panel data of firm input/output data.


Quantity supplied & demanded equation with tax Here's the simple question I can't get my head around :(

QD= 120-P
QS= 2P-10
Tax= 25 euro per unit

How much does the government receive?

The government revenue is going to be 1500 euros.
The tax shifts the supply or the demand curve vertically depending on wether the tax is charged to the consumer or the producer (turns out it doesn't really matter at the end you get the same government revenue).

Here you can find a graph representing the situation if the consumer is charged the tax.

https://www.desmos.com/calculator/8unflceczk

The demand curve shifts from the $Q^{D}=120-P$ (red line) to $Q^{D,tax}=120-(P+25)$ (green line). The supply curve is unchanged (blue line).

The new equilibrium quantity is 60 (instead of 76.667 in the case with no tax), and the revenue is equal to the unit tax times the quantity $25\times60=1500$, which is equal to the area of the orange rectangle.


lowering minimum wage by half, effect on population of Puerto Rico I am reading about a new bill to lower the minimum wage in Puerto Rico from \$7.25 to \$4.25 per hour.  This comes at a time, when both the New York and California have chosen to raise their minimum wages from \$9/hr to \$15/hr.

Are there any theories of how this affects work in a population?

Have any economists chimed in on the topic of minimum wage in general in general?  Can any of it be used to predict what will happen to PR?

Why might policy makers feel a decrease is warranted in one situation while an increase is warranted in another?

Typically, what happens when a minimum wage is relaxed is that a plethora of jobs that were illegal under the previous doctrine become available on the market for workers.

The common metaphor used by its supporters for describing the minimum wage is that a minimum wage is a "price floor" under which wages are not permitted to fall, ostensibly to protect workers.

The accurate metaphor for describing the minimum wage is a price hurdle which each person's productivity must clear in order to sell your product (i.e. your labor)  If your productivity is not valued by a buyer at a higher rate than the strictures placed upon it by legislation, it is illegal for you to have that job.

All other things held equal, reducing the minimum wage will create options for suppliers of cheap labor to actually have their product clear the market rather than having it denied by the State.


Mixed strategies: Nash equilibrium I'm working on a game theory problem.I'm having trouble understanding what the mixed strategy nash equilibrium is exactly in this game.

The game is :Two players have to choose how distribute a piece of land ($size = 1$). Each player (1, 2) send his decision $x_i \in{[0, 1]}$ to an external agent.

If $x_1 +x_2 \leq 1$, each player gain a land portion equal to $x_i +\frac{1-x_1-x_2}{2}$

If $x_1+x_2 > 1$, they end up with nothing.

The first part of the problem is to solve the game in pure strategies. I figured out that the answer of this part is:

Player 1 should pick $1- x_2$, any higher and he gets 0. The game is symmetric so the same hold from player2's perspective. The optimal strategy is the intersection of these two functions.

The second part is to solve the game in mixed strategies (if exist). But I don't know how to aproach this part.

Hint 1: Suppose a mixed strategy NE $(\sigma_1,\sigma_2)$ exists, where $\sigma_i$ is a distribution over $[0,1]$. By the property of MSNE,
$$u_i(x_i,\sigma_j)=u_i(x_i',\sigma_j)$$
for all pure strategies $x_i,x_i'$ in the support of $\sigma_i$.

Hint 2: Note that a segment of $u_i$ is linear in strategies, and thus
$$
x_i+\frac12(1-x_i-\mathbb E[x_j])=x_i'+\frac12(1-x_i'-\mathbb E[x_j])
$$


Does the separation of FinCEN, and The Federal Reserve protect the integrity of a representative democracy? From my understanding, FinCEN is controlled or heavily influenced by the UN.  In addition, The Federal Reserve is not a governmental body, yet it has appointees from the current administration.

I'm concerned that a democratic influence in economics (currency, M1, etc) could remove the "purity of intent" of an election, or the policy resulting from an election.

What have we learned from FinCEN, the IMF, and The Federal Reserve in relation to maintaining the integrity of the democratic voice?

I suspect that if the two are combined, the democratic "wants" will re-prioritize its actions based financial matters, not the democratic consensus.  If taken to an extreme, this lack of "democratic consent" consensus could result in chaos, anarchy, or other frightening outcomes.

What review boards, governance controls, or other systems prevent the academic research of financial systems from contaminating democratic outcomes?

Your understanding is wrong. FinCEN is a bureau of the United States Department of the Treasury. The director reports to the Secretary of the Treasury, who is appointed by the President and confirmed by the Senate.

Further, the Federal Reserve system is also a government entity. It was established under the Federal Reserve Act. The Federal Reserve Board of Governors, which supervises the Federal Reserve Banks, is an independent agency of the federal government. Its members are appointed by the President, with the advice and consent of the Senate. The system's structure was deliberately designed by Congress to grant it independence in its conduct of monetary policy, with the intent of minimizing political interference in monetary policy. However, this independence was granted and is maintained via democratic consensus.


Pareto curve vs Pareto chart I was searching online for some notes on how to draw a Pareto curve on income distribution. That's when I came across Pareto chart which is a bar diagram and is used in quality control.
Are these the same and are both curves drawn using the same method?
Kindly help.

The only relation I see is that they are both named after Vilfredo Pareto. The Pareto curve is related to efficiency, and I see no way of connecting the Pareto chart to the same concept. Since Pareto was an engineer before becoming an economist, it seems most likely to me that its just that two distinct techniques from two different fields were named after him. I suppose you could use a Pareto chart as a tool to make efficient engineering decisions, so they are minimally related.


Why does the yield curve flatten? I find the yield curve for bond rates confusing. For example, the current yield curve for US treasuries is shown below:

The difference between the 10-year bond and the 30-year bond is tiny, just 0.15%. This seems like a negligible premium to receive for assuming an additional 20 years of risk.

Is there a theory that explains this counterintuitive (to me) condition?

There is the market segmentation theory.

The demand on the longer end of the yield curve in theory comes from institutional investors, pension funds, insurance companies, foreign central banks etc. who prefer longer durations.


Why does Samuelson say common stocks are better than bonds and preferred stocks during inflation? I’m reading the first edition of Paul Samuelson’s Economics (1948). In Chapter 6, “Business Organization and Income,” after describing bonds, preferred stocks, and common stocks, he writes:

  To test his understanding of these three forms of securities, the
  reader should make sure that he understands why common stocks
  are better investments in time of inflation than the other two. (p. 124)

I can’t get a grip on the question, in some part because I don’t know what it means and in another part because I don’t know what background assumptions we are supposed to make. Does it mean: if one wants to buy a security from a profitable company during inflation, which should one buy?

Even then I’m not sure how to proceed merely on the assumption that the economy is seeing some generic increase in prices. I’m looking for some help interpreting the logic Samuelson is trying to get at.

This was most likely reference to the Fisher hypothesis. As argued by Engsted & Tanggaard (2002):

classical economic theory, especially the Fisher hypothesis, according to which expected nominal asset returns move one-for-one with expected inflation such that expected real returns are independent of expected inflation. A related implication is that assets which represent claims to real payments, such as common stocks, should offer a hedge against unexpected inflation, while assets which represent claims to nominal payments, such as bonds, should not be expected to offer such hedge possibilities.

Essentially this is because payment on both bonds and preferred stocks are usually fixed nominal terms. For example, bonds pay fixed coupon payment that is predetermined at a time you buy bond.  Preferred stocks also usually stipulate some dividend payment that is fixed. This means that inflation makes the value of the principal as well as the fixed stream of coupon payments/dividends lower in relative terms.
Moreover, as explained here bond prices fall when nominal interest rises and vice versa.
$$  P = \sum^T_{t=1} \frac{C_t}{(1+i)^t}+\frac{M}{(1+i)^T}$$
Where P is the price of the bond, C is the coupon i the interest rate, and M the value at maturity (i.e. the face value). By Fisher equation $i \approx \pi +r$ where $\pi$ is the inflation rate so as inflation rate increases the market value of the bond will be lower. Furthermore, as explained in this investopedia article proffered stocks are very similar to bonds except for legal treatment that is unrelated to this particular discussion. This being said bonds should according to theory still offer hedge against expected inflation because rational person would take any inflation expectation into account before investing into bond (although of course in real world people's expectations might not be completely rational).
A common stocks essentially represent claims to real payments as mentioned above and hence they should offer better hedge against inflation in general as they should also cover the unexpected inflation.
However, few caveats:

The empirical literature actually does not confirm the above result. See for example, . Fama and Schwert, 1977, Gultekin, 1983 or Barnes et al. (1999). The Samuelson's textbook was first published in late 40's even though it is being regularly updated with new edition it might be that this statement was not updated or perhaps Samuelson wanted to teach people about the Fisher hypothesis - that is up to speculation.

Inflation adjusted bonds and floating dividend preferred stock exist, but I think that Samuelson was implicitly talking about the  'standard' bonds and preferred stocks. Although of course we can only speculate about what Samuelson was thinking the passage would not make sense otherwise.


How do increasing tax rate helps control inflation? Also, do the opposite that is lowering tax rate controls deflation?

If the government taxes people but does not spend the money, accumulating surplus, it will decrease aggregate demand. Aggregate demand depends on consumption, which depends on disposable income and taxes reduce disposable income. A decrease in aggregate demand will decrease the price level, reducing inflation or causing deflation, if nothing else happens (see this article by Pettinger).


Worth of collectables - predatory pricing If I traveled around the world, to collectors shops, finding a specific Coin (or other collectible object) something that had a standard value as well (such as a gold coin) and broke it (later melted it) in-front of the shop keeper, so it became known that I had destroyed 1 of the copies of this rare coin/object,

Could I measure the increase of the wealth of the coin to determine IF and WHEN such coins would become 'priceless' so that the final sale of one of the last coin/objects would pay for all costs (purchase & travel to acquire)

Edit for less ambiguity: What Economic parameters would be worth researching to determine the viability of such an endevour?

[Not 100% sure this is Economics, feel free to bump it to a different group, but I couldn't find anything more pertinent than economics]

The way you describe this object (I will call it a coin) it exists in some finite quantity with no reasonable substitute and no new coins can be made. Suppose before you go on the proposed endeavor the world starts with a Pareto efficient allocation of these coins. Additionally, assume the act of destroying a coin has no impact on how much other owning these coins value their collection. This implies a few things:

Each individual who has a coin values the last coin in their collection more than anyone who does not have a coin, otherwise it would be Pareto-improving for someone with a coin to sell it to someone with a higher valuation.
The market-clearing price of coins is the lowest valuation of anyone who owns a coin.
Every individual values their first or an additional coin at something equal to or less than the market clearing price, otherwise they would purchase the coin.
You will never pay less than the market-clearing price for a coin, otherwise someone with a higher valuation would have bought it already.

These facts imply that you can never make money in your endeavor. When you buy a coin you will pay a price equal to the lowest valuation of anyone that already has a coin. But after destroying the coin you haven’t changed the price because the marginal buyer is still the same and has the same valuation.  You can repeat the process and pay a higher price for the next coin, but you still haven’t changed the valuation of the marginal buyer, so the market-clearing price will not change.
This conclusion relies on two assumptions, which may not be true in the real world. If the initial allocation isn’t Pareto efficient, you could make more money simply acting as a broker, buying coins from people with low valuations and selling them to people with higher valuations (since the coins are clearly less valuable after you destroy them). This could even pay for your travel.

It’s more complicated if valuations are impacted by your act of destroying the coins.  In this case, you could make money, but it would be difficult to determine ahead of time.  As a buyer/destroyer of coins you can observe the total number of coins, the number of people who own them, and the market-clearing price of coins. That price tells you nothing of how the preferences of people with valuations higher than the market-clearing price change with each coin you destroy.  For example, if you destroy a coin and the market-clearing price goes up by $100 it may be that everyone increased their valuations or only the marginal buyers increased their valuation. Predicting how prices would change after each coin destruction given what you observe would require assuming the highest-valuation buyers behave similarly to the marginal buyers, which can be a stretch.


Ambiguity on a relation between inflation, interest rates, and central banks When working on inflation, central banks, interest rates etc., I summarized the info in various sources as follows:

When there is not enough money in the economy system, the money in circulation becomes scarce.
This shortage of money increases the value of money.
However, central banks generally do not want money to be over-valued;
for a central bank, negative inflation is almost as dangerous as excessive inflation.
Therefore, the central bank controls interest rates in both ways to keep inflation close to its target rate.

What could be the logical interpretation of the phrase "in both ways" in the above paragraph?

a) Does it refer "(target inflation rate - epsilon, target inflation rate + epsilon)" (sor some plausible epsilon)?
b) Does it refer "(interest rate - epsilon, interest rate + epsilon)" (sor some plausible epsilon)?
c) Does it refer "under-valued money" and "over-valued money"?

Or any other interpratation that explains the phrase "in both ways" better than the above three meaning...

One of the sources reads as follows:

In the 21st century, most economists favor a low and steady rate of inflation. In most countries, central banks or other monetary authorities are tasked with keeping their interbank lending rates at low stable levels, and the target inflation rate of about 2% to 3%. Central banks target a low inflation rate because they believe that high inflation is economically costly because it would create uncertainty about differences in relative prices and about the inflation rate itself. A low positive inflation rate is targeted rather than a zero or negative one because the latter could cause or worsen recessions; low (as opposed to zero or negative) inflation reduces the severity of economic recessions by enabling the labor market to adjust more quickly in a downturn, and reduces the risk that a liquidity trap prevents monetary policy from stabilizing the economy.

I could not find exact source from where I deduced that this "in both ways" phrase.

The sentence:

  Therefore, the central bank controls interest rates in both ways to keep inflation close to its target rate.

does not make sense to me, and I am having a difficult time parsing the three suggested alternatives. (“Money over/under-valued” does not appear to make sense, since the value of money is always 1.)

In most cases, a central bank has a symmetric inflation target (e.g., the Bank of Canada has had a 2% inflation target). It will attempt to raise the inflation rate if it is below 2%, and reduce it if inflation is above 2%. Thus it is concerned with deviations “both ways.”

The inflation target need not be symmetric. E.g., one interpretation of the ECB mandate is to keep inflation below 2%. In which case, policy direction does not work “both ways”, since inflation does not need to be pushed up.

It will raise and lower interest rates (as well as other policy actions) in an attempt to steer inflation. That is, interest rates move “both ways” to hit its target. However, it is unclear why that would be specified.


Why doesn't Dollar exchange rate go down? I am from India and my question is related to conditions based in India which may be applicable to other countries as well.
Dollar value is gradually rising in India. I was trying to understand why. During this COVID season I was expecting the Dollar value to go down base on my below reasons and it didn't happen.
I read about a little bit about it and trying to make connection between the below points to understand why.
India's usual major expense for Dollar in large scale

Crude oil purchase and Defense purchase expense.

India's Rupee(currency) gain

Huge remittance from US and middle east countries
India's forex reserve increase because of increase in foreign remittance
Crude oil prices were down before a few months due to COVID
India's IT service sector performance was excellent and got many US deals worth billions.

What perplexing me are

How can the foreign reserve go high without reducing Dollar exchange rates? The country holding more Dollars and still the exchange rate is high.
When the main expense of Crude oil purchase was down(also demand was down) why didn't it affect the exchange rate?

Dollar is a safe heaven currency, when there is crisis or economic uncertainty like the one we are in now (i.e., Covid) most people start to hoard US dollars.
USD is the world reserve currency and it provides unmatched privilege to USA, any attempt to by pass it in international trade is fatal, you get boomed to ashes like Iraq or Libya.


Microeconomics question I'm given this question. I'm not sure if I'm doing it right. Can any one help?
 Given the following short-run cost function: C=0.04q3 - 0.9q2 + 10q + 5

    And the constant price of the final commodity of $4 for the firm, determine:
a. The best level of output for the firm;
b. The level of profit the firm makes at this level of output;

My answer:
a) Best level of output would be: MR which is 4, since price is 4, perfect competition, MC is the derivative of total cost, which is 0.12q^2-0.18q+10, then equating, 4=0.12q^2-0.18q+10, so q=0.75
b) putting q=0.75 and multiplying price by quantity, level of profit would be 4*0.75

Your first answer would be correct conceptually if this was an interior solution. (The math is incorrect because 2*0.9=1.8 and not 0.18).
However, note that the price falls below the average variable cost. So the firm is better off not producing at all both in the short and long term.
As for your second question: you confuse revenue with profit. Revenue is $p*q$, profit is $p*q-c(q)$
For good measure here are two graphs: one depicts profit for q=0 to 20. Clearly it's negative for the full range
And here's one depicting average variable costs which you can see never falls below 4.


Examples of Factors in the ICAPM The intertemporal capital asset pricing model (ICAPM) is different from the CAPM in that in the ICAPM, utility is conditioned on some set of state variables. The ICAPM results in a multifactor pricing model of the market if investor care about hedging against changing investment opportunities and exposure to these factors. Are there any canonical examples of these factors?

I know that the Fama-French multifactor models (e.g., the three factor model) are often justified on grounds of the ICAPM (or APT -- arbitrage pricing theory). What are the underlying risk factors that justify this model? Are there any other examples of underlying risk factors that show up a lot?

ICAPM Factors

People have chosen different ways to pick factors. Chen, Roll and Ross are a classic example of attempts to find reasonable ICAPM factors. Fama-French factors are often explained as correlated with underlying ICAPM factors. Other researchers have chosen to look for factors without assuming outwardly observable exposures by analyzing returns using factor analysis or principal components.

Explanations of Fama-French

I don't know if there are "commonly accepted" explanations for the Fama French factors. This is not to say that there aren't explanations, there are a lot of them. Just no one seems to agree on which ones are "best". Candidates include both consumption based explanations AND production based models, each of which relates Fama-French factors to underlying economic variables. Cochrane has a nice summary of the performance of both in pricing Fama-French portfolios here.

Additional factors commonly used

Fama and French are now talking about a five-factor asset pricing model which also includes profitability and investment, similar to Novy-Marx's paper and work by Chen, Novy-Marx and Zhang which more directly relates to production asset pricing. Momentum is also a consistent candidate, although it's a real pain to put any kind of explanation to. There are tons of others. This paper lists many of them, as well as calling the significance of some of them into question.


I cannot understand Sobel & Crawford 1982 (cheap talk) I am a master student, currently reading this paper for fun during the break. I got lost during the part $U^S(\bar y, \bar m, b) = \max_{y \in Y} U^S(y,\bar m, b)$ on page 5. I dont understand why they wrote this without any explanation. Then I got lost again during proof of lemma 1. Should I read other paper first before approaching this?${{}}$

$U^S(\bar y,\bar m,b)=\max_{y\in Y}U^S(y,\bar m,b)$ is standard notation that says $\bar y$ is the action (taken by receiver) that would maximize sender's utility given message $\bar m$ and bias parameter $b$. In other words, sender would prefer receiver to choose $\bar y$ when he sends message $\bar m$. Sender's maximized utility is $U^S(\bar y,\bar m,b)$.
For a simpler introduction to Crawford and Sobel, you can read Chapter 18 of Tadelis's Game Theory textbook on cheap talk games.


How can a sovereign debt ratio be high, but debt-servicing ratio be low? I'm quoting this May 22 2020 interview with NYU Stern Prof. Nouriel Roubini.

In other words, you’re saying that because of structural weaknesses in the economy, even modest inflation would be crisis-inducing because key economic actors are dependent on near-zero interest rates?
For the last decade, debt-to-GDP ratios in the U.S. and globally have been rising. And debts were rising for corporations and households as well. But we survived this, because, while debt ratios were high, debt-servicing ratios were low, since we had zero percent policy rates and long rates close to zero — or, in Europe and Japan, negative. But the second the Fed started to hike rates, there was panic.

I never studied accounting and don't understand the embolding. Investopedia defines Debt to Asset ratio = Total debt/Total assets. I can't find the definition of sovereign debt-servicing ratio on Google! The one for family on Investopedia appears irrelevant.
Debt-Service Coverage Ratio $= \dfrac{\text{Revenue $-$ Certain Operating Expenses}}{\text{Total Debt Service also known as  Current debt obligations}}$

This is because the cost of servicing debt depends critically on the interest rate on that debt. When interest payments are low the cost of servicing debt will be lower as well.

A general debt servicing ratio can be expressed following this Fed study as:

$$  DSR = \frac{i_t}{1- (1+i_t)^{-s}} \frac{D_t}{Y_t}$$

While the authors from Fed apply this debt service ratio for households -  the formula is generally valid and can be easily repurposed and applied to government or any other organization. It is not necessary the best way of measuring servicing ratio for government (as explained below), but its a good way to understand the intuition.

You can think of the $D_t/Y_t$ part as debt to GDP ratio. The $i$ is the interest on debt, and $s$ is the average remaining maturity. To see how even with high debt ratios the debt servicing cost ratios can be low lets consider few examples. Lets suppose for the sake of argument the $s$ is always $1$ to simplify calculations. Moreover, lets assume that country has debt-to-GDP ratio of $200\% $ (thats quite high - according to the World Bank data it would be higher than the most recent debt-to-GDP of any country they report - although the WB data are not very recent). Now lets consider 4 scenarios, scenario 1 where interest rate is $5\%$, scenario 2 where interest is $1\%$, scenario 3 where $i$ is $0\%$ and 5 where it is $-0.5\%$.

In scenario 1 the $DSR$ will be: $\frac{0.05}{1- (1+0.05)^{-1}} 2 = 2.1$

in scenario 2 the $DSR$ will be  $\frac{0.01}{1- (1+0.01)^{-1}} 2 = 2.01$

In scenario 3 the $DSR$ will be  $\frac{0}{1-(1)^{-1}} 2  $ which is undefined as it would require you to divide but zero, but the limit of this function from both sides approaches 2 which is the debt to GDP ratio - implying there is no extra cost of servicing the debt beside paying down the principal

In scenario 4 the $DSR$ will be  $\frac{-0.005}{1- (1-0.005)^{-1}} 2= 1.99 $ implying that the servicing debt is now even cheaper than just paying down the principal - you get paid for borrowing.

So as you can see that low interest rates make debt servicing progressively cheaper and the rate is non linear - moreover, the above examples all include average debt to maturity 1 for simplicity but actually allowing for it to be higher the effect would be even stronger due to compounding.

Hence while the debt-to-GDP ratio can be very high, borrowing at low (or even negative) interest rates results in progressively lower debt servicing ratios.

As mentioned above the first formula is not necessary the most appropriate for measuring the servicing costs of government. A common debt servicing ratios applied to sovereigns reported by institutions such as World Bank is servicing cost over export, defined as:

$$X_t = S_{t}/E_{t} $$

And this ratio is more relevant when it comes to the government since as for example Frank and Cline point out:

  the rationale for the use of the debt service ratio [authors reference the above service costs to export ratio] as
  an indicator of a country’s debt servicing capacity is that an increase in
  the debt service ratio indicates increased vulnerability to foreign exchange crises. Any shortfall in foreign exchange earnings or capital imports which is not covered by exchange reserves must be met by reducing imports: since aebt service is a fixed obligation, the higher the
  debt service ratio, the greater is the relative burden on import reduction
  for a given shortfall in foreign exchange.

This being said, I think that the intuition behind the quote can be better understood from that repurposed household debt service cost ratios and caries to this. Moreover, as correctly pointed by @BrianRomanchuck in his +1 answer there is no standard definition for countries with no external debt which is important thing to keep in mind.

However, all above being said from the context of the article I dont think the author had in mind any accounting debt servicing ratio. Based on the context of the article "debt-servicing ratios were low" it seems to me that the author just wanted to say the relative costs of servicing debts are low thanks to the low interest rate which logically also implies that any servicing cost ratio (which will presumably have servicing cost in numerator) will be low. The article is an interview, I think the author just could not think of better way to say it on the spot, I would not read too much into it.


Would a sudden increase in population, increase inflation? Let's say, for the sake of the argument, that the US population grows from 320 millions people to 420 millions overnight, wouldn't that increase inflation?

What if in reaction to this, the monetary mass is left untouched?

Thanks

It would lead to demand pull inflation as the goods in the said economy would not match the demand. But this depends on the time frame and how the producers in the said economy react.
Let me give you an example of immigration. Let's say large numbers of people from a country leave their country for the said country. Ignoring all social issues let's see what would happen. On one hand inflation would increase as the immigrants would cause high demand for goods and services which would drive the prices up. On the other hand, the immigrants would bring in supply of labour which  lead to a drop in real wages and decrease the prices of goods thereby reducing prices. So an increase in population may or may not lead to inflation


Find a separating perfect Bayesian equilibrium Exercise Question 2, Chapter 28, Strategy: An Introduction to Game Theory 3rd Edition by Joel Watson

In part (a) of the question, we have to check if any separating perfect Bayesian equilibrium exists.
Now the solution manual says that there is not any separating perfect Bayesian equilibrium.
My attempt:
The separating strategy profiles are AB’ and BA’.
Let us take AB’. P1 plays B’, then P2 knows that P1 must be L-type. P2 will prefer playing Y, so P1 will not prefer playing B’. No PBE here.
Let us take BA’. P1 plays B then P2 knows that P1 is H-type. P2 prefers playing X, so P1 will not prefer deviating from B since 6 > 4. So, A’B is a separating perfect Bayesian equilibrium here.
What is wrong with my understanding here?

$BA'$ doesn't work because $A'$ is not a best response to $X$, which is a best response to $B$.


What's the economic effect of a country reducing its imports? If a country enacts a program that successfully reduces its imports, eg:

A 'buy local' advertising campaign
A program of training mechanics to maintain older cars, rather than buying new imports
An extensive public transport program that reduces the country's oil imports.

(These programs aren't reducing imports by imposing tarrifs).

What would the effect on that country's economy be?

Under existing trade rules, are any of these examples likely to breach free trade agreements?

On the face of it, a reduce demand for imported goods would correspond with a lower supply of that country's currency, as they need to sell less of their own currency to buy the imports they need. This would raise the price of their currency, and that would in turn reduce demand for the country's exports.

However, I'm wondering I'm missing another side of the equation here - eg, selling currency for international investment.

The short unqualified answer is 'it depends'. Are we talking about a 'small' or a 'big' economy? Is that economy 'wide' open or sealed tight to factor movements? Does it issue its own currency? What's the exchange rate regime it uses? Furthermore, what are its developmental goals, in general? The answers are going to be different, depending on what kind of countries we are talking about eg US vs Belgium, or Singapore, to take two extreme cases.

In general, directing consumers towards domestically produced commodities would increase the demand for local commodities at the expense of imported ones as long as there are local substitutes for foreign imports. It seems plausible to substitute imported beer for domestic wine. The catch is that the domestically produced substitutes should actually be price competitive to foreign alternatives otherwise no amount of 'national pride' can compensate for a price tag eg twice as high (I'm assuming that quotas, tariffs and the like are not sought for).

As far as the 'training program' is concerned, it could be a more all-encompassing venture that extended beyond cars. The 'training' could affect the total of local manufacturing and durables' production. Such a substitution of 'old' for 'new' would probably reduce manufactured imports, industrial machinery imports etc at a significant cost of maintaining and operating an aging infrastructure.

Practically that means higher costs for operation and maintenance and higher prices for the finished products (although that could be offset with appropriate industrial policies-in a hypothetical scenario, using appropriate subsidies etc). It could also mean an increase in imports of spare parts because old equipment tends to break down more often.

The major drawback would be the impact on the distance of the domestic economy from the technological frontier. To the extent that technological innovations are embedded in new equipment and machinery (and tools and parts), 'shutting down' imports implies skewing the age-structure of the domestic capital stock to less productive older technologies (such an occasion might not be necessarily as bad as it sounds as long as the consumption structure is similarly skewed).

Finally, when it comes to overhauling public transport, that is something that would require significant investment. Usually, such 'efficient' technologies are more likely to be 'modern' than 'mature' ones hence this consideration introduces the reservations related with the previous point regarding the age-structure of the domestic capital stock and the distance from the technological frontier. Nevertheless, the significant cost of such an investment could be-in principle-justified by an appropriate investment horizon.

Also, without playing down the costs of oil imports, the price of oil is really not where it used to be and supposedly with the advent of fracking that is going to continue indefinitely. Oil is generally related to energy production, so having a small energy footprint would be more effective in curbing energy needs and related imports.

Where do all that leave us?

Directing resources from tradables to non-tradables will change relative prices. Investing in public transportation infrastructure will have a similar effect of what constitutes productive investment.

A plausible scenario is that resources will be pulled away from the tradables sector (exports) and will be directed to the non-tradables sector (which will now be more profitable that before). That will decrease the output of the tradablers sector. Also, the product mix of exports will be skewed to older technologies (courtesy of the 'training' policy). That would imply decreased price competitiveness in the international market. Such an occasion by itself could imply a deterioration of the trade deficit which is arguably the opposite of the intended result of the proposed reforms. Also, incomes might increase courtesy of the multiplier effect (assume that the non-tradables sector is labor intensive). That could potentially introduce another snag, to the extent that the income elasticity of imports is significantly large. Although, the 'buy local' campaign could potentially be effective in this regard.


Why did the Greek bailouts "fail" whereas the Portuguese bailouts succeeded? While Greece has required several bail-outs and is on the brink of falling back into recession, the Portuguese economy has seemingly recovered.

Why has recovery gone so well in Portugal but failed abysmally in Greece, even though seemingly similar institutions and approaches where taken to both?

(or are we somehow deluded about Portugal's long term recovery and or Greece's problems)

Greece had more debt, less growth and higher budget deficits than Portugal throughout the crisis.

As a result, the Greek bailout should have been even bigger, but this was politically untenable, while the Portuguese bailout proved sufficient in size.

The lower budget deficits in Portugal, for example, also made it easier to comply with the austerity imposed by international organisations.

The Portuguese economy was also better able to adjust by virtue of being more competitive. It was recently ranked 38 on competitiveness vs Greece ranked 81.

http://reports.weforum.org/global-competitiveness-report-2015-2016/competitiveness-rankings/


Are state owned enterprises really inefficient? The typical right wing/free market argument, that leads to privatisation of government assets is that the government assets will be far more efficiently managed when in the hands of profit seeking capitalists, rather than being owned by the government.

Certainly it's fair to say that government departments are inefficient - a department that is directly funded by the government can't go bankrupt, so long as the government keeps funding it.

However, for a SOE the company still needs to stand on its own right, the SOE doesn't receive funding directly from the government.

The SOEs management structure is exactly the same as a privately owned company, except that the government is choosing who the board of directors is.

So the question is, unless the government is electing a board of directors that have different priorities to profit seeking capitalists, how is it that a SOE would be less efficient than a privately owned company?

Is there any research showing that SOEs are less profitable than privately owned companies?

SOE's don't have to perform worse that private enterprises, but they often do.  The reasons are manifold:

Some SOE's are not set up for profit motive, but rather to seed strategic industries for a nation (e.g. Port of Singapore, or Huawei Telecom).
Frequently, state influence at market-oriented is counterproductive because politicians placed in leadership positions are not good business managers (different skillsets), and political contacts can have a detrimental effect on competitiveness (overreliance on government contracts, etc).
Even if the SOE is run by market-selected managers and employees, states often have different shareholder incentives and objectives as owners, so they may not exercise market-driven ownership which leads private firms to attempt maximizing equity value and earnings.

Note that it's not true that SOE's are not funded directly by government.  Many SOE's receive partial funding through government, and many others receive heavily subsidized contracts from governments.

There is quite a lot of research on SOE performance.  Do a search.  For example, McKinsey did a study on Chinese SOE's and concluded that on average they deliver less than half the return on assets as their public counterparts:

http://www.forbes.com/2004/11/04/cx_1104mckinseychina6.html


Autonomous or non-autonomous optimal control system? I have a following system with endogeneous discounting.
$c,k$ and $h(k)$ are consumption, capital and endogeneous discount function based on physical capital. (the properties of this function are not relevant with the question, so I don't write them in order to take less space in this post. The production function is increasing and concave as usual.)

$$\underset{\left\{ c_{t}\right\} }{max}\int_{t=0}^{\infty}\left[u\left(c_{t}\right)\right]e^{-\triangle}dt$$

My state variables are

$$\begin{align}
\dot{k_{t}}=f\left(k_{t}\right)-c_{t}\\
\dot{\triangle}_{t}=\rho + h\left(k_{t}\right)
\end{align}$$

I note $\triangle=\int_{0}^{t} (\rho + h\left(k_{t}\right))dt$

I write the present-value Hamiltonian as

$$\mathcal{H}^{present}=u\left(c\right)e^{-\triangle}+\tilde{\lambda_{1}}\left[f\left(k\right)-c\right]+\tilde{\lambda_{2}}\left[\rho + h\left(k\right)\right]$$

  In this model, my doubt is that if the system is autonomous or not because when I integrate $\dot{\triangle}$, I have $\triangle=
\rho t+ \int_{0}^{t}h\left(k_{t}\right)dt$, which depends explicitly on time $t$. So, evidently, this differential equation is non-autonomous.

Is this system really non-autonomous ?

What I try to do, in order to have an autonomous system is to define variables. Let's say $\lambda_{1}=\tilde{\lambda_{1}}e^{\triangle}$ and $\lambda_{2}=\tilde{\lambda_{2}}e^{\triangle}$. In this way, I write the current-value Hamiltonian ;

$$\mathcal{H}^{current}=u\left(c\right) +\lambda_{1}\left[f\left(k\right)-c\right]+\lambda_{2}\left[\rho + h\left(k\right)\right]$$

I am really stuck at this point. For the moment, the system seems to be autonomous as the Hamiltonian does not depend explicitly on time here but I can not really be sure.

Hints or suggestions are all welcome.

What about rewriting the problem in the following way?

$$\underset{\left\{ c_{t}\right\} }{max}\int_{t=0}^{\infty}\left[u\left(c_{t}\right) e^{y_t}\right]e^{-\rho t}dt$$

with the new state variables defined as

$$\begin{align}
\dot{k_{t}}=f\left(k_{t}\right)-c_{t}\\
\dot{y}_{t}=-h\left(k_{t}\right)
\end{align}$$

given the initial conditions $(k(0),y(0))=(k_0,0)$.


Static wage posting model and indifference to wage levels Suppose a monopsonistic firm has the following simple profit function:
$$\pi (w) = PL(w) - wL(w) $$
where $L(w)$ is the labor supply, $P$ is the constant output price, and it has a linear production technology.

What is a labor supply schedule $L(w)$ that would make the profit function insensitive to the wage?

The profit function is an optimal relation. So it must satisfy the first-order conditions for a maximum:

$$ \text{f.o.c} : w^*: PL' - L - w^*L' =0 \implies L\left[ (P-w^*) \frac {L'}{L}-1\right] = 0$$

In order for this condition to be satisfied no matter what the wage is, it must be the case that, for all wage-levels we have

$$(P-w) \frac {L'}{L}-1 = 0 \;\;\forall w \implies L' = \frac{1}{P-w}L \;\;\forall w$$

Of course this looks exactly like the first-order condition - the critical difference is that it now must hold for all $w$, and so it is not any more a condition that can hold for a specific $w$, but a differential equation in $w$, that falls in the general category $y'_x = f(x)\cdot y$. It can be solved (it is "separable").

I guess you can finish this.


Good Europe focused economics blogs Who can recommend any good blogs or other news sources on economics with a European view. I'm looking for something in the vein of FT, which is already an extremely good source, but I'd like to broaden my intake.

With a European view:

The CEPR VOX EU: an economics blog created by the Centre for Economic Policy Research, which promotes research excellence and policy relevance in European economics. It covers a diverse range of research based analyses on policy and economic issues.
The Economist a global scope with a European perspective.
EconomicsUK: personal website of The Sunday Times' Economics Editor. A perfect blog to learn about European economics.
Alpha.sources: personal website of a Eurozone Economist. Covers macroeconomic issues.
Thomas Piketty's Blog: Economist views on current social and political issues in France, Europe and the world.


Why don't governments mandate a wage decrease in recessions? I have an amateur interest in economics so forgive me if I display my ignorance. From my understanding, both in the Keynesian and monetarist theory of recessions, the recession occurs because aggregate demand decreases and wages are sticky/rigid. Measures like quantitative easing or government stimulus spending try to raise the level of aggregate spending relative to these "sticky" wages. However, what is to prevent a government taking a much more direct method and just mandating a wage cut throughout the whole economy? Wouldn't this be far more effective and far less prone to abuse than fiscal or monetary stimulus?

I will only attempt to give a partial answer, since the full answer is very large. You could possibly create new questions that are narrower to follow up. (My feeling is that this website works best on narrower questions.)

One possibility is that New Keynesian theory is just plain wrong. As a disclaimer, that is my view. However, that is a controversial view.
The next issue are practical problems that standard New Keynesian models ignore.

I am not going to discuss (1) in great length. I think the standard critique of sticky prices (which goes back to Keynes) is that you are cutting nominal demand at the same time. The economy will not return to full employment, partly for reasons I cover in (2).

The problems with trying to cut wages and prices are as follows.

Legal. Does the government have the authority to do so?
Practical. How do we know whether a firm has complied, without having a ministry in charge of price administration? It’s not as if workers will voluntarily run to the government to say that their wages were not cut. We cannot put in place such a ministry during a recession, which typically lasts months.
Ignores the effect of debt. Most people and firms have mortgages and other fixed obligations. Broad-based income cuts would result in a mass default event, which will cause a recession to turn into a full-fledged financial crisis.
The government has just seized control of price setting (which was historically done in the 1970s to control inflation). How does it set prices in order to achieve its objective? How does the government exit?


Leontief Tableau Économique (produit net) I’m doing some practice questions and I found this one about calculating produit net. I know that produit net or surplus is the amount that has to be paid to the landlords, and which becomes available at the start of the whole process all over again.

I also know that 1/2 of the expenditure revenue goes to the productive sector (farmers) and 1/2 goes to the sterile sector. Farmers produce 100% of it, and the sterile sector sends 50% to the farmers. Basically a zig zag table.

My questions: what does the attached table mean (why is there a purchasing industry and a producing industry), and what is the produit net?

Thanks

In this transaction table, farmers produce 5 as a producing industry and consumes 2 (out of 5) as a purchasing industry. This means that they retain 2 as food for themselves and sell the remaining.

A hint: The physiocratic "net product" is equivalent to agricultural rent payment.


Individual Firm and Market Demand Curve In Section 10.2, Monopoly Power, in Pindyck's text on Microeconomics, an example says that suppose $N$ firms produce a particular product and the market demand curve is $P = -aQ + b$. An individual firm is likely to face a demand curve which is more elastic than the market demand curve.

Problem here is, while finding the individual demand curve, we first find $Q = (b-P)/a$, which is the market demand. We divide this by $N$ to get the individual firm's demand curve, given by $Q = (b-P)/Na$

If I compute the elasticity of demand in both cases, which is just equal to $(dQ/dP)(P/Q)$, I get the same value, which is not expected. Is there some mistake in my calculation, for finding the elasticity? Could someone please explain what's going on, and possibly show the exact calculation.

A good check would be that as $N \to \infty$, there is perfect competition and hence perfectly elastic demand (right?)

Thank you!

What you're doing when you calculate $dQ/dP$ is assuming that all forms change their process by $dP$. This is the same as saying that the market price changes by $dP$ and is why you get the same number.

The main difference here is that when the book says price elasticity of demand is higher for an individual firm, it means that, holding the prices of other firms constant, a 1 percent change in a firm's price would result in a greater change in quantity demanded than when all forms change the price.


Dataset on university enrollment? I'm looking for a dataset with stats on tertiary education enrollment in the US, per state, at least a couple decades back. I've searched but cannot seem to find anything. Could someone help me out?

The National Center for Education Statistics , Digest of Education Statistics does have post-secondary education (university and community college) enrollment in the US per state from 1995 to 2017. There are some tables that has the data going back to 1970 but it skips some years so you may want to perform a  some sort of missing data imputation method (i.e. linear interpolation) to impute the middle years,  if you need all the years for your analysis.
However, their website does require some skillful navigation to say the least.
Hopefully,  my instructions will help.  Once you go to this website: https://nces.ed.gov/programs/digest/
On the left pane of your window go to the List of tables and figures section.  There is a  dropdown box below, select a year.
It goes to 1995.  Once you have selected a year go to chapter 3  Postsecondary Education, then select degree-granting institutions, then enrollment.   At this point you will need to find the table that has the state data.
From what I understand of the data that you are looking for, I saw it is in table 195 for most years (1995- 2006) , then its table 190 in 2007,  2008- its table 203  , 2009 - table 219 , going forward for most years the table number that has the state data your looking for seems to change but I am pretty sure its there in chapter 3.
For your research project a recommendation is to pay attention to how the NCES Digest of Education Statistics changes how define their state level enrollment data.   They also have more education data by state if you are curious to see what they have that could support your work.
If you run into trouble with these tables I would recommend to call their office.  The staff list is located here https://nces.ed.gov/ncestaff/stafflist.asp
I hope this helps.


Medium run conclusions from Okun's Law and Expectations-Augmented Philips Curve In Blanchard's Macroeconomics, page 211, 5th edition, the author using the following three mathematical equalities

Okun's law : $u_t-u_{t-1}=-\beta(g_{yt}-\bar{g_y})$, where
$\bar{g_y}$ is defined as the output growth rate when the
unemployment rate is constant, $g_{yt}$ output growth rate from year
t-1 to t.
expectations-augmented Philips curve,
and assuming a functional form  for the aggregate demand relation
that allows to deduce  $g_{yt}=g_{mt}-\pi_t$, where $g_{mt}$ is nominal
money growth rate

makes a reasoning on what happens in the medium-run when the central bank maintains a constant growth rate of nominal money, concluding that although changes in the growth rate of nominal money doesn't change unemployment rate, it does change the inflation rate one-for-one. One of the first assumptions of the reasoning is that in the medium run the unemployment rate is constant. But why can we assume this?

In previous chapters, we had assumed that output would change one-for-one with employment, and that the labour force was constant. Then, when the expected price level were equal to the actual price level, the economy would be in natural output level, and that would imply from previous two assumptions that unemployment rate would also be the natural one. However, in this chapter, when the author was deriving the Okun's law, we explicitly assumed that labour force was no longer constant, and that employment would respond less than one-for-one to output, and that changes in employment are not negatively reflected one-for-one in the unemployment.
Also, in same page 211, it's the author's conclusion that the unemployment rate in the medium-run is the natural unemployment rate. So, we cannot assume what we're trying to conclude...

Therefore, why can we assume that the unemployment rate must be constant in the medium run?

Any help would be appreciated.

At least in the 3d edition, Blanchard writes:

  "In the medium run, the unemployment rate must be constant (my emphasis).
  The unemployment rate cannot be decreasing or increasing forever."

This is an inherent characteristic of the definition of the "medium run": that in it, some core magnitudes are constant. In some models, levels are constant (eg. aggregate consumption, aggregate capital stock, etc). In other models, growth rates are constant, and the model "has a steady-sate in growth rates". This means that levels grow indefinitely of course, but it is not wise (or useful, or meaningful) to project economic concepts to "infinite future".

Now for unemployment, it makes no sense to not be constant in equilibrium (at this simple level of exposition). In more sophisticated models, one could have the unemployment rate approaching asymptotically a constant (zero or not) without ever actually reaching it, but this is usually mathematical gadgetry with not much of economic intuition. (And in futuristic models, one could have unemployment approaching asymptotically unity, as machines and Artificial Intelligence take over all jobs).

Can this constant-by-conception-in-the-medium-run unemployment rate $u^* =const.$ be something else than the "natural rate of unemployment" $u_n$?

The natural rate of unemployment is  defined through the Phillips Curve, as that rate of unemployment at which realized inflation equals expected inflation (see previous chapters). Note that it is not assumed a priori that the natural rate of unemployment will be strictly positive -it could very well be zero. It is actual data that tells us that inflation stabilizes at strictly positive rates of unemployment. Then it is constant when inflation is a constant, and Blanchard discusses why inflation will also be a constant in the medium run. So it obtains that in the medium run $u_t = u_n =const.$.

Since the current unemployment rate stabilizes when inflation becomes constant, which happens in the medium run, the constants must coincide. If $u^* \neq u_n$ inflation will not be constant and we would violate another condition for the characterization of the medium run.

And Blanchard writes correctly

  "In the medium run the unemployment rate must be equal to the
  natural rate of unemployment".

So it does not assume what he wants to prove. The natural rate of unemployment is defined separately and with its own logic to be a constant, from the medium-run unemployment rate which is constant based on other arguments than those related to the natural rate of unemployment.

I hope this helps.


How is wealth created? The production of 'goods and services' and 'innovation' is the usual answer. I feel that doesn't really answer the question.
These things can be traded for wealth but they don't generate new wealth. They essentially take wealth from others and depend on there being wealth already. At least that is how I understand it.

My question is, how is the world so much more well off than it was a century ago? (Please don't mention the industrial revolution)

How did China raise a million people out of poverty without plunging another million into poverty?

How does trade create wealth?

First we need to discuss what wealth is. Is it just the amassment of valubles? In the 16th-18th century, rulers thought so. This notion is called mercantilism. This idea was rejected by Adam Smith in book IV of The Wealth of Nations.

The current meaning of wealth is not the amount you own, but rather how much you can consume (sustainably). Formally, the definition is Total of all assets of an economic unit that generate current income or have the potential to generate future income. This is of course the same amount as the amount that you can sustainably consume. This means that we can measure wealth either as production or as consumption.

Thus, there is not just how much riches you own, but also how much you can create. Also, remember that you cannot consume money. You can only consume goods and services. Amassing riches has little value in itself. It is mainly a way (for an individual or group) to postpone consumption to some point in the future.

Thus, wealth is measured not just by the current riches you own, but also by the ability to create more riches in the future. A man with 100,000 and no income is poorer than a man with no money but with an income of 50,000 a year.

  These things [...] don't generate new wealth.

But they do.

Labor

Let's look at how labor increases wealth by looking at a couple of examples:

Example 1. I work at a farm. The result of my work is some farm produce worth X. For that I am paid Y. The farmer that hired me will receive X-Y.
The net wealth gain for the society is Y + (X-Y), or X.

Example 2. I work as a barber. I charge X for a haircut. The customer gets a haircut worth X. Net wealth gain for the society is X + (X-X), or X. Since the haircut is consumed immediately, the amassed riches don't increase. Note that the customer didn't lose out - to him a haircut was worth at least X or he wouldn't have gotten one. In macroeconomic terms the GDP increases by X and net savings is unaffected.

Trade

Trade increases wealth by transferring a good or a service to someone that values it higher.

Example 1: I buy a used car from a neighbour for X amount of money. I get a car that is worth Y to me (Y>=X, or I wouldn't have bought it). My neighbour gets X for a car that was worth Z to him (Z<=X, or he would have kept the car). The wealth produced is (Y-X) + (X-Z), or Y-Z, which is >= 0 because Z<=X<=Y. In GDP terms the wealth produced is X - X, or 0, because GDP only measures how much is paid.

Example 2: An electronics company imports batteries from China for 10 cents each. They sell the batteries to customers for \$3 each. The wealth increase in GDP terms is \$2:90 per battery. The wealth produced is shared by the electronics company, the shipping company, the store salesman and any others that provide services to the electronics company.

Innovation

Innovation is both the invention of new and the improvement of the existing. Actually, most innovation is small improvements in existing technology or design.

Example: I improve a machine that makes nails so that it can make twice the number of nails in the same time. This means that more nails can be produced (and thus consumed) using less labor.