Statistical models which represent the impact of strict measures vs no strict measures (and less economic impact), enforced due to Covid-19 I have been wondering whether there are statistical models like this one, (which estimated the deaths caused by the virus itself) that estimate the deaths caused by the economic turndown. There is an estimate of how much the pandemic would cost the Israeli health system, and just a general economic analysis of the impact of the pandemic. I was wondering if there are for example models which show the impact of the strict measures(deaths caused by the economic crisis due to lockdown) and just models which show how much more deaths would occur if there was no strict lockdown (and hence the no economic crisis, or at least not as drastic as after complete nationwide lockdowns) than the economic crisis itself.

I am not particularly interested in any specific country, just examples if such exist.

I'm looking for a model that shows the consequences of lockdowns and its economic impacts. ie how much more/fewer people will die from economic collapse rather than the virus given there was no lockdown (but social distancing and mass testing involved).

"The Benefits and Costs of Using Social Distancing to Flatten the Curve for COVID-19", Thunstrom et al.

  We examine the net benefits of social distancing to slow the spread of COVID-19 in the United States. Social distancing saves lives but imposes large costs on society due to reduced economic activity. We use epidemiological and economic forecasting to perform a rapid benefit-cost analysis of controlling the COVID-19 outbreak. Assuming that social distancing measures can substantially reduce contacts among individuals, we find net benefits of about $5.2 trillion in our benchmark case. We examine the magnitude of the critical parameters that might imply negative net benefits, including the value of statistical life and the discount rate. A key unknown factor is the speed of economic recovery with and without social distancing measures in place. A series of robustness checks also highlight the key role of the value of mortality risk reductions and discounting in the analysis and point to a need for effective economic stimulus when the outbreak has passed.

"A Simple Planning Problem for COVID-19 Lockdown" (NBER) Alvarez, Argente, and Lippi

  We study the optimal lockdown policy for a planner who wants to control the fatalities of a pandemic while minimizing the output costs of the lockdown. We use the SIR epidemiology model and a linear economy to formalize the planner's dynamic control problem. The optimal policy depends on the fraction of infected and susceptible in the population. We parametrize the model using data on the COVID19 pandemic and the economic breadth of the lockdown. The quantitative analysis identifies the features that shape the intensity and duration of the optimal lockdown policy. Our baseline parametrization is conditional on a 1% of infected agents at the outbreak, no cure for the disease, and the possibility of testing. The optimal policy prescribes a severe lockdown beginning two weeks after the outbreak, covers 60% of the population after a month, and is gradually withdrawn covering 20% of the population after 3 months. The intensity of the lockdown depends on the gradient of the fatality rate as a function of the infected, and on the assumed value of a statistical life. The absence of testing increases the economic costs of the lockdown, and shortens the duration of the optimal lockdown which ends more abruptly. Welfare under the optimal policy with testing is higher, equivalent to a one-time payment of 2% of GDP.

Also

"The Macroeconomics of Epidemics" by Eichenbaum, Rebelo, and Trabandt. Published in NBER in March when it got NYT coverage; there's an "April update" now. The abstract of that paper isn't very revealing (as it only describes one scenario), but they actually consider several scenarios in the paper, with various exogenous constraints like treatments being found effective or not, vaccines being discovered etc. And then they consider a lockdown sequence optimization problem [in each scenario] as a Ramsey problem; see section 5 in the paper... and then some "exit strategies" from each. (Even that can be formulated as an optimization problem, which they call "smart containment" but it requires knowing the immunity status of everyone--which is a bit unrealistic as they admit.) Teaser figure from the paper (I won't try to explain it here):

"Macroeconomic Dynamics and Reallocation in an Epidemic", (NBER, also in CEPR with somewhat more copyediting) Krueger, Uhlig, Xie

  In this paper we argue that endogenous shifts in private consumption behavior across sectors of the economy can act as a potent mitigation mechanism during an epidemic or when the economy is re-opened after a temporary lockdown. Extending the theoretical framework proposed by Eichenbaum-Rebelo-Trabandt (2020), we distinguish goods by their degree to which they can be consumed at home rather than in a social (and thus possibly contagious) context. We demonstrate that, within the model the "Swedish solution" of letting the epidemic play out without government intervention and allowing agents to shift their sectoral behavior on their own can lead to a substantial mitigation of the economic and human costs of the COVID-19 crisis, avoiding more than 80 [percent] of the decline in output and of number of deaths within one year, compared to a model in which sectors are assumed to be homogeneous. For different parameter configurations that capture the additional social distancing and hygiene activities individuals might engage in voluntarily, we show that infections may decline entirely on their own, simply due to the individually rational re-allocation of economic activity: the curve not only just flattens, it gets reversed.

"Internal and External Effects of Social Distancing in a Pandemic" (NBER) Farboodi, Jarosch, Shimer

  We use a conventional dynamic economic model to integrate individual optimization, equilibrium interactions, and policy analysis into the canonical epidemiological model. Our tractable framework allows us to represent both equilibrium and optimal allocations as a set of differential equations that can jointly be solved with the epidemiological model in a unified fashion. Quantitatively, the laissez-faire equilibrium accounts for the decline in social activity we measure in US micro-data from SafeGraph. Relative to that, we highlight three key features of the optimal policy: it imposes immediate, discontinuous social distancing; it keeps social distancing in place for a long time or until treatment is found; and it is never extremely restrictive, keeping the effective reproduction number mildly above the share of the population susceptible to the disease.

Not strictly about Covid-19, but also recent paper from FRB members (and one MIT faculty):

Correia, Luck and Verner. "Pandemics Depress the Economy, Public Health Interventions Do Not: Evidence from the 1918 Flu",

  what are the economic costs and benefits of non-pharmaceutical interventions (NPI)? Using geographic variation in mortality during the 1918 Flu Pandemic in the U.S., we find that more exposed areas experience a sharp and persistent decline in economic activity. The estimates imply that the pandemic reduced manufacturing output by 18%. The downturn is driven by both supply and demand-side channels. Further, building on findings from the epidemiology literature establishing that NPIs decrease influenza mortality, we use variation in the timing and intensity of NPIs across U.S. cities to study their economic effects. We find that cities that intervened earlier and more aggressively do not perform worse and, if anything, grow faster after the pandemic is over. Our findings thus indicate that NPIs not only lower mortality; they may also mitigate the adverse economic consequences of a pandemic.

A 2nd (recent) paper from a FRB author on the 1918 pandemic, albeit a bit more descriptive: "What Happened to the US Economy During the 1918 Influenza Pandemic? A View Through High-Frequency Data" (and the part most relevant to the question here is left in teaser form in the abstract...)

  Interventions to hinder the contagion were brief (typically a month) and there is some evidence that interventions made a difference for economic outcomes.


Interpreting how graphs of Cobb-Douglas utility functions. How does MRS vary as we vary $\alpha$? Suppose I have the following Cobb-Douglas function $$U(x,y) = x^\alpha y^{1-\alpha} = 1$$ where $\alpha \in [0,1]$.

$$MRS = -\frac{U_x}{U_y} = - \frac{\alpha}{1-\alpha} \frac{y}{x} $$
$$\frac{\partial MRS}{\partial \alpha} = -\frac{1}{(1-\alpha)^2}\frac{y}{x}$$

So suppose I have the following set of graphs:

Here I just picked some values. Red is $\alpha = \frac{1}{4}$, blue is $\alpha = \frac{1}{2}$, black is $\alpha = \frac{3}{4}$

I understand how the steepness and flatness of the different curves change as I vary $\alpha$. But I am confused as to what $\frac{\partial MRS}{\partial \alpha} $ tells me about the graph. In particular, $\frac{\partial MRS}{\partial \alpha} $ is dependent on $\alpha$. So even though I know $\frac{\partial MRS}{\partial \alpha}$ tells me how much $MRS$ changes as I change alpha....changing $\alpha$ changes $\frac{\partial MRS}{\partial \alpha}$...so I am very confused!

My Question

What is $\frac{\partial MRS}{\partial \alpha}$ telling me about the graph? Since $\frac{\partial MRS}{\partial \alpha}$ is dependent on $\alpha$, how does this affect things?

If $\alpha$ rises, the utility puts more weights to the $x$. Then you must give up more $x$ for one $y$ (for the same utility). Your MRS, for a given $y$, increases in absolute value. Graphically:

If you set $y$ and $x$, the slope is lower for higher $\alpha$ (be careful to only change one thing at a time).

Concerning your "loop" problem, look at the function $1/x$, the first derivative is also a function of $x$, like the 2nd and so on. What matter is the value at one particular x.


Dealing with Missing Data when Testing the CAPM Question
How should I deal with missing data when trying to test the CAPM? Specifically, there are some stocks that are newly listed and/or delisted at any time. I don't want to exclude assets for which I don't have complete data because this would create a kind of survivor bias.  I know that CRSP provides delisting returns that should, but how do I manage the missing data in practice? For example, in the unconstrained model, the procedure looks like this:

(More details about the procedure are given below.) Now, if I wanted to take a bunch of random stocks at some point in time and look at them over some time period, what should I do with the values ($Z_it$) for these stocks that aren't listed at time $t$. Should I use the de-listing returns where appropriate and then fill in zeros everywhere else? But this would do weird things to the beta of the stock. Should I try to constrain the beta (the factor loadings) of the stocks to be zero in all the places where the stock is unlisted? This would require me to change the model (requiring a model that somehow allows for time varying factor loadings). How do people usually handle this problem? Is there an easy way (even if it is slightly more incorrect)?
Some Detail about the Estimation Procedure
For concreteness, suppose I wanted to test the CAPM using the time series regression framework outlined in chapter 6 of Campbell, Lo, and MacKinley (The Econometrics of Financial Markets). Some of the assumptions are listed in this image:

Easiest fix: if you're worried about it you should value weight your results. This is suggest by, for instance, Kothari, Shanken and Sloan (1995). Firms that are delisted tend to have extremely small market cap, so value weighting gives them very little impact on summary statistics. Delisted returns should also be used, although I'm not sure how much impact they'll have. I've seen the delisted return stuck into the month after a stock ceases to be traded.

In finding $\beta$'s, I tend to see the regression used only on those dates for which the stock return is observed. The correction really comes in value weighting summary statistics afterwards. Whether all this is "correct" or just the practice I've seen is not something I'm sure about.

Edit: here's a different perspective.


What is this economic theory? Cost of investment vs production accounting for time? I know there has got to be a standard set of theories or formulas to chart this but I don't know how to search for it. Other than a great place like this. :)

I'm a software developer and not an economist but I need to analyze data of factories that have simple defined expense to set up, each has a specified output and a length of time to build.

While a larger factory might have the lowest cost per unit of production and therefore be the best bang the buck (assuming the setup cost was zero), the actual setup cost might be so large that it would take a long time to actually build the factory. It is actually more economical in the long run to build less costly and lower performing factories because in the long run you will have produced more and aquire the cost of the larger factory faster.

What I am attempting to build is a formula/program that will advise on the next most profitable move and the required time to get there.

If you haven't guessed this is actually to be tested an ran on a game scenario. However, I have many other applications and thought this would be a good start.

I hope that makes sense. The cost of production, the output and such are all intentionally simplistic. There's no need to account for outside/variable factors in this particular scenario.

If you can lead me to a theory/concept, perhaps a link or two or examples of this type of analysis given as set of inputs that would be great!

Thanks!

Sorry I don't have enough reputation yet in the Economics community to comment. But the answer provided by @Alecos Papadopoulos can be illustrated further. Please feel free to move my "answer" to comments of his answer.

With the assumption of only $F' > 0$ and $F > 0$ and $h' > 0$, then there is a simple case where the minimization problem has no solution. Consider when $F(q) = \sqrt{q}$ and $h(x) = x$. Then the objective function becomes $1 / \sqrt{q} - \sqrt{q} - c$, and if you're considering for any $q > 0$, then there is no global minimizer for this (i.e. globally decreasing for all $q > 0$ and hence the minimizer is $q \to \infty$. Thus, the FOC you'd derived is not true. Indeed, the condition you'd provided would render as $4 \le 1$ --- clearly impossible.

In general, an increasing function $F$ over a linear function (i.e. say $F(x) / x$ in your case) will not necessarily be convex. And furthermore, when you subtract off the form $h \circ F$, the resulting $-h \circ F$ could again depend on the form of $F$ (which may not have any particular geometric form you could exploit). I think what would fix this model is a form such that $F(q) / q$ is convex in $q$ and $h \circ F$ is concave, so that $-h \circ F$ is convex, then the whole problem will be convex.


Prove that a continuous $\succsim$ is quasilinear This question is closely related to Mas-colell, Whinston, Green: Microeconomic Theory, Question 3.C.5b

  Let $\succsim$ be a strictly monotone, continuous, and rational
  preference relation on $(-\infty, \infty)\times \mathbb{R}^{L-1}_{+}$.
  Furthermore, suppose $\succsim$ is quasilinear in good $L$. Let us
  write $x \in X$ as $x=(y,x_{L})$ where $y \in  \mathbb{R}^{L-1}_{+}$.

  It can be shown that if $v(y,x_{L})$ is a utility function that represents $\succsim$, then there
  is a unique $x_{L}(y) \in \mathbb{R}$ such that  $v(y,x_{L}(y))=0$.

  Let $\phi(y)=-x_{L}(y)$ and show the utility function of the form
  $u(x) = x_{L} + \phi(y)$ represents $\succsim$.

Proof:

To show that $u(x)$ represents $\succsim$ I need to show that for every $x,x' \in X$, $x'\succsim x \iff u(x') \geq u(x)$.

However, I have found an example that may not be satisfied: suppose that $x$ and $x'$ are such that $x=(y,x_{L})$ and $x'=(y',x'_{L})$, with $x\precsim x'$, $(y,z_{L}) \precsim (y',z_{L})$  $\forall z_{L}$ and $(z,x'_{L}) \precsim (z,x_{L})$  $\forall z$.

These preferences imply:

$(y,x_{L}') \precsim (y,x_{L}) \precsim (y',x_{L}') \precsim (y',x_{L})$

To show that $u(x)$ is consistent with this I need to show that this preference implies:

$u(y, x_{L}') \leq u(y,x_{L}) \leq u(y',x_{L}') \leq u(y',x_{L})$

and not

$u(y, x_{L}') \leq u(y',x_{L}') <  u(y,x_{L}) \leq u(y',x_{L})$

However I can find no reason why 2. presents any sort of contradiction! I have been thinking about this for two days, and am sure by now I am making some logical errors. Either the example I have come up with is not valid, or it must imply some sort of contradiction!  Any comments will help. And please hints only, no full solutions.

First off it seems to me you are proceeding in a manner more complicated than necessary. (Perhaps this is intentional because you wish to face a harder exercise.) Since it is given that $v(x)$ represents $\succsim$ you only have to show
$$
\forall x,x' \in X: v(x') \geq v(x) \iff u(x') \geq u(x).
$$
I think this would be a lot simpler than what you are currently doing.

On to your question:
 The function $u(x)$ is very well defined, as
$$
u(y,x_{L}) =  x_{L} + \phi(y) = x_{L} - x_L(y)
$$
and we know that $v(y,x_L(y)) = 0$ describes the indifference curves of $\succsim$. The conditions you describe would violate this assumption because from
$$
(y,x_{L}) \precsim (y',x_{L}')
$$
it follows that
$$
v(y,x_{L}) \leq v(y',x_{L}').
$$
We can assume $v(y,x_{L}) = 0$, this is an affine transformation of any $v(y,x_{L})$. So $x_L(y) = x_{L}$.
 (I am not crazy about the notation, feel free to edit my post as long as it remains consistent with the question.)

 Then we also have $0 \leq v(y',x_{L}')$, and because of monotonicity this means
$x_L(y') < x_{L}'$.
 Then
$$
u(y',x_{L}') < u(y,x_{L})
$$
cannot hold as
$$
u(y,x_{L}) = x_{L} + \phi(y) = x_{L} - x_{L}(y) = 0
$$
and
$$
u(y',x_{L}') = x_{L}' + \phi(y') = x_{L}' - x_{L}(y') > 0,
$$
because of what we have shown earlier, $x_L(y') < x_{L}'$.


Analyzing Farm Bureau's claim that milk prices would double at the retail level if all the illegals were deported A 2015 article on the Farm Bureau's website states:

  Half of all workers on U.S. dairy farms are immigrants, and the damage
  from losing those workers would extend far beyond the farms, nearly
  doubling retail milk prices and costing the total U.S. economy more
  than $32 billion, according to a new report commissioned by the
  National Milk Producers Federation.

According to an analysis at Progressive Dairy, out of the 3.40 a consumer pays for a gallon of milk at the supermarket, 1.53 goes to the farmer. In terms of hundredweight, the numbers are 39.40 cwt and 17.85 cwt.

According to a survey of dairy farms in the Northeast, the labor costs of running a dairy farm in terms of cost/hundredweight were [also] about 3.40 (with variations by herd size, etc).

Various sources put the hourly wage for illegals on dairy farms between 10.00 and 14.00 dollars per hour. Let's assume a dairy farmer hires only illegals and he pays them 12.00 per hour. Then they are all deported. In order to attract quality legal workers to take their places, lets say he needs to pay 24.00 per hour and that the full amount of that cost is passed directly to the consumer.

Since 24.00 is twice 12.00, we can multiply the labor share of a dairy farm's expenses per hundredweight by 2 which equals 6.80 and then add the increase into the farmer's share of the consumer's dollar / hundredweight, or 17.85 + 3.40 = 21.25.

A gallon of milk weighs about 8.6 pounds which means there are about 11.63 gal of milk in a hundredweight. So we take the 3.40 new labor costs and divide between the 11.63, which is a .29 per gallon increase.

So, the next time you bought a gallon of milk it would be 3.69, up from 3.40--a very far cry from "nearly doubling".

Question: How can we analyze the veracity of the claim that milk prices would double at the retail level if all the illegals were deported?

The article was a press release from the "National Milk Producers Federation", which is located in the heart of dairy country, Arlington, VA.

It is worth noting that OP's original question before I edited it asked, "why would economists lie to us?" This already leaves a poor taste in my mouth; such a question is loaded enough as it is, only good for picking fights. The author stated at the bottom of the Progressive Dairy article is a lawyer, not an economist, and seems to be the basis for some of your figures in your analysis. The article from the Texas A&M AgriLife study cited by the Farm Bureau/NMPF did have economists writing on the topic, which I'll discuss briefly later.

Related to denesp's comment on cost of labor share, consider the firm's cost of milk production:

$$p_L q_L + \sum^n_{i = 1} p_iq_i = C$$

The cost $C$ is made up of the cost of labor (price of labor times quantity of labor) plus the cost of all other factors of production. The labor share of cost that was mentioned by OP would be:

$$\frac{p_L q_L}{C} \equiv \boxed{s_L = \frac{p_L q_L}{p_L q_L + \sum^n_{i = 1} p_iq_i}}$$

Suppose as in the hypothetical that the cost of labor doubles. OP argues that then,

  we can multiply the labor share of a dairy farm's expenses per hundredweight by 2

but this is clearly not true from a mathematical standpoint.

$$2s_L \neq \frac{(2p_L) q_L}{(2p_L) q_L + \sum^n_{i = 1} p_iq_i}$$

More than this, it also assumes there are no cross-price effects. That is, if the price of one good changes, it will not change the quantity demanded of other factors of production. If there is any sort of substitutability OR complementarity between labor and any other factor of production, this cannot hold. Empirically, low-skill/blue-collar labor is a complement to high skill labor and a substitute with capital.

All of this walks around a bigger issue. The article in question makes a claim about the effect of disemployment on doubling milk prices. It does not say that it will come about by doubling labor prices, so the argument posed above is just a strawman. That is, it may very well be that doubling labor price would not double the final price of milk, but that is not what the article is arguing.

That said, I don't particularly like the analysis done in the Texas A&M AgriLife study cited either. Ultimately, it has no inference/causal modelling and is just a survey with some summary statistics, with a lot of questionable assumptions.  There is like one price elasticity in that whole analysis as I could see, and its use was not compelling.

The lazy way to interpret this is to just say the methods of the study are bad and that its conclusions have no value and only serve to mislead the public. I don't think this is particularly true either. Private sector market analysis is definitely in some ways less stringent than publishing in, say, an economics journal however.

So what can we do?

The long, boring, rigorous way to estimate the impact of a large shock to the labor supply is to look at labor demand and labor supply simultaneously.

Consider an extremely simple set of linear estimations:

$$\ln(L_s) = \alpha_s \ln(w) + \vec{\beta}_s \vec{Z} + \epsilon_s$$
$$\ln(L_d) = \alpha_d \ln(w) + \vec{\beta}_d \vec{X} + \epsilon_l$$

Where $Z$ is a vector of control variables/supply shifters (e.g. non-labor income), and $X$ is the same but for demand. Notice that labor, $L$ and wage, $w$ are endogenously determined, which nudges us towards the use of IV estimation, rather than the typical OLS.

Labor Demand:

From here you'd have to think about what kind of functional form production should take: $Y = f(K, L, \cdots)$, where $K$ is capital, and you can put in some other factors if you want (legal labor vs illegal labor perhaps?), and derive conditional factor demands, which you can plug into the equation for cost which gets some $C(w, r, \cdots, Y)$, with $r$ representing the rental rate of capital.

Applying Shephard's Lemma, you can then derive the elasticities of substitution between two different factors of production, which are used to calculate the cost shares of of each production factor, and eventually, we can then find the own-price elasticity of the factors, used to help estimate $\alpha_d$.

Labor Supply:

Similar line of thought, but with a specification of utility and working with Frisch elasticities.

Plugging in the data (number of laborers, capital stock on farms, etc.) could prove difficult or impossible without existing data of course.

This is obviously a very rough sketch for an empirical framework for analyzing labor supply, but it is a foundation for analyzing all sorts of shocks to the labor supply. For a more detailed analysis, you can refer to Cahuc, Carcillo, and Zylberberg and their first few chapters on labor supply and labor demand.

Sometimes in the economic literature, undertaking a more detailed study like this requires a lot of funding and time, with in mind particularly the hassle of data. People want practical policy answers in the short run, particularly in the private sector. With limited resources, sometimes studies like the ones you've looked at provide "second-best results" and that is the analysis we have to work with. The productive, honest thing to do with studies that take on partisan issues is to think about how to feasibly improve them and ask specifically about how to look at the research being done on the topic.

There are plenty of voices accusing all manner of partisan research/analysis as misleading, and still plenty polemics out there who would waste their time writing polemics. It is not for this site.


What do supply-demand curves really look like? In my basic high school economics course, we've always used supply-demand curves that are lines to simplify calculations. In real markets for real goods, what do the supply and demand curves look like? From a mathematical perspective, what would be the concavity, asymptotes, and intercepts?

I would imagine the quantity demanded would tend to zero as the price increased to infinity and the quantity demanded would grow very large as the price approached zero, but that is just what my intuition tells me.

You sometimes find textbooks drawing the supply and demand curves as concave upwards, as such:

The straight-line supply and demand curves can be thought of as a magnification of this graph, where the two intersect. Thus, the units on the axes would give you a clue as to how high up the graph is being drawn, or how far to the right (if the units start at a number other than 0 or skip an interval). This shows you why they are indeed called 'curves', even when they are sometimes straight lines.
Supply and demand curves are drawn using straight lines for simplicity. For example, two straight-line equations may be given, from which it is relatively simple to calculate the point of intersection.
In the real world
Supply and demand curves are an approximation of what happens in real life. The curves are a simplified model which show the general trend in the two functions. In reality, supply and demand curves are approximated using data that is collected over many years, with many short-term variables affecting the results, if the curves are even drawn up at all (the curves are more a theoretical model than a calculative method).
Economic factors which affect supply and demand

Price elasticity at different points of output affect the gradient of the curve at those points. A higher price elasticity results in a shallower gradient and vice versa. A unit price elasticity at all points on a demand curve will result in a hyperbola. In that case, the asymptotes of the demand curve are the x and y axis. FYI, the asymptotes of a demand curve will always be the x and y axis if the graph is drawn using this definition of price elasticities, but different elasticities will change the compression or expansion of the graph either vertically or horizontally so that it becomes not a hyperbola, but a hyperbolic graph.
The supply curve for a firm (with any level of competition in the market) is the marginal cost curve faced by that firm. The marginal cost curve looks like this:

However, due to the firm's variable costs, output is always greater than that at the turning point of the marginal cost curve.

For interest, in the special case of an oligopoly, there exists a kinked demand curve faced by an individual firm, as shown:


Effect of price on utility A consumer has an endowment vector $w$; at prices $p$ his demand for the first good exceeds his endowment; $x_1^+(p; pw)>w_1$ then a small increase of $p_1$ will lower his utility.
I was discussing this with a friend and he believes that it's based on the walras law. Prices go up, demand goes down and converges to walras law equilibrium in order to find the $z(p)$ vector which makes excess demand 0, price goes up, excess demand goes down, walras eq. will be satisfied  and this is optimum so the utility cannot decrease. (something along those lines as far as I remember)
But I'm more concerned that it has to do with the Income and Substitution effect more than the Walras law. But we both agree that it won't lower the utility level. However, I'm kind of stuck on the math proof behind it.

That was tricky. The idea is as follows: First, under standard assumptions, demand is continuous. If you change prices a little bit, demand will not change a lot. In particular, if your excess demand for the first good was initially strictly positive, it will still be strictly positive for small changes in price. Now, the new bundle after the price was slightly raised was affordable at the old price with some money left to spare on more stuff. So the old bundle must be at least as good as the new bundle with some additional stuff on top and, therefore, be better than the new bundle.
Let's make this formal: So let $p=(p_1,p_2,\ldots,p_n)$ and $p'=(p_1+\epsilon,p_2,\ldots,p_n)$ with $\epsilon>0$
and we assume that $x_1^*(p,pw)>w_1$ and $x_1^*(p',p'w)>w_1$.
Let $x=(x_1,\ldots,x_n)=x^*(p',p'w)$. We first show that
$px<pw.$ Indeed,
$$p'x=(p_1+\epsilon)x_1+ p_2 x_2+\cdots+p_nx_n\leq(p_1+\epsilon)w_1+p_2 w_2+\cdots+p_nw_n.$$
$$(p_1+\epsilon)(x_1-w_1)+ p_2 x_2+\cdots+p_nx_n\leq p_2w_2+\cdots+p_nw_n.$$
$$p_1(x_1-w_1)+\epsilon(x_1-w_1)+ p_2 x_2+\cdots+p_nx_n\leq p_2w_2+\cdots+p_nw_n.$$
Therefore,
$$px=p_1x_1+ p_2 x_2+\cdots+p_nx_n\leq p_1 w_1+p_2w_2+\cdots+p_nw_n-\epsilon~\underbrace{(x_1-w_1)}_{>0}<pw.$$
Now, we need an assumption that guarantees that a consumer is better off if they spend all their income. Then we know that the consumer is better off under $x^*(p,pw)$ in which they would spend their whole income of $pw$ instead of choosing the bundle $x$, which costs only $pw-\epsilon(x_1-w_1)$. An assumption that guarantees it is optimal to spend the whole income is exactly what guarantees Walras' law.


Is there a universal type space involving infinite players? Having just dabbled in 7.1of rationality in extensive games by Andres Perea, I got an impression all constructions of universal type space are restricted to finite players. What's the obstacle to extend it to countably infinite players? For example, is it trivial to extend them to cover OLG games in which each stage game is only played by finite players?

Countably infinite is easy to extend to, no obstacles. You can use results by Moss and Viglizzo (2006). I will also shamelessly promote my own work Universal type structures with unawareness that mathematically treats each of (possibly countably infinitely many) awareness levels as a player.


Walrasian Equilibrium intuition given prices and some initial allocation Suppose we have two agents who are each assigned some initial allocation of two different goods, where the prices of each good are given. Also, suppose the utility functions for each agent are weakly concave and strictly increasing.

If, after receiving their allocations, no trades occur between the two agents, can we infer that this initial allocation represents a competitive equilibrium (CE)?

My intuition says that it may not be a CE, because perhaps agent 1 has an optimal allocation, but maybe agent 2 wishes that he could trade with agent 1 to change his (agent 2's) allocation. Although this would not be a competitive equilibrium, this scenario would still be Pareto efficient. Is my analysis correct?

The "trick" of this question is that the fact that agents do not want to trade at the given prices does not mean the allocation is Pareto. The only thing you know is that if there is an allocation that is not a CE, there exists a vector of prices at which agents want to trade. Let me give an example:

You have 2 apples and I have 2 bananas. I'm willing to give you half a banana for an apple and you are willing to exchange a whole apple for a bite of a banana. Clearly, the initial allocation is not Pareto Efficient, nor a CE since it is profitable to trade and trade will occur if prices are somewhere between a bite of a banana and half a banana for an apple. The problem, however, assumes that prices are given. So in this toy example, if the price of an apple is set to one banana, there will be no trade (since I won't be willing to accept the prices).

From the lack of trades, it cannot be assumed that you are in a CE since the prices are not allowed to adjust to allow for mutually beneficial trading.


Monopolist engaging in international trade A  monopolist faces a demand curve given by $P=60-2Q$ and has total costs given by $TC=Q^2$. Now suppose that the country in which this monopolist is located decides to engage in international trade. The world price of the product produced by the monopolist is $10. What is the firm's profit-maximizing output level?

My attempt:

$P=60-2Q$

$P=10\implies 10=60-2Q\implies 2Q=50\implies Q=25$

Unfortunately, this isn't the right answer. How do I solve this problem?

Because the monopolist is only a monopolist in its own country, it is basically in perfect competition in the international market and cannot influence the world price. Therefore, it will have to use the condition that price is equal to marginal cost. His marginal cost (MC) is the first derivative of total cost, i.e. TC'=2Q=MC. If MC=P, then 2Q=10. Therefore, Q=5.

Is that the correct answer from your solutions?


Nash Equilibria in Target Destroying-Guarding Game Army A has a single plane which can strike one of three possible targets, A, B and C. Army B has one anti-aircraft gun that can be assigned to one of the three targets to guard it. The value of each target, $v_k$ is $v_A>v_B>v_C>1$. Army A can destroy the target only when it is unguarded and A attacks. Army A wishes to maximize the damage whilst Army B wishes to minimize the damage. Find all Nash Equilibria.

I tried formulating the game into a $3*3$ payoff matrix game, by giving Army A $0$ if the target it aimed at was guarded and the value of the target if it was unguarded.
Similarly, for payoffs of Army 2, I assigned $-v_k$ added to the valuations of other two target which were not destroyed, if Army A succeeded in destroying the target and $v_A+v_B+v_C$ if Army A failed to destroy any target, i.e., by aiming at a guarded post.
Given this setup, I found that there was no Pure Strategy Nash Equilibria in the game. I do not know how to proceed with the Mixed Strategy Nash Equilibria, if any.

I'm very doubtful of the approach that I tried to employ. I would really appreciate a little help!

Excuse the formatting for the game's normal form. This is a zero sum game, so I've written only the payoffs for the attacker:

$$\begin{pmatrix}
    A|D & a & b & c\\
\hline
a & 0 & v_{A} & v_{A}\\
b & v_{B} & 0 & v_{B}\\
c & v_{C} & v_{C} & 0
\end{pmatrix}$$

Evidently, since $v_{A} > v_{B} > v_{C}$, there may be payoffs such that there exists some $\lambda$ such that $(1-\lambda)v_{B} > v_{C}$ and $\lambda v_{A} > v_{C}$.

First, suppose that the parameters are such that there exists such a $\lambda$ e.g. $v_{A} = 20$, $v_{B} = 10$ and $v_{C} = 1$. In this case, $c$ is strictly dominated and so we can eliminate $c$ from the support of the attacker's mixed strategy, and hence we may also eliminate $c$ from the support of the defender's mixed strategy. Write the new matrix as

$$\begin{pmatrix}
    A|D & a & b\\
\hline
a & 0 & v_{A}\\
b & v_{B} & 0\\
\end{pmatrix}$$

Hence, the unique mixed strategy equilibrium is $p := \Pr(a|A) = \frac{v_{B}}{v_{A}+v_{B}}$ and $q := \Pr(a|D) = \frac{v_{A}}{v_{A}+v_{B}}$. Note that as the value of target $A$ increases, the attacker will actually attack it more infrequently.

If, $c$ is not dominated (strict or weak) then the algebra becomes more tedious, but the unique equilibrium will be a mixed strategy with full support over all three pure strategies. I leave this to you.

Finally, I leave to you the case in which $c$ is only weakly dominated. Hint: In general there can be weakly dominated strategies in support of a mixed strategy equilibrium, but if the opponent's mixed strategy has full support, there cannot be.


Why cannot I compare AIC values obtained from nonlinear least squares and the ordinary least squares? I have a time series dataset on UK consumption. I can
(1) estimate an exponential trend
(2) take the logarithm of UK consumption, estimate a linear trend for this logarithm, and exponentiate the result
Why cannot I compare AIC values from these two methods?

In short, because AIC takes the log of the max value of the likelihood function.  Except under strong conditions there is no a priori reason to assume that these values will be the same after log-transforming your model.  In fact, a priori one should assume they will not be the same, since one of the reasons people log-transform their models is to change the sample distribution to be a little closer to normal.

So, you can't simply look at the two AIC values and conclude that they convey the same information, because in general, they do not.


Target2 Balances at the ECB-will it lead to the collapse of the Euro? Target 2 imbalances within the Eurosystem have continued to grow during 2020.  Currently Germany is owed Eur 1TN by the other countries, principally Italy and Spain.  If Germany at some point insists on redressing these balances, is the collapse of the Euro inevitable?

Although possible it is not necessary for several reasons.

Optimal currency area (OCA) can in principle exist even without fiscal transfers/excessive borrowing if there is perfect factor mobility within the OCA that can absorb the asymmetric shocks that countries in the monetary union face (see De Grauwe Economics of Monetary Union).

In the European Monetary Union (EMU), at a present, the factor mobility is not perfect because while there are no direct legal restrictions on movement of capital and labor it is not easy for people to move due to language barrier and poor integration of social security at EU level. However, as time progresses we see English becoming world-wide lingua franca. For example, in the Netherlands (where I live) a reasonable EU citizen can live and work never learning to speak Dutch in virtually any industry that does not require direct contact with consumers. All government forms and interactions are in both Dutch and English, and the same holds for doctors, and  virtually all retail/service businesses. This significantly lowers barriers to labor mobility. In addition all the social security systems are getting more and more integrated within EU. For example, when it comes to healthcare the system in EU is already integrated in a way that switching is not a hassle but same does not hold for pensions.
Since we are talking about some unspecified future it is possible that at that time the labor mobility will be sufficiently perfect that any shocks can be absorbed via  labor mobility and mobility of other factors as well. Indeed, if in past there would be no implicit restrictions on people moving from one EMU country to another, instead of fiscal transfers you would see large flow of people that would eventually correct the imbalances.

Germany presently sends fiscal transfers to the Southern Europe because it was fortunate enough to experience positive productivity shocks while southern Europe experienced negative ones. I am not trying to minimize the role of good governance and policy in German robust productivity and also economic growth in recent decades, but no matter what policy  this is to a significant extent also driven by random technological (where I am using the word in broad economics sense) or other macroeconomic shocks. Even the best govern country can't do much about that. In addition, random demand shocks or even monetary policy (e.g. low interest rates for too long) is also one of the issues that can contribute to macroeconomic imbalances that necessitate fiscal transfers (Pierluigi,  Sondermann 2018; Blanchard and Giavazzi 2002; Lane and Pels 2012;  Chen et al 2012).

Since  we are discussing the future it is entirely possible that in 10 or 20 years Germany will be the country experiencing negative productivity/demand etc shocks while southern countries will be experiencing positive ones, as often macroeconomic shocks can be asymmetric.  If the Germany starts insisting that South redressing its debt/fiscal transfers imbalances to Northern countries at that point in time - when it is from macroeconomic perspective optimal for South to actually do so, it won't cause any problem for the Euro, if anything it would be the optimal response.

Euro, is not just economic but also political project. In principle, even if Germany does not want to send fiscal transfers or lend to southern countries, if ECB conducts monetary policy in a way that addresses only macroeconomic shocks in countries experiencing negative shocks (which in case of asymmetric shocks would be at an expense of countries not experiencing negative shocks), or if EU leaders decide they are fine with living with financially instable EMU it is still possible to keep the euro.


Aggregated demand of households given utility function I have an utility function given,

$\ u_j(q_{j1},q_{j2} )=q^{3/4}_{1j}*q^{1/4}_{2j}  $

$\ s.t.:  y=p_1*q_{1i} +p_2*q_{2i}$

I do know that the for $\ q_{1j}$ the marginal prospensity to consume is 3/4 of y given prices $\ p_1$.
But I dont acutally get how my teacher calculated the aggregated demand:
$\ q^*_j(p_1,p_2)=(\frac{1/4y}{p}, \frac{3/4y}{p}) $.

I  set up the Lagrangean but then end up with $\ p_1=\frac{1}{3}\frac{q_2}{q_1}*p_2$, which does not seem too helpful for me.

Can someone give me a hint how to derive aggregate demand from a given utility function, please.

Thanks

You just need to use the condition $$ MRS_{q_{1j},q_{2j}} = \frac{p_{1}}{p_{2}} $$ to obtain $$ 3 \frac{q_{2j}}{q_{1j}} = \frac{p_{1}}{p_{2}} \;\;\;\; \text{(1)}$$ Then solving for $p_{1}$ and plugging this into the budget constraint you obtain: $$ y = 3p_{2} \frac{q_{2j}}{q_{1j}}q_{1j} - p_{2}q_{2j}$$ $$ \Rightarrow q_{2j} = \frac{y/4}{p_{2}} $$ Accordingly, solving for $p_{2}$ from condition (1) and plugging this into the budget constraint yields: $$ q_{1j} = \frac{3y/4}{p_{1}} $$.

From this you can obtain your function for the aggregated demand for goods $q_{1j},q_{2j}$, as a function of the prices.


Why is buying a put option a cash outflow, but shorting inflow? What advantage are there to shorting the stock as opposed to buying put option : finance

  Buying a put is a cash outflow, while shorting is an inflow. One advantage is that you can reinvest this inflow into another position.

In both cases  you're hoping to profit, and have money flow INTO your account, from a stock price's decrease.

When you buy a put option, you're taking possiession of something from someone else, and paying for it.

When you short, you're borrowing shares, and selling them, which brings cash in for you.


Do recessions matter? One common definition of recession is "two consecutive quarters of negative GDP growth". GDP growth affects other variables, such as stock prices, interest rates, unemployment, and personal income. Has research found there to be a nonlinearity such that GDP growth falling from 0.5% to -0.5% has a bigger effect on other variables than GDP falling from say 1.5% to 0.5%?

Not all components of the economy vary with the same intensity. As you can see in the figure below, consumption is about as volatile as output (GDP), but investment is much, much more volatile. You can also see the grey bars, which indicate NBER recession dates for the US, line up nicely with these dips in investment.


Is the income derived from owning a live animal profit or rent? Natural resources are considered non-produced and yield rents, including land and the fruits of the land, e.g. trees. Does this extend to live animals? Or are live animals considered “produced” goods (capital) that yield profits?

Does it make a difference whether the tree or animal is wild or has been planted on a plantation or bred in captivity respectively?

Live animals held and raised in captivity (and any products created) are counted as production. In particular, they're counted as "livestock value-added". From World Bank (2014):

Outputs from the livestock sector include the increase in the number of animals and the production of livestock products.
The increase in number of animals is represented by both fixed capital formation — i.e. animals that are inputs into the production process, such as breeding animals and adult males for breeding or animal traction — and by so-called ‘work-in progress’ animals, namely those reared for slaughter and young animals reared to become fixed assets.
Livestock products include meat, milk, eggs, hides and skins and other by-products, such as manure, hides and skins, fat, offal, honey, transport services, etc.

You also ask:

Does it make a difference whether the tree or animal is wild or has been planted on a plantation or bred in captivity respectively?

Yes. From UN System of National Accounts (2008, PDF, emphasis added):

Certain natural processes may or may not be counted as production depending upon the circumstances in which they occur. A necessary condition for an activity to be treated as productive is that it must be carried out under the instigation, control and responsibility of some institutional unit that exercises ownership rights over whatever is produced. For example, the natural growth of stocks of fish in the high seas not subject to international quotas is not counted as production: the process is not managed by any institutional unit and the fish do not belong to any institutional unit. On the other hand, the growth of fish in fish farms is treated as a process of production in much the same way that rearing livestock is a process of production. Similarly, the natural growth of wild, uncultivated forests or wild fruits or berries is not counted as production, whereas the cultivation of crop-bearing trees, or trees grown for timber or other uses, is counted in the same way as the growing of annual crops. However, the deliberate felling of trees in wild forests, and the gathering of wild fruit or berries, and also firewood, counts as production. Similarly, rainfall and the flow of water down natural watercourses are not processes of production, whereas storing water in reservoirs or dams and the piping, or carrying, of water from one location to another all constitute production.


What is the difference between conditional and unconditional risk premia? This is an asset pricing question. What is the difference between conditional and unconditional risk premia? Here's the context:

  The fact that carry trade strategies typically earn positive average returns
  is a manifestation of the failure of the uncovered interest parity (UIP) hypothesis, a major longstanding puzzle in international finance. A longstanding consensus in the international finance literature attributed all of carry trade average returns to conditional risk premia, finding little evidence of nonzero unconditional risk premia on individual currencies throughoutmost ofthe 20th century (e.g., Lewis (1995)) Consequently, much of the literature has focused on explaining conditional currency risk premia by ruling out asymmetries (e.g., Verdelhan (2010), Bansal and Shaliastovich (2012), Colacito and Croce (2013)). However, Lustig, Roussanov, and Verdelhan (2011) show that unconditional currency risk premia are, in fact, substantial and Hassan and Mano (2014) further argue that they drive the bulk of carry trade profits.

Some explanation, and / or a reference would be greatly helpful.

In case someone finds this helpful, I'll answer my own question.

Risk premium, say for example on some risky assets such as stocks, is the expected return on the risky asset less the risk-free rate.

However, empirically we have that this risk premium on stocks is much larger than the riskfree rate and also that it varies quite a bit more. So we introduce the idea of conditional vs. unconditional, which speaks to this time-varying aspect.

Conditional risk premia means risk premia conditioning on time-$t$ information (so with a time-$t$ subscript as in conditional moments, conditional variance, etc.). So it is the conditional expectation of the return of a risky asset over the risk free rate, where the conditioning is done on the agent's available information at time-$t$. Although it depends on the model, this is an object that is in general time-varying.

Unconditional risk premia just means risk premia without conditioning on time-$t$ information. Generally, this is not time varying.

A good reference for learning about conditioning information on asset pricing models is Chapter 8 in John Cochrane's book "Asset Pricing".


Does endogeneity matter when neither independent variable nor error term are correlated with dependent variable? if the double arrows show that X and the error term are correlated, but that neither variable affects Y, is endogeneity a problem in this scenario? Why or why not?

Assume the simplest linear regression model

$$y = bx + u$$

The OLS etimator for $b$ is

$$\hat b_{OLS} = \frac {\sum x_iy_i}{\sum x_i^2} = b + \frac {\sum x_ie_i}{\sum x_i^2}$$

Whatever the true $b$ is (it is zero in your case, as another answer pointed out) , the fact is that

$$\text{plim} \frac {n^{-1}\sum x_ie_i}{n^{-1}\sum x_i^2} \neq 0 $$

and so the OLS estimator will be inconsitent (and also, biased too).


What famous company that turned a loss at its first year(s) but then became profitable? In a discussion with a friend, he mentioned that a new company may fail to gain profits for several years before it becomes profitable. I asked him for examples but he did not know any. I though of Amazon, but I think they made "some" profit in their first year. Could you please tell me What famous company name that turned a loss at its first year(s) but then became profitable? It would be great if you have an easy reference for me to refer to. I am not in financial business.

It is very common for a company to have a loss (i.e. expenses > revenue) in the first year. Amazon is actually a very good example of that. It’s also a good example of ‘growth before profit’ strategy.

Amazon was incorporated on July 5, 1994, and begun service in July 1995. This means that not only it did not generate profit in its first year, there were also no sales. Even after the launch the company generated loss:

  Amazon had stated from the outset that it did not expect to turn a
  profit for four to five years, and it duly delivered on its promise.
  The firm grew quickly but failed to generate profit, making a net loss
  of USD -303,000 on net sales of USD 511,000 during its first six months of
  trading. At the beginning of 1996, Amazon employed eleven people and
  moved out of Bezos’s home to a small warehouse nearby. By the end of
  the year, Amazon.com offered 2.5m titles online, although it still
  carried only a minimal inventory. By this point, the firm had 151
  employees and relocated once again to accommodate its growing
  workforce. Sales for 1996 were USD 15.7m, with the company making a net
  loss of USD 5.7m.

Please see below historic results from Amazon’s first public annual report from 1997 (the year of IPO):

                           1997 |   1996  | 1995|   5 Jul 1994 - 31 Dec 1994

(1) net sales            147758 |   15746 | 511 |   0
(2) cost of sales        118945 |   12287 | 409 |   0
(1+2) gross profit        28813 |    3459 | 102 |   0
                            ---       ---   ---     --
(4) total operating
expenses                  58022 |    9438 | 406 |   52
(5) profit from interest   1619 |     202 |   1 |   0
                            ---       ---   ---     --
(1+2+5-4) net loss        27590 |   5777 |  303 |   52

As for an easy reference, @denesp cited an interesting source on this. There are some slight differences in the data, so I thought I would cite it alongside with annual report data, which is more precise.


Marginal rate of substitution notation: I am having a dumb doubt in writing some slides for an undergraduate class.
I want to be consistent with the use in microeconomics but this easy thing is really bugging me:

Mas-colell pag. 54

$ MRS_{lk} = \frac{\frac{\partial u}{\partial x_l}}{\frac{\partial u}{\partial x_k}} $

"tells us the amount of good k that the consumer must be given to compensate her for a one-unit marginal reduction in her consumption of good l"

Reny advanced micro pag. 18

$MRS_{ij}(x) ≡ \frac{\frac{\partial u}{\partial x_i}}{\frac{\partial u}{\partial x_j}}$

" ..MRS_{ij}(x) is again a positive number, and it tells us the rate at which good j can be exchanged per unit of good i with no change in the consumer’s utility"

I know also how to derive this result with the total differentiation but one thing really confuses me:

$du = \frac{\partial u}{\partial x_i}*dx_i+\frac{\partial u}{\partial x_j}*dx_j$

$ 0 = \frac{\partial u}{\partial x_i}*dx_i+\frac{\partial u}{\partial x_j}*dx_j $

$ \frac{\partial u}{\partial x_i}*dx_i = -\frac{\partial u}{\partial x_j}*dx_j$

$ \frac{dx_j}{dx_i} = - \frac{\frac{\partial u}{\partial x_i}}{\frac{\partial u}{\partial x_j}}$

The last equation expresses the differential increase in $x_j$ correspondent to a marginal increase in $x_i$ just as the two formulas above. Where does the minus go in the two books? Am I neglecting something?
Thanks.

It is implicit in the interpretation:

Mas-Collel: the amount that must be given (+)  to compensate for a reduction (-).

Reny: The rate at which good j  can be exchanged (+ & -) for good i.

The derivation from total differentiation only requires the utility to be constant, so the derivative must be negative to express that if the quantity of good $i$ increases, the quantity of good $j$ should decrease.

Another reason why some authors omit the negative sign is that in equilibrium  $|MRS_{ij}|=|\frac{P_i}{P_j}|$ So either you use the derivation from total differentiation and also the negative ratio of prices, or leave both sides as positive and focus on interpretation. Most people prefer the latter.


How exactly can blockchain technology be used to make a supply chain more efficient? I am a software developer, and have been studying Bitcoin, Ethereum and blockchain technology over the last 8 months or so. I have read a lot on the Internet about how blockchain technology will revolutionize the supply chain. The content I found was either on:

websites of tech companies working on this, so I guess they do not want to reveal the details of how exactly their solution works.

OR

commerce news sites, written by people not knowledgeable about the technical aspects, describing the benefits of blockchain technology and what it would enable in the supply chain but only at a very high level without any explanation of how those goals would be achieved in the supply chain space.

I want to understand how exactly people in the business / commerce / economics world see blockchain technology being applied to supply chains to achieve the stated benefits of "eliminating inefficiencies, speed up transactions, enable innovative new business models, transparency, trackability,... on and on, including but not limited to "tracking freshness of produce".

I am looking for someone who knows the technology and the domain and can explain how these business goals can be achieved using blockchain technology.

I am an economist and I am skeptical that the value will be large, remember that the planet has a 65 trillion dollar economy and so while a billion dollars is a lot of money to me, it isn't a lot of money in the big scheme of things.

On the surface, blockchain appears to improve accountability and reduce fraud.  I said on the surface because very few large scale blockchain frauds have happened yet.  Also, the most inefficient components of the world economy usually depend upon graft and those systems are resistant to implementing processes that improve accountability.

I do think that adding blockchain will improve system integrity, but I am wondering how the mafia will get to the outside nodes to degrade the information quality before it enters the process.  Consider a WalMart buys a set of goods numbered X0001 through X0050 and they are physically delivered.  Imagine that the shipping container is surreptitiously intercepted and a general manifest marking X0001 through X0050 as received goes through the process rather than the time consuming manual process of scanning each good.  The blockchain is defeated.

Now let us imagine that the packaging for each good is given a RFID with a unique encryption.  This is costly.  The mafia hires hackers to break into the system from the source and determine the encryption system itself.

Learning from this, they hire amazing network security, so the mafia hires a janitor to bug the place and steal documents.

Blockchain is nothing more than a distributed information recording system.  It is resistant to system destruction, facilitates verification and validation, and improves accountability but we have seen very few large scale failures.  Consider this, the Internet is resistant to system destruction, facilitates verification and validation of actors and nearly guarantees signal propagation as long as enough underlying communication systems survive.

The Internet's value has been heavily located in porn and cat videos.  Fraud is rampant and it is an open system, largely.  So is blockchain.  Open systems, like public highways, still depend upon policing and monitoring.

Although blockchain is proposing to replace centralized systems, as the Internet did for the postal service and BBS, it isn't clear that it will be of GREAT value for strong centralized systems.  Instead, the gains will probably be in poor centralized systems such as the international wire system.  It is aged, outmoded and outdated and hasn't seen real improvements in my lifetime.  It hasn't changed greatly since its 19th-century antecedents.  The same is true for the ACH system because Congress refuses to allocate the money.  On the other hand, the Swedish or British systems are great.

My guess is that its greatest value will be in exposing graft.  For example, if you could continuously track a container in a port in Ghana, then you could track what workers actually did what work and you would be able to expose clearly the pattern of bribes which speed up or slow down the harbor.  That is, you could if the customs and dock workers use the tools as intended.

Blockchain just decentralizes signal.  It is a human system and it will be implemented as part of greater human systems.  I think roving bandits like hackers and stationary bandits like customs workers haven't had a real chance to attack it yet.

If I were working in blockchain, I would be working on the inputs to the system and not the system itself.  The money is still in preventing GIGO.


Is it possible for a Central Bank to escape from a deflation trap by 'hiding' information? I'm reading this book on macroeconomics.

When determining the nominal interest rate, the Central Bank has in mind its real interest rate goal. By the Fisher Equation: $i_t=r_t+\pi^{E_{CB}}_{t+1}$, since at time $t$, I would need to know the price level at time $t+1$ to know inflation for next period, we use an expected value for inflation. I put the superscript $^{E_{CB}}$ to denote that the expectancy is formed by the central bank.

In the usual Philips Curve, we have $\pi_{t+1}=\pi^{E_{SS}}_{t+1}+\alpha(y_{t+1}-y_e)$ I put the superscript $^{E_{SS}}$ to denote that the expectancy is formed by the Supply Side (wage and price setters, i.e., with all available public information).

Recently, from a talk with someone who worked at a central bank, I learned that there's some difference in amount/quality of information that it's publicly available to wage and price setters, and that which is available to the Central Bank.

In the book I'm reading, the authors state one possible way of escaping a deflation trap, even if in practice it will not always work, is that to have higher expectations so that the minimum threshold for the real interest rate is lower enough to increase output until equilibrium.

Now I was wondering if it was not possible for, in some situation, the CB publicly divulged information lead to workers and firms have higher expected inflation, while the CB would know those expectations to be a bit too optimistic, such that in reality that period real interest rate would be much lower to be enough to get out of deflation trap?

I think I must be making some errors in this reasoning.

Any help would be appreciated

It is certainly possible for a central bank to move the economy away from liquidity trap or deflation trap by proper signals. Signals and targets are undoubtedly effective, as this NBER paper discusses http://www.nber.org/papers/w13932. I read an article, which I cannot find now, saying that signalling and targeting by central banks are sometimes more effective than actual policy changes. The problem is that the economy and financial markets have a huge amount of different players with different interests and goals so it is hard to predict with certainty the effect of the CB revealing certain information.

One thing I have to disagree with is that signalling higher expectations would reduce real interest rates and move the economy away from deflation trap. The equation  it=rt+πt+1 would be more accurate as it+1=rt+1+πt+1. If you write it like that, then you can see that signalling higher inflation expectations would also signal an incoming interest rate hike, given that any central bank has the policy to keep inflation low and stable. When markets expect a rate hike, they reduce their equity and commodity positions (sell stocks, oil, gold etc.) and move into bonds and other cash positions. This sucks the money out of economy and creates more deflation. So if the CB wants to reduce deflation, the ideal strategy would be the opposite: signal sluggish growth and prolonged low interest rates. This is just what Fed has been doing for several years now and, arguably, it has worked.

I can also add, as @ChingG noted in comments, the CB has to maintain credibility and not lie. On top of hurting its reputation, the central bank board members are also liable to the government for saying the truth. For example, if the Fed Chairwoman lied to Congress, she would be breaking the law. It makes more sense for the CB disclose the true data and to interpret the information the way the CB sees fit and give the signals and targets it deems necessary, but not "hide" information.


Why are labor, capital, and land traditionally denoted by the letters L, K, and T? AFAIK, at least in the English-speaking world, labor, capital, and land are (in economics) usually denoted by the letters L, K, and T.

Who first popularized the use of these letters and why?

My uneducated guesses are that:

L would certainly make sense in English.
K I think is from the German Kapital.
T I think is from the French or Latin Terre or Terra.

I'm only guessing (sorry) that $T$ for terre comes from the Physiocrats' work. K for capital is easiest than $c$ (for consumption).

Btw, labor is not always $L$ but sometimes $N$ depending of if you mean labor force vs working population (or hours). And I've no ideas why $N$!


Difference between merchandise trade and trade in goods? What is the difference between merchandise trade and trade in goods? Are they the same? If so, would total trade be just trade in goods + trade in services, aka merchandise trade + trade in services?

As far as I understand merchandise trade and trade in goods are the same.

The IMF Balance of Payments Manual breaks down international transactions according to standard categories. Trade is one of these categories. Trade is defined as international transactions involving products, i.e. exports and imports of goods (or merchandises) and services.

Merchandise or good trade are transactions involving the transfer of ownership of a tangible and moveable object from a seller to a buyer.
Services are transactions in which a consumer benefits from actions taken
by the service provider.

There is a subtle sub-category, which is

Goods for processing that are transactions in which raw goods (e.g. cotton thread) from country A are exported to country B, where
they undergo processing, and are then imported back into country A (e.g. t-shirts) without a transfer of ownership.


Is Firing Costly in the US? I suppose that it doesn't cost most firms much to get rid of cheap labor, and that high wage workers typically have contracts that imply high compensations in case of firing.

But what about the remainder? Since Macroeconomics is mostly about the art of writing linear models, what evidence is there for average firing costs from the view point of the firm?

Interestingly I could not locate quantitative data on Firing Costs (aka Separation Costs aka Severance Pay) for the US Economy. Perhaps because, as US Dpt of Labor says

  There is no requirement in the Fair Labor Standards Act (FLSA) for
  severance pay. Severance pay is a matter of agreement between an employer and an employee (or the employee's representative).

A  world map  and another one for separation costs measured in weeks of wages -but none of the two include data on US Economy.

ILO's new data base does not seem to have quantitative data on Firing Costs.

Kugler, A. D., & Saint Paul, G. (2000). Hiring and firing costs, adverse selection and long-term unemployment. deal with  some US data but qualitatively and indirectly.

Abowd, J. M., & Kramarz, F. (2003). The costs of hiring and separations. Labour Economics, 10(5), 499-530. Data from the economy of France, related to year 1992. Extensive treatment of various costs associated with labor, including costs of separation treated distinctly. Note: monetary values are in French Francs. Conversion Rate: 1 FFr = 0.152449 EUR.


Use of the term "effective" in economics I've seen the terms "effective demand" and "effective wages" bandied about in papers, but I'm not sure what these refer to. Please could someone explain both these concepts? Thanks!

In economics, we are mostly interested in studying how incentives shape decisions. In many situations, there is a gap between the concept that captures the incentives that a person is facing, and the name it receives in the real world. For example,  in general, wages are what provide incentives for people to work. However, most people pay taxes or have other deductions. Therefore you can define the "effective wage" as the money the person gets to keep after taxes are taken out, etc. Now, the effective wage is really what is shaping the decisions of the person.

As you can see, the use of "effective" can vary a lot from topic to topic, but it almost always refers to some adjustment in the variable so that it really captures the incentives agents are facing.


The existence of solution for profit maximization problem I'm thinking about the conditions for existence of solution of this profit maximization problem(PMP), i.e.,
$\max_{z \in R_+^{K-1}} pf(z) -wz$,
where $z \geq 0$: input vector, $p>0$: the price of output, $w \gg 0$: an input price vector, and $f:R_+^{K-1} \rightarrow R_+ $: the production function.
Of course, if production set $Y$ is compact, by Weierstrass theorem, we can prove there exists a solution of this PMP. But many cases, $Y$ is closed but not bounded. Then what kind of assumptions on function $f$ are needed to show the existence of a solution, instead of Weierstrass theorem?

A possible approach is to find a compact set $Z$ of inputs and show that the PMP has an optimal solution if and only if the PMP has an optimal solution in $Z$.
If so, we can replace the PMP by the following problem.
$$max_{z \in Z} \,\,p f(z) - w z.$$
If $f$ is continuous and if $Z$ is compact, the existence of a solution follows from the Weierstrass theorem.
An example of a sufficient condition for $Z$ to exist is to assume that $f(0) = 0$ and that there exists an input level $z_0$ such that for all $z > z_0$, $p f(z) - w z < 0$. In words, there is an input level $z_0$ such that having a higher input level will generate negative profits. Then we can set
$$
Z = \{z \in \mathbb{R}^{K-1}_+: z \le z_0\}.
$$
Notice that $Z$ is compact. In order for this to work we need to show that the PMP has an optimal solution if and only if it has an optimal solution in $Z$.
To see that this is true, first notice that $z = 0$ is a feasible solution for the PMP and it is also in $Z$. As such, the optimal solution to the PMP will always generate a profit that is larger or equal to zero, which means that no solution $z$ to the PMP will be outside the set $Z$.


Why is the law of diminishing marginal returns justified? Shouldn't it be easier to produce more quantity of goods for a producer?
Isn't it the case that the ease of production is inherently tied to the quantity you produce?
Shouldn't it be the case that the more you produce , the more easier it becomes to produce a bit more?
I understand why the marginal cost drops for lower quantities but am not sure why it should steadily climb up if the quantity crosses some threshold.

Of course , the fixed costs and variable costs as a result of increase in quantities produced could play a local effect in the increasing marginal cost but I don't see why in general the marginal cost curve seems to be increasing by the argument that it should be easier to produce a bit more when you are already producing a lot.

Marginal product can be constant, increasing or diminishing depending on Returns to Scale (also called Economies of scale). If Returns to Scale is constant, it means that each extra unit of product/output takes one extra unit of input. In this case, marginal product will be constant. In other words, the efficiency of production is constant.

However, take the case of increasing Returns to Scale, which is usually seen in the real world in a typical factory. In this case, one extra unit of product takes less than one extra quantum of cost inputs. In such a case, the firm has high fixed costs as compared to variable costs and said to possess an operating leverage (in financial terms). And, the efficiency of production increases. Same inputs produce higher outputs.

Example: a software company selling products has high fixed costs and close to zero variable costs. So, selling one extra copy of software can happen at a much lower increase in inputs. This is however, till you reach the ceiling where you have to employ additional fixed cost resources to generate the next item of product. Say, when the next version/iteration of the software has to be produced, it would need additional fixed cost resources to develop it.

So, yes it isn't necessary that marginal product will always have a diminishing curve.


What is the market value of an object over time? Recently many news articles mentioned the new luxury car Maybach Exelero. Only 2 cars have been manufactured. Moreover, one of the cars has been sold for 8 million dollars, which makes this car one of the most expensive cars ever sold.

Now, once you buy a car, the market value of the car depreciates once you drove it outside of the factory. For example, price of a new  6000 dollars car, will be  5800 dollars. Although, the market value of the car should be the same, no one will buy the car for the same price you bought it from the dealer.

There are two scenarios that I'm proposing. The first one is: the owner buys the car and never drives it (i.e., keeps it in a garage/show room). The second one is: he drives it every day like any other car.

My question is: what is the value of an object over time? how does it vary? The context of this question has been described above. Which are the properties of the object described above? and how do these compare with other properties of similar objects? (i.e., luxury products).

The value of a tradeable good is equal to what the marginal buyer will pay for it.

I will explain further, but first let me correct one misconception in your question. You state:

  Now, once you buy a car, the value of the car depreciates once you drove it outside of the factory. For example, price of a new 6000 dollars car, will be 5800 dollars. Although, the value of the car should be the same, no one will buy the car for the same price you bought it from the dealer.

The value of the car should not be the same. There's a very well-known reason that cars lose value as soon as they are sold used, rather than new: there might be something wrong with them which the seller might be aware of, but the buyer might not be able to spot. This is discussed at length in a well-known paper titled "The Market for Lemons: Quality Uncertainty and the Market Mechanism" (see link for Wikipedia discussion).

Having said that, we can return to the discussion of the value of a car. Like any other tradeable good (it's easier to determine the value of a good that can be bought and sold than the value of services provided by an ecosystem, for example), a car is worth whatever someone is willing to pay for it.

You ask about two scenarios, one in which the car is kept in a showroom, and another in which it is driven. The difference between these two scenarios is what is known as depreciation— as you drive a car, things wear down, and its future life becomes shorter, while it also becomes less good at being a car. Both because the car isn't as nice (maybe it's scratched up, or it is a bit slower, or it requires more maintenance), and because it won't last as long, all else equal (i.e., so long as nobody wins a famous race while driving that particular car) driving a car decreases its value.

In practice, the value of many cars decreases for a long period, until at some point, the value slowly begins to increase as the number of cars dwindles and the model attracts interest from collectors. The collectors' market is actually in many ways a very different market from the original market for a car— the people buying a collectible car generally aren't interested in its value as an automobile; a classic car will tend to be slower, get worse gas mileage, be dramatically less safe, have higher maintenance costs, and offer fewer amenities than a modern car that costs a similar amount. Because this market is driven by factors other than the value of the services provided by the car (because, ayou are aware, most rare collectible cars are driven rarely, if at all), the value of these cars tends to be determined more by factors like taste or the value of financial assets held by the wealthy than by anything else. Nobody will be driving an Exelero to the grocery store; anyone who has one has another car to use for that task (or, more likely, someone to go to the store for them and cook them dinner).


Modern descendants of Frank Ramsey's paper "A Mathematical Theory of Saving"? I haven't studied economics, but I'm interested in applied ethics, and I came across Frank Ramsey's paper "A Mathematical Theory of Saving". I thought his application of calculus to a normative economic question was very interesting ("How much of its income should a nation save?"), and I was wondering whether this approach is still pursued in the field, and whether anyone could recommend some modern papers which attempt/accomplish something similar.

If I understand correctly you are not interested just in saving but to mathematical approach to normative questions in general. This approach is actually quite common in the whole literature that uses normative economics.
For example, the question of redistribution is predominantly normative question,  because as opposed to questions of social efficiency, how much our society should redistribute depends on normative judgment. For example, optimal redistribution and marginal tax rates under Rawlsian social welfare function (based on Rawls MaxMin principle and his moral philosophy) will look different than tax system if one adopts utilitarian moral philosophy.
You could have a look at Saez  (2001) or Diamond (1998). Here is an example from Saez which shows how different marginal tax rates look under different normative judgements:

The simulations above are based on:
$$ \frac{T'(z_n)}{1-T'(z_n)} = \left( 1 + \frac{1}{\epsilon_{lT}} \right)\frac{\int (1-b_m)f(z_m)dz_m}{1-F(z_n)} \frac{1-F(z_n)}{z_nf(z_n0)}$$,
with $b_n \equiv \frac{\Psi'(u_n)u_c}{\eta}+ nT'(z_n) \frac{\partial l_n}{\partial \rho} $.
I wont go over every single term in the formula as this would turn this answer into a book but broadly speaking the first part $\left( 1 + \frac{1}{\epsilon_{lT}^*} \right)$ is given by elasticity of labor supply to income taxes and you can think of it as an 'efficiency' parameter, the second part $\frac{\int (1-b_m)f(z_m)dzm}{1-F(z_n)}$ tells us what the marginal benefit of redistribution is and this marginal benefit factors in underlying actual welfare which is captured by $b_n$ which depends on social welfare function,  and finally $\frac{1-F(z_n)}{z_nf(z_n0)}$ s the part that captures the relative magnitude of distortions created by this taxation.
In turn the social welfare function is nothing more than just mathematized version of some moral philosophy, the most common ones I seen in literature are utilitarianism, Rawls MaxMin, libertarianism or sometimes called conservativism - especially in US and some variations of those (although sometimes you will see more exotic ones as well).
Generally, I think it is fair to say that most economic papers that discus normative judgements mathematize these. You should look at various graduate textbooks or notes on public economics/economics of public sector or on economics of inequality or public choice (this is because these are the sub-fields that deal with normative judgments most frequently as opposed to let's say monetary theory).


What does it mean to have a strictly increasing transformation in consumer theory? We're discussing utility functions

If I'm understanding your question correctly, you are referring to increasing transformations of a utility function. Suppose I have a set of alternatives $X$, a rational preference relation $\succsim$ on $X$, and a function $u:X \rightarrow \mathbb{R}$ which represents this preference relation. Then it can be shown that for any $v:\mathbb{R} \rightarrow \mathbb{R}$ which is monotonically increasing, $v \circ u:X \rightarrow \mathbb{R}$ also represents these preferences. Try to prove this; it's a good exercise.

So in classical economic theory, we never have a "unique" utility function which represents preferences. This is because we can always take an increasing transformation of the function and get something else which contains all the relevant information with respect to our preferences.


Setting prices in mobile telephony Can someone please explain or provide some useful link on factors affecting setting prices of mobile telephony services?

This paper may be of interest:

This paper examines the impact of regulatory intervention to cut termination rates of calls from fixed lines to mobile phones. Under quite general conditions of competition, theory suggests that lower termination charges will result in higher prices for mobile subscribers, a phenomenon known as the waterbed effect. The waterbed effect has long been hypothesized as a feature of many two-sided markets and especially the mobile telephony industry. Using a uniquely constructed panel of mobile operators’ prices and profit margins across more than twenty countries over six years, we document empirically the existence and magnitude of this effect. Our results suggest that although regulation reduced termination rates by about 10%, this also led to a 5% increase in mobile retail prices. We also provide evidence that both competition and market saturation, and most importantly their interaction, affect the overall impact of the waterbed effect on prices.

TESTING THE “WATERBED” EFFECT IN MOBILE TELEPHONY (Genakos and Valletti (2011))


Empirical research into sectoral comovement I'm looking for some empirical studies into sectoral comovement. In particular, I'm interested in how manufacturing and services industries move together both in the long run and over the course of a business cycle. Most importantly, I'd like to know more about how the performance of manufacturing affects the performance of services. Are there any papers on this topic that you'd recommend?

So far I've only found a few papers which study sectoral comovement in more general terms and a few which only touched on this topic very briefly as an aside.

Many thanks!

A relevant paper could be:

Veldkamp, Laura & Wolfers, Justin, 2007. "Aggregate shocks or aggregate information? Costly information and business cycle comovement," Journal of Monetary Economics, Elsevier, vol. 54(Supplemen), pages 37-55, September.

NBER Working Paper version: https://www.nber.org/papers/w12557

Published version: https://www.sciencedirect.com/science/article/abs/pii/S0304393207000529


Uniqueness of OLS estimates Wooldrige says that ‘intuitively, to estimate k+1 parameters, we need at least k+1 observations’. Why is this the case?

The $k+1$ parameters are $k+1$ unknowns. In general, you need at least $k+1$ equations (which are observations in the context of OLS estimation) to uniquely pin down those $k+1$ unknowns.


Question regarding couple economic terms and concepts I am trying to read some economic articles for future use.

However, as a statistics major student, I am quite unfamiliar with couple of economic vocabs and concepts. Followings are the very vocabs.

-Aggregate Fluctuations/Shock

-Idiosyncratic Shock

-Granular economy

And the following is the concept

-What does it mean to have a fat tailed distribution. What does "fatter-tailed" distribution indicate? ex) A prominent exception is a recent contribution by Gabaix (2011), which argues that because the firm size distribution is extremely fat-tailed – the economy is ‘granular’.

If I may could any one of you awesome experts explain this for me ? If there is a great website where I could learn simple economic concepts please give me some ideas. Thank you so much and have a great day!

Aggregate fluctuations are changes in aggregate variables, for example changes in aggregate supply and demand. If we are talking about shock it is usually implied the event was unexpected but the term is sometimes used loosely.

Idiosyncratic shock is an unsystematic shock, in macroeconomic models it is the shock not correlated with other variables. If you are coming from statistics it’s similar to residuals in OLS - in fact when estimating macro models with econometrics the residuals are often assumed to be the representation of idiosyncratic shocks.

Fat tailed distribution in economics has the same meaning as in statistics - the area in the tails/tail, or more specifically kurtosis and skewness of distribution is relatively large compared to Gaussian distribution.

Granular economy - well this could have different meaning depending on the exact subfield/context. In macroeconomics I saw this terminology being applied to economy that could be described by power law or Zipf law (see this IMF paper). Interestingly many social relationships (city distribution and size, words used in language, firm sizes etc.) follow Zipfian distribution. But I also saw it applied differently in industrial organization but I assume you are looking for something related to macroeconomics.

Good sources to learn some basics/simple concepts in economics are:

khan academy - they have free highs school level micro and macro courses and the quality is good.

Jason Welker - this YouTube channel has also very good high school economics, again for both micro and macro and also for some international economics.

However, from your questions I feel you would more likely need something more advanced (for example I don’t think you will find any discussion of fat tails or probably not even idiosyncratic shocks in the simple sources above). I don’t know any good online source for more advanced concepts but textbooks such as Macroeconomics: A European Perspective from Blanchard Gavazzi and Amighini or for something more advanced the advanced Macroeconomics by Romer are good (you can find pdf versions online). However, when it comes to granularity I did not see that in textbooks much, so there you will probably have to dig into some papers.


How to engineer the economic system, so that an individuals self interest leads to fulfilling collective interest So it is said that Adam Smith said that self interest leads to collective interest.

This is obviously not the case. We do not have a society that maximises the collective good*.

My question is, Is there a way to engineer society such that self interest will lead to a collective interest?

*It can be argued that the very poor are not as poor as they were a short time ago, but this is not what I am asking about.

Well, there's mechanism design. We use game theory to study what people do and then reverse it and ask ourselfs what set of rules induce people to rationally choose to do what the mechanism designer wants them to do.

In an auction, we charge the second highest price to the winner, that's a Vickrey-Clark-Groves mechanism. In voting, one might want to apply the Goeree-Zhang mechanism, for example.


Is the mainstream against agent based modelling? I have heard it said that mainstream economists disapprove of agent based modelling and some of the most prestigious economics journals will not accept papers that employ them. Is this true? And if so, why?

I'm an outsider, so I can't speak of what the boards of prestigious economic journals think of this, but...

I suspect it has something to do with the opacity of computer simulations using agent-based models (ABM) compared to math proofs or even the statistical models that are the staple of applied econometrics... although simpler computer simulations like Monte Carlo methods are well accepted.

E.g. Arnold Kling, who has some academic and some Federal Reserve credentials, writes

  My concern with ABM is getting a result and not really knowing why you got it. Alternatively, if you really understand how the ABM is getting its result, you should be able to show how to get that results in a simple model, perhaps with a numerical example.

He doesn't seem to be on the board of any journals, but I doubt his opinion is uncommon.

BoE economist A. Turrell has written a (lengthier) paper containing a fairly balanced (IMO) list of pros and cons of ABM. "Calibration and interpretation" takes most space there when it comes weaknesses. He also mentions the Lucas critique as relevant, and notes that the most fertile cases for ABM being behavioral-economics oriented, e.g. using bounded rationality, also makes them most difficult to proof against the Lucas critique.

At least currently, the staple of macro-economics models is DSGE, which nearly always include a representative-agent:

  All the different views mainstream macroeconomists have about the state of their field and about possible areas of improvement should not diminish the degree to which they converged methodologically in studying fluctuations. They all analyse such phenomena usually through a dynamic stochastic general equilibrium model with a representative agent, firmly grounded on microeconomic principles. Moreover, several of them agree with Chari (2010: 2) that “any interesting model must be a dynamic stochastic general equilibrium model. From this perspective, there is no other game in town.” Therefore, he continues, “a useful aphorism in macroeconomics is: ‘If you have an interesting and coherent story to tell, you can tell it in a DSGE model. If you cannot, your story is incoherent.’”

Generally DSGE models assume a representative agent (in part because they need to side-step Sonnenschein–Mantel–Debreu type results).

  The theorems of Hugo Sonnenschein, Rolf Mantel and Gerard Debreu in the early 1970s established that the restrictions that generate well-behaved individual demand functions do not constrain aggregate demand functions to exhibit the same properties [...]. The new classicals sidestepped the problem of aggregation either by imagining an economy composed of identical individuals or by assuming that there is one individual who represents the whole economy, so that the solution to the optimization problem of this representative agent gives the aggregate relationships in that economy.

There were more steps before the current new synthesis DSGE approach, but I don't want to get into that here. My point with this is that if you have an optimizing representative-agent (RA), you don't need much computer/behavioral simulation... Of course, RA models are criticized (Fagiolo and Roventini summarize RA/DSGE criticism from much more famous economists, Stiglitz etc.) exactly because of this, e.g. their inability to predict (or supposedly even explain) the Great Recession etc. But this criticism seems to not be enough to dislodge DSGE from the current mainstream macro, presently. (There is a bit more subtlety to RA than what I've covered here; RA can include some sources of parametric heterogeneity but assumes a sort of "structural" homogeneity, if I understand that correctly.)

Fagiolo and Roventini have a detailed comparison of DGSE with ACE/ABM  approaches, and while they find that the two approaches share some criticism, they point out the following difference:

  The last issue worth mentioning is specific to ACE and it concerns the comparability of
  different agent-based models. DSGE models are all built using a commonly-shared set of behavioral
  rules (e.g., representative agents solving a stochastic dynamic optimization problems)
  and their empirical performance is assessed with common techniques (i.e., VAR models). This
  allows to develop a common protocol about "how to do macroeconomics with DSGE models"
  and it eases the comparison of the results produced by competing models. Given the relatively
  infancy of the ACE paradigm, the lack of such a widespread agreement among the ACE community
  hinders the dialogue among different ABMs, reducing the comparability of their results,
  and possibly slowing down new developments. In that respect, the development of common
  documentation guidelines (Wolf et al., 2013a), dedicated languages and platforms can surely
  improve the situation, increase the exchanges among ACE scholars, and reduce the entry cost
  to agent-based modeling.

In other words, because of its infancy, there's a lack of standardization in ACE/ABM (unlike DSGE), which presently also hinders wider adoption for the former. (As minor point of terminology, they use ACE/ABM interchangeably: "ACE [agent-based computational economics] models (often called agent-based models,
ABMs)".)


Meaning of $dF(z)$ in expected utility framework Background: from a Microeconomics course,

  $F$ is a cdf. In other words, if $F$ has a density function $f$, then
  $$F(z)={\int_{-\infty}^z f(x) dx}  $$

  Write the Bernoulli utility function $u: \mathbb R_+ \rightarrow \mathbb R$ such that the preference is represented by
  $$U(F) = \int u(z) dF(z)$$

  If $F$ has density $f$, then $U(F) = \int u(z) f(z)dz$

I am unfamiliar with the notation $dF(z)$, and don't quite understand what this means. Can someone help?

Not all cdf’s have a density function, (for example if $F$ is not differentiable). However, when they do have a density, the notation $dF(z)$ is equivalent to $f(z)dz$. When performing integrals. However, even if the density does not exists, you can still write the expectation using the notation $dF(z)$. The details of what it actually means and the subtle differences can be learned in any measure theory course. But hopefully this short explanation helps you not freak out every time you see that notation.


Effect of change in discount rate on consumption -- (Samuelson, 1958) I was reading this paper by Paul Samuelson. I am puzzled by a bit on page 470, left column. Here he claims that $\frac{\partial C_3}{\partial R_{t+1}}>0$. Let me give a short description of what exactly this means and then I'll explain why I disagree.
In this model every individual lives 3 periods. Every person produces 1 unit of output in period 1, one unit in period 2 and no output in period 3. He can however trade some of his output in the first 2 periods for consumption in the last period and this gives rise to his consumption pattern $(C_1, C_2, C_3).$
Suppose a person is in period 1 at time $t$. So he is in period 2 at time $t+1$, and in period 3 at time $t+2$. He can earn an interest rate of $i_t$ on savings at time $t$ for all $t$ (that is $i_t$ is the interest rate earned on savings you carry from time $t$ to period $t+1$). Now define $R_t=1/(1+i_t)$ for all $t$.
The claim by Samuelson is that $\frac{\partial C_3}{\partial R_{t+1}}>0$. Or equivalently: $\frac{\partial C_3}{\partial i_{t+1}}<0$. How can this be true? If $i_{t+1}$ goes up (down), sacrificing a fraction of $C_1$ and $C_2$ to increase $C_3$ becomes more (less) profitable. So common sense would suggest: $\frac{\partial C_3}{\partial R_{t+1}}<0 \Leftrightarrow \frac{\partial C_3}{\partial i_{t+1}}>0$.
Samuelson gives no proof of his claim but he does claim it can be inferred from the following: "Of course, these functions are subject
to all the restrictions of modern consumption theory of the ordinal utility or
revealed preference type. Thus, with
consumption in every period being a
"superior good," "
Please enlighten me. Is Samuelson wrong/am I wrong?

Consider the life-time utility maximization problem of the individual. At this stage of the paper, while the utility function "has the usual regular indifference-curve
concavities" as Samuelson writes, nothing has been assumed about the form of the intertemporal utility function, so the problem is stated as
$$\max_{C_1,C_2,C_3}U(C_1,C_2,C_3),\;\;\; s.t.\;\;\;  C_3 = \frac {1+ R_t}{R_tR_{t+1}} - \frac{C_1}{R_tR_{t+1}} - \frac{C_2}{R_{t+1}} \tag{1}$$
where the constraint comes from re-arranging the intertemporal budget expression (eq. 1 of the paper), and interest rates/discount factors are treated as exogenous. Since this is an equality constraint (implying no bequest motive and no debts at the end of life), we can incorporate it into the utility function and solve with respect to $C_1$ and $C_2$ only. The first-order conditions are then
$$\frac{d U}{d C_k} = \frac{\partial U}{\partial C_k} + \frac{\partial U}{\partial C_3}\cdot \frac{\partial C_3}{\partial C_k} =0, \;\;\; k=1,2 \tag{2} $$
Because consumption is a good, marginal utility is positive. This implies that at the solution also,
$$\frac{\partial C_3}{\partial C_k} < 0,\;\;\; k=1,2 \tag{3}$$
By the chain rule we can write
$$\frac{\partial C_3}{\partial R_{t+1}} = \frac{\partial C_3}{\partial C_k} \cdot \frac{\partial C_k}{\partial R_{t+1}} , \;\;\; k=1,2 \tag{4}$$.
Due to $(3)$ we obtain the fundamental result that, at the solution, the $t+1$ discount factor (or equivalently, the $t+1$ interest rate) will tend to affect $C_3$ in the opposite direction than $C_1, C_2$.
This is crucial, because it says that changes in the exogenous interest rates will  lead to solutions where we will observe higher (lower) $C_1,C_2$ and lower (higher) $C_3$.
Samuelson asserts that  $\partial C_3/\partial R_{t+1} >0$, which is equivalent to assert that
$$\frac{\partial C_k}{\partial R_{t+1}} < 0 , \;\;\; k=1,2$$
or equivalently, that
$$\frac{\partial C_3}{\partial i_{t+1}} < 0,\qquad \frac{\partial C_k}{\partial i_{t+1}} > 0 , \;\;\; k=1,2$$
Is this the case?
For given interest rates we obtain a solution for the consumption vector that implies certain savings and a certain interest income. If we contemplate an increase in $i_{t+1}$, total income, $I$, will tend to increase, $\partial I/\partial i_{t+1}>0$ . Then, because consumption is assumed to be a "superior" good, $C_k,\; k=1,2$ are certainly normal goods, $\partial C_k/\partial I >0$, and so
$$\frac{\partial C_k}{\partial i_{t+1}} = \frac{\partial C_k}{\partial I}\cdot \frac{\partial I}{\partial i_{t+1}} >0$$
Then for $C_3$ the same relation implies that $\partial C_3/\partial I <0$, at the solution. This does not make $C_3$ an inferior good, when viewed on its own, but it is the result of it being determined residually, as the last element in a fixed-horizon intertemporal problem.


Clarification of iterated prisoners dilemma In the description of an iterated prisoner's dilemma on Wikipedia, it states that in order for a game to be considered iterable, it must conform to the rule 2R > T + S, where R is the reward for cooperation, T is the temptation payoff, and S is the sucker's payoff. Could someone provide an example of a dilemma in which this would not be the case, i.e. it would be non-iterable?

The payoff depends entirely on how you set the game up. Here's one example of the case where $2R \leq T + S$:

                                  Player B
                           Cooperate  |    Defect
Player     Cooperate        (1, 1)    |  (-2, 100)
A          Defect          (100, -2)  |  (-1, -1)

Here, $R = 1$, $T = 100$, and $S = -1$, and $2R < T + S$.

Edit: To add a bit more value to the answer... any game could be played repeatedly (and thus is "iterable" in that sense.) However, my understanding is that the Wikipedia page writer means that for (Cooperate, Cooperate) to be sustained, you at least need this condition to be true.