Is the time value of money natural or artificial? Certainly there is a time value of money: If the nominal interest rate of treasury bonds is 5%, then if one has a choice between receiving a hundred dollar bill now and receiving it a year from now, the better option would be to receive it now.

But what if we lived in a society where charging interest is illegal? Would there still be a time value of money? In other words, if we lived in such a society, then if one had a choice between receiving a hundred dollar bill now and receiving it a year from now, would the better option still be to receive it now?

So the essence of my question is "Is the time value of money natural or artificial?" If it is natural, then a law against charging interest would have no effect on the reality that there is a time value of money. And if it is artificial, then the law which states whether charging interest is illegal or not is what determines whether there is a time value of money.

Let's first write down two realistic reasons as to why the "time value of wealth" (since here "money" is considered in its function as store of value), is "natural and not artificial", to use the OP's words.

1) The phenomenon of inflation. If we expect to see price inflation, then a given amount of nominal "wealth tomorrow" will buy for us less goods and services than the same amount of "wealth today". So "wealth today" is preferable than "wealth tomorrow", since what we care about, is goods and services which are the things generating utility for us.

But note that inflation is not some always-present phenomenon in all economic systems, economies, countries, eras: for example the 19th century has been largely a deflationary period, with prices tending to fall during the century, in the main capitalistic economies.

2) The uncertainty of the future. This is always present, even if it has to do with the possibility of unexpected death. So "wealth tomorrow" may not be enjoyed because I will have die suddenly and unexpectedly till then. So "wealth today" is preferable, and so more valuable.

In a lending and borrowing situation, we can also map to the "uncertainty of the future" the risk of not-repayment etc. and so view the time value of wealth as being also a compensation for undertaking these risks.

Also, in a long-term approach, eventually we all die, so the very finiteness of our horizon creates a situation where "wealth today" is more preferable and so more valuable than "wealth tomorrow", if this "tomorrow" is far in the future.

The thing is, economists argue that "wealth today" is always preferable to "wealth tomorrow"
a) even if there is no inflation, or alternatively, if we examine wealth in "real terms" (i.e. in terms of goods and services),
b) even if there is no uncertainty at all,
c) even if we have an "infinite" time horizon, i.e. even in the hypothetical situation that we are certain that we will never die, not even from "natural causes."

This is why in intertemporal models of consumer choice and utility optimization that are deterministic /incorporate no uncertainty, and assume an infinite time horizon, still, a "discount factor" exists that discounts future certain utility in real terms, which indirectly reflects that "wealth today" is preferable to "wealth tomorrow".

What is the argument behind that? Well, sometimes there is no philosophical argument only a methodological argument: "a deterministic economic model with infinite time horizon and in real terms is an approximation to reality, which is uncertain and has finite horizon for economic agents, and so we include the discount factor to keep it a little closer to reality". That's fine, that's what economic models do (models in general actually).

But could we come up with an argument that even an immortal living in a perfectly deterministic world, would prefer "wealth today" to "wealth tomorrow"?

We can. It's called "opportunity cost". It can stand on its own without invoking uncertainty or the possibility of death. It depends on the following very simple axiom, which is supported by timeless experience related to human behavior: "more is better". Under this axiom, having wealth today will permit me, if I choose so to have more wealth tomorrow and for all tomorrows. So it potentially expands my "choice set" for all eternity.  If more is better, then I want a larger choice set, so I would prefer to have all my future wealth today rather than tomorrow.

...one could of course argue that the "more is better" postulate is not an independent trait of humans, but is one more incarnation of the "survival instinct" and so it is in reality a response to uncertainty and risk of death. Certainly, but everything can be eventually attributed to the "survival instinct", and what explains everything explains nothing.


Is whatever they calculated a valid "demand elasticity"? https://medium.com/@kwrdarisipudi/demand-elasticity-of-iphones-1e3a7bbb9eac
They are saying iPhone demand is less responsive to price over time, but I disagree.
Income shifts the demand curve. Higher income exposes preference to more expensive phones, which makes it appear the consumer doenst care about price when in reality they have the same preference just scaled by income.
And it doesnt look sustainable, either, because the latest apple phones are price cut. There's additional factors like financing availability and competing products that make this not useful as a demand elasticity.
Am I right or they?

The way how they estimated elasticity is definitely not an accurate and unbiased way.

You are correct that when you estimate elasticity it is important to control for income, but not only for that you should also have controls for prices of competing products and  other relevant controls.

Supply-Demand is an endogenous system and every observed price and quantity is result of an interaction of the two. In order to estimate elasticity some method that can model them simultaneously or allows for endogeneity is required. The author does not specify methodology used in the blog post but there is no indication that this was acknowledged.

In order to make valid inferences from data when using parametric models you need at least 25-30 observations per independent regressor (see Newbold et al statistics for business and economics for example). The blog post tries to estimate the elasticities from 3-6 data points (depending on the model). That is woefully inadequate.

So in conclusion even though the blog you refer to does not share it's  methodology, it seems to be acknowledging neither of the issues above so their estimates of elasticities are likely biased.


How does buying more of a foreign currency devalue a nation's currency? If a country wants to devalue their countries, why does buying more of a foreign countries currency devalue their currency?

I was reading the top answer from this question How does a country devalue its currency? and it states that buying more of a foreign currency will increase the supply of the yuan. Why and how is that?

Simply because buying country A's currency priced in country B's currency means selling country B's currency.

Simplified but not simplistic example: say that you have 80¥ and want to buy 10€. When buying/demanding these 10€, you will actually simultaneoualy also sell 80¥ i.e. by doing so you become a supplier of (€-priced) yuans. And because selling an asset generally exerts a downward pressure on its price, the price of 1¥ expressed in euros will decrease. Hence the explanation you read.


The Cake Eating Problem with Depreciation (Modelling difficulties) How does one go about modelling the cake eating problem with depreciation? (i.e The cake goes bad over time)

The problem I have is the following.

Lets define a cake eating problem sequentially as:

$$\max_{c_t} \  U(c_t)=\sum_{t=0}^\infty\beta^t\ln(c_t) $$

Subject to:

1.$ \ \  f(k_t)=c_t+x_t$ (resource constraint $c_t$ is consumption, $x_t$ is investment).

2.$ \ \  f(k_t)=k_t$ (Goods defined as dependent on cake size/capital at time $t$ as denoted by $k_t$).

3.$k_{t+1}=(1-\delta)k_t+x_t$ (law of motion).

4.$k_0>0$ (Initial capital stock).

when dealing with the case where $\delta=1$ the problem is fairly straight forward to solve recursively with the bellman equation of:
$$v(k_t)=\max_{k_{t+1}} \left\{\ln(k_t-k_{t+1})+\beta v(k_{t+1}) \right\}$$

However If we were to consider the case of where "the cake goes bad" over time (meaning there is a cost to saving) it seems that modifying the standard framework would be necessary.

This is because if we allow for $\delta\neq0$ we end up with a result of "re-eating" of previously consumed cake. How do we go about addressing this problem?

It would seem that the way you've formulated your production function/law of motion has introduced double counting into the problem. Note that substituting 1 and 2 into 3 gives:
$$k_{t+1}=(1-\delta)(c_t+x_t)+x_t$$
Where investment in period t is counted twice.

The correct law of motion is simply:

$$ 3. \: k_{t+1}=(1-\delta)x_t $$

And the general form of the Bellman equation would be:
$$v(k_t)=\max_{k_{t+1}}\left\{\ln\left(k_t-\frac{k_{t+1}}{1-\delta}\right)+\beta v\left(\frac{k_{t+1}}{1-\delta}\right)\right\}$$

Hope this helps!


What are accepted econometric methods to find out if a time series is I1 or not? An important issue in deciding how to specify an time-series econometric model is deciding whether to use series in levels or in differences (or second differences!). However, to decide this, you often have to find out if the series are integrated or order 1 or not (I1). What are the current accepted tests to find out? Are there trade-offs between the tests? It seems hard to know whether interest rates for example are I1 or not!

An I(1) series is also known as a series with a unit root. Therefore, the econometric tests to inquire on the order of integration of a time-series are referred to as "unit-root tests".

There are three widely used unit-root tests: Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS).

The null hypothesis (H0) in the ADF and PP tests assumes the presence of a unit root. For KPPS it assumes no unit root.

The tests often give different results, and best practice would require to report all three statistics as a robustness check.

There are many drawbacks of using these tests. The major issue lies in the lack of power of PP and ADF to reject H0 when the series is I(0) but close to I(1), that is when the series is highly persistent but stationary. To avoid this low power, other tests have been devised by Elliot, Rothenberg and Stock (1996), as well as Ng and Perron (2001).


2 firms production decision for one agent I'm trying to solve the optimal production $\{x,y\}$ for a risk neutral agent with weight $w$ in firm $X$ and weight $1-w$ in firm $Y$. Each firm has marginal cost $c^X$ and $c^Y$ respectively. The firms face a linear demand where $P(Q)=a-b Q$ and the total production of the economy $Q=x+y$. This risk neutral agent maximizes profits so his/her utility will be:

$U(x,y)=w(x(a-b(x+y)-c^X))+(1-w)(y(a-b(x+y)-c^Y))$

If I take first order conditions to maximize this utility I get:

$(a-2b x-c^X)w-by=0$

$(a-2b y-c^Y)(1-w)-bx=0$

Which solves to:

$x=\frac{(1-w)(2 c^X w-c^Y+a(1-2 w))}{b(1-2w)^2}$

$y=\frac{w(2 c^Y(1- w)-c^X-a(1-2 w))}{b(1-2w)^2}$

Assuming this is all correct, I don't understand why when $w=0$, then $y=0$!!! and $x=\frac{a-c^Y}{b}$ maxing the utility $U(x,y)=0$.

I think this doesn't make sense and can't be the optimum because having $x=0$ and $y=\frac{a-c^Y}{2b}$ (monopoly production) would give $U(x,y)=\frac{(a-c)^2
}{2b}>0$

I must have something wrong, the derivatives and solutions are correct, does anyone see what I'm missing here?

Seems like you are assuming there will be an interior solution.
$$
(a-2b x-c^X)w-by = 0
$$
only needs to hold if the value of $x$ is positive. If it is not, but $x = 0$, the lowest possible amount, then
$$
(a-2b x-c^X)w-by < 0
$$
is not a contradiction. Further decreasing $x$ would increase utility, but it is not possible. Therefore in the case when $w = 0$ and
$$
(a-2b x-c^X)w-by = -by
$$
you do not necessarily have $y = 0$.


On what does currency value depend How is the currency value estimated? Why India has lowest prices to dollar? For example if you buy bread in India it will cost you 1 dollar and in USA 5 dollars

I will answer your question from the economic point of view, not financial. Your question can be understood from several differents positions. Im from Argentina and nowadays Argentina has devaluated the money nearly 50% agains USA dollar. When I analize why, it comes clearly when I see macroeconomics data. Speaking about INDIA, in general terms the relation Country Money/North American Dollar is explained economically with the macroeconomics equilibium result. Lets see what we have in India. The GDP per capita is low, as you can see in the image, meaning that the value added per capita is poor against USA. You can imagine like you do a simple job, may be Rural job, against USA (industrial work) . The Debt (% GDP) is near 68% (think that as you have an important DEBT to attend annually. The Debt Per Capita is near $1183 dollars, so you can imagine that you have that debt. Your Education Expense (% GDP) is 14%, that number is not so great if you want change the economic structural problem and economic development. Health expenditure is near 5%, that is low, so you may be dont have a huge life expectancy, in fact is 68 years!. People in your country tends to Emigrate rather than inmigrate, so imagine that you dont like to much live in India. Each marriage has 2.33 sons and you have a tremendous amount of people to feed (2.400 millons or persons). There is more, you spend the money buying GUNS more than EDUCATION, your Defense Spending %GDP is 14% (very big) and ending, your imports are bigger than your export so you spend more money than you should.

As a conclution, India´s value added is low, so the income is low, India spend few in education and Health but too much in military stuff. India has debt and Buy (gold and crude petroleum) more than sells (diamonds, refined oil). If you have an expensive dollar your petroleum will be more expensive. The value of a Rupia agains USA Dollar is calculated by the Central Bank of India, and it is not easy to explain because it has a complex macroeconomic impact and reasons, but, in general, it needs to be one value that maximize the Indian macroeconomics indicators and gives an improvement trend for the society.


Are there "Grossman/Hart/Moore" models without efficient negotiation outcomes? Sanford Grossman, Oliver Hart, and John Moore have developed a theory of the firm based on incomplete contracting (Hart was awarded the Nobel Prize in 2016 for this branch of the literature). In the Grossman/Hart/Moore model, ex-post negotiations always yield an efficient outcome. (Ownership rights influence only the division of the ex-post surplus, which in turn influences incentives to make investments.) In contrast, Oliver Williamson (who was awarded the Nobel Prize in 2009) emphasizes that ex-post negotiations may well yield inefficient outcomes (see e.g. Williamson’s article on the new institutional economics in the Journal of Economic Literature, 2000). Are there any formal models (assuming standard profit-maximization goals of the firm owners) that somehow incorporate Williamson’s insight in the Grossman/Hart/Moore theory of the firm?

Yes, there are models that reconcile Hart’s property rights theory with Williamson’s emphasis on haggling and ex post inefficiencies.

Hart and Moore have developed a behavioral theory of contracts as reference points. They argue that contractual parties engage in ex post inefficient shading activities when they are aggrieved (which happens when they do not get what they feel entitled to given the reference point that was set by a contract). In this sense, the theory is based on non-standard preferences: Hart, O. and Moore, J. (2008). Contracts as Reference Points, Quarterly Journal of Economics, Vol. 123, pp. 1–48. See also Hart (2009) for an extension of this approach.

Another possibility to formalize ex post inefficiencies in a Grossman/Hart/Moore framework is to allow for asymmetric information: Schmitz, P.W. (2006). Information Gathering, Transaction Costs, and the Property Rights Approach, American Economic Review, Vol. 96, pp. 422–434. This approach maintains the standard assumption of profit-maximizing behavior and studies the trade-off between investment incentives and ex post inefficiencies (see also the more recent contribution by Schmitz (2017) and the literature mentioned there).

Finally, while less related to the Grossman/Hart/Moore framework, there are also models that study property rights in adverse selection models without investments (building on the prominent paper by Myerson and Satterthwaite, 1983), where the optimal ownership allocation minimizes ex post inefficiencies: McKelvey, R.D. and Page, T. (2002). Status quo bias in bargaining: An extension of the Myerson–Satterthwaite theorem with an application to the Coase theorem, Journal of Economic Theory, Vol. 107, pp.336–355. A literature review with particular emphasis on models building on the Myerson/Satterthwaite framework: Segal, I. and Whinston, M.D. (2012), Property rights. Handbook of Organizational Economics, pp. 100–158.


Minimization of costs combination of factors of production Given the production function $D(x,y,z)=\min\{2x, \left( 2y+4z\right)\}$, and knowing that P-price $P_x=30,P_y=20,P_z=5$ and volume of production $D=200$. How much of x,y and z is needed to minimize the costs?

I know that i should write:
$2x=2y+4z=200$ but how to find proper values for x,y and z? I general i think i should write this because those factors are complementary thus each of the "components" of the function should be equal to 200 which is the production volume.

The only thing i've managed to do is to guess the numbers: $x=100,z=50, y=0$.
Is there a method to justify that those numbers will minimize the function?

Working with $\min$ (or $\max$) functions can be tricky, especially if one wants to write down the general solution in a fully rigorous way.

But in your case you have simple linear functions and a numerically given fixed production level ($200$) for which you want to minimize costs.

First, make sure you understand the production function $\min$  expression and what restrictions it poses: A frequently seen initial approach here is to think

"ah, this means either the one, or the other. So I will either use $x$ only, *or* a combination of $y$ and $z$ and perhaps only one from the two. There is no point in buying, say, $x$, if production is to be determined by the a combination of $y$ and $z$".

What is the fallacy in this line of reasoning? And what the resolution of the fallacy implies?

Next, think what it means to want to examine only a given fixed production level: on the right hand side you have the $\min$ function. On the left hand side, you have a specific number, not a general label/symbol anymore.
So you have an equation, not a function anymore. And then you have the cost function. And you want to minimize the cost function given the equation, and given what the "fallacy resolution" mentioned previously implies.

Take it from there.

And please, once you figure it out, post it as an answer here (you can answer your own question is perfectly fine, and even encouraged).


Two Endogenous Variables and Two Instruments I have a model $Z = \alpha X + \beta Y + \gamma C + \epsilon$. I am interested in the relative effects of $X$ and $Y$ on $Z$. However, $X$ and $Y$ are endogenous. I have identified two instruments $X'$ and $Y'$ respectively. $C$ is an exogenous control variable (fixed effect).

How do I go about estimating the model with these two instruments for the two endogenous variables? Do I need to use 3SLS? I am fairly new to this field. Any resources that address this would be very helpful, thank you.

I don't think you need anything like a 3SLS. Just run the first stage for the two endogenous variables separately:

$$\tilde{X}=\alpha_1+\beta_1X'+\beta_2Y'+\beta_3C+\epsilon$$
$$\tilde{Y}=\kappa_1+\gamma_1X'+\gamma_2Y'+\gamma_3C+\delta$$

Then run a regression of Z on the predicted value of $\tilde{X}$, $\tilde{Y}$ as and $C$. If the assumptions are all satisfied, this should give a consistent estimate of the coefficients.

I also found this thread online. It might be helpful.
https://www.stata.com/statalist/archive/2012-08/msg01238.html


Why is investment included in GDP? Why is real investment included in GDP?  I thought GDP is only supposed to measure final goods produced?  I thought capital is an intermediate good but I guess I am wrong. An intermediate good is sold eventually to the customer so prevent double counting we don’t count it. But I guess with capital it is not sold to other firms. Am I correct"

Investment is the value of machinery, plants, and buildings (capital) that are bought by firms for production purposes.

Investment contributes to many macroeconomic situations to include:

A.  Contributes to current demand of capital goods, increasing domestic spending

B.  Modernizes production processes and improving cost effectiveness

C.  Allows for the production of new and improved products, increasing value added in production

D.  Increases production capacity

The Investment types (machinery, plants, buildings) are directly linked to current and future sales (sales of final goods) of the firm.

An intermediate good is defined as the goods and services (including energy, raw materials, semi-finished goods, and services that are purchased from all sources) that are used in the production process to produce other goods or services rather than for final consumption.


How to estimate parameters in a utility function? Utility function is $U = X^aY^b$.

It is a Cobb-Douglas function, and there are data for $X$ and $Y$.

I would like to know how to estimate $a$ and $b$.

as @ts_highbury mentioned above you can take the natural logarithm on both sides of Cobb-Douglas equation $$\ln(U) =a\ln(X)+b\ln(Y)$$ after that "obviously" you can notice the equation became linear in parameters (i.e linear equation), so you can use a various types of estimation methods but most famous also easy one is the Least squares method.

P.S: be careful in interpreting the results after taking the natural logarithm or you can just take the exponentiation on both side of the linear Cobb-Douglas equation (after taking natural logarithm) and you will have the original form of Cobb-Douglas equation.


Market Value Changing in Response to News On May 24th the DJIA dropped and the news has been attributing it to Donald Trump's cancelation of a talk with North Korea (see image below).

My understanding is that the companies making up the DJIA haven't lost any substantial amount of money because of this decision-so why has the DJIA fallen?

In general,

How & Why does this news negatively effect the US economy when the overall value of companies haven't declined?

There are likely two major (and closely related) reasons for this:

First- stock prices aren't purely reflective of what a company is worth today, instead, stock prices reflect the expected future prices as well. Events like this, which increase uncertainty and instability, might change expectations about future stock prices. This is then incorporated into current stock prices, which leads to a fall.

Second- a lot of automated trading algorithms incorporate news keywords into their pricing structures (for example), which can lead to reactions based on the headlines themselves. These can then create a feedback loop with other funds, like ETFs, which trade based on volatility indexes.

I'm sure there are other reasons as well, (perhaps the breakdown in the summit led some traders to reevaluate the relative bargaining power of the US and China in their upcoming summit, which in their mind might lead to an increased likelihood of a trade war, as a hypothetical), though those two can explain many large fluctuations!


Empirically checking efficiency and equity I am aware that because of externalities or public goods (or for other reasons) there can be no allocative efficiency on the market. I am also aware that policy makers' subjective judgement of the situation on the market (if market outcomes are distributed "fair") can be considered as equity in economics.

I wanted to empirically check if government spending can potentially increase efficiency or equity (as I think it should). I took labor productivity (a percentage of GDP) as a measure for efficiency and Gini index in disposable income as a measure for equity. While I am quite convinced with my measure of equity, as Gini tells me about the inequality of income distribution - I am not entirely sure about labor productivity. I am curious if I could choose better statistics to measure either efficiency or equity?

In my results I got that government spending on environment is positively correlated with increase in efficiency in only about 30% cases and in equity in about 50% cases. This seems a little bit counter-intuitive as environment seemed like a textbook example where there is a negative externality, so the firms maximizing their profits based on private costs tend to overproduce - and that the government intervention in that case is justified. So that I thought after the intervention, there should be increase in allocative efficiency, right? But it is a case in only around 30% of cases. What could be a reason for that?

Similarly, government spending on health. To my contention, it should increase both, equity and efficiency - but from what I've got it seems to be true in about 20% of cases. Why would that be a case?

Is it because of the measures I chose? Or my logic was simply wrong and government spending on environment causes efficiency to decrease and on health cases both, efficiency and equity, to decrease?

Several things:

It is not clear that labor productivity as a share of GDP tracks allocative efficiency.  For example, it could rise simply because the returns to capital (capital's share of GDP) are falling, which would most obviously be a consequence of allocative inefficiency through over-investment in capital inputs.  There are potentially many other things that would confound this as an "efficiency" metric.
Gini Index isn't the only measure of inequality, and in fact it doesn't do a very good job of capturing differences in economies at the extremes of their income distributions.
You may have the causal arrow backwards: the most widely accepted model I'm aware of (which is not without controversy, mind you) is that of the Environmental Kuznets Curve, which assumes that wage growth (not labor's share of GDP) drives environmental improvement, not the other way around.
Because "equity" in the probability-distribution sense is attainable both by improving and destroying quality of life (e.g., everyone earns zero dollars), it's not clear that you should expect a positive correlation between this and "environmental spending".  In fact to first-order, your 50% split is consistent with what I've just pointed out.


Is there an economic analysis of the rationality of buying lottery tickets? It's quite clear that the expected return on a lottery ticket is less than 1.

However, I think it can still be argued that buying lottery tickets is still a economically rational decision by consumers.

There are a few lines of reasoning:

The consumer isn't just buying an expected payout, they're buying 'a dream'. Much like watching a fantasy movie or reading a book is an economically rational decision, (even though the story isn't 'real'), the thoughts of 'what would I do if I won the lottery' is a commodity that the consumer is buying.
The value of a lottery payout is worth more than its face value. When analysing the expected return on an ordinary decision, we assume that the return is given in the same context. (For example when Bob is choosing between Stock A, Stock B or saving his money in the bank, regardless of which payout he gets, the rest of his circumstances stay the same). Winning the lottery means, for most us, that we'd quit our jobs, which is worth more than just the payout itself.
It also needs to be considered that the cost of the lotto ticket is often mitigated by that it can also be partially considered as charity.

The question is - is this subject well considered in economics?

Perhaps a good answer would iterate the economic reasoning of buying lottery tickets.

NB. I'm planning asking a separate follow up question regarding point two, question at what lottery payout the expected return increases.

There are definitely economic justifications for playing the lottery, even if all (I hope) players understand that it is unlikely to pay off.

One such justification is that what you actually buy when purchasing a lottery ticket is the fantasy of winning.

Here are a few sources. Lotterys are relatively well understood in economics.

The Economics of Lotteries: A Survey of the Literature(pdf)  - is an excellent article covering basically your entire question. It discusses the microeconomic forces at play, particularly income elasticity and risk aversion.
This source (note: this is now a dead link) has some excellent lecture notes on the market for risk. I recommend it highly. Some basic points are:

people don't want actuarialy fair games, often they would decline a coin flip with a payoff of \$1mil for a win and a cost of \$1m for a loss. Also, an actuarialy favourable game isn't necessarily desirable. If the payoff was \$1.1m people would still decline the game as the cost is just so high. In that sense, a lottery has an advantage. The payoff can be huge but the cost in the event of losing is almost negligible.

Lastly, this source is an article from the NY times. Definitely relevant, highlighting similar points to the first two articles but is a lot more accessible.


The government is issuing massive debt for coronavirus relief - why aren't interest rates rising? As I understand it, the US Treasury Department issues bonds to pay for the government's coronavirus rescue spending. I might have thought that such a large input to the fixed income market on the demand side would increase prices, i.e., that interest rates would rise.

This hasn't happened though, in fact, the opposite seems to have happened. For example, the yields on 10 year treasuries have gone down since the beginning of 2020 (ref).

Why is this happening?

One standard way of determining the fair value of a bond yield (for a country that controls the currency it borrows in) is to say that it is the sum of two factors.

The expected (Geometric) average of the overnight rate (that is set by the central bank) over the life of the bond. This equals the expected return of holding money market instruments instead of the bond.
A term premium, which is compensation for taking the returns risk associated with a bond instead of investing in money markets.

Under this view, the lack of a rise in bond yields is easily understood - almost no market participants expect rate hikes.

It should be noted that there are a variety of academic disagreements with the previous explanation. However, if you browse the FRED database, you will see that during recessions, bond yields fall and deficits rise. This is because the rate expectations view is much closer to reality than supply/demand arguments based on deficits being large.

There should be other related questions on this website, but I did not spot any that were directly useful.

FRED 10-year yield
FRED Federal deficit


Any interior solution for $u(x,y) = min\left \{ x,y \right \}^{2} + max\left \{ x,y \right \}$? Will all the solutions be in the corner or will the cusp in the middle give us any interior solution? This is by the intersection of the budget line.

I am getting this type of a shape:

But I am not sure if there will be interior solution. If there is we can't use differentiation because of the cusp. I think that there will only be corner solutions but it depends on the shape of the indifference curve.

Because the two segments of the IC bend away from the origin, the only possible solutions are at the corners or at $x=y$.

Write $p_x$ and $p_y$ for the prices, and $M$ for the budget.

Suppose we try to set up a corner solution in which only one of the two goods is consumed. Since utility is symmetric, it makes sense to spend all of your money on whichever good is cheaper. Suppose this is good $x$. We then have $x=\frac{M}{p_x}>0=y$ and $u=x$.

The best $x=y$ bundle that can be afforded is such that $x p_x+x p_y=M\iff x=y=\frac{M}{p_x+p_y}$. Utility is then
$$\frac{M^2}{(p_x+p_y)^2}+\frac{M}{p_x+p_y}.$$

You should easily be able to compute a condition on $M$ such that the bundle with $x=y$ is optimal: $$M>\frac{p_y(p_x+p_y)}{p_x}.$$

You can see this dependence on M if we look at a contour plot of the indifference curves:


Using a Logit model to predict unknown outcome Usually when fitting a logit or probit model to data, one has a dependent binary outcome variable (say, university attendance = [0, 1]) and the usual set of independent variables (for the sake of it, say, parent income, gender and some measure of ability).

In my case, things are a bit different. To stay within the example, for my main data set I do not know whether people attended university. The only aspects I have information about are parent income, gender and other independent variables. However, I was able to obtain data on university attendance for a random subset of the data. Using this subset I fitted a logistic model, obtaining coefficients for all independent variables.

How can I use these coefficients to predict the probability of university attendance for everyone else?

[Please note that the education example is only made to simplify things.]

If I understood you correctly, $\Lambda(x_i'\hat\beta)$, where $\Lambda(x) = e^x / (1+e^x)$. You can use predict in both R and Stata. Try in Stata:

clear all
*** Generate data
set obs 10
set seed 1
gen x = rnormal()
gen y = 1+x+rnormal() > 0
replace y = . in 7/10
list
*** Estimate
logit y x
*** Predict
predict phat, p
list

For clarification, I presumed that your outcome variable is in $\{0,1 \}$ (not in $[0,1]$). You observe $y_i$ for some $i$ but not for all, you fitted a logit regression, and then you want to predict the probability for every $i$. Please let me know if I misinterpreted your question.


If Bitcoin becomes a globally accepted store of value, would it be liable to the same problems that mired the gold standard? I am reading this article here that explains why bitcoin is a better store of value than gold.
In sum, here are some of the reasons proposed:

If someday a "bitcoin standard" does come to fruition, would it still be susceptible to the problems that plagued the gold standard?

It would not just be plagued by the same problems it would create some new ones.
Following the Weber (2016) who actually written research exploring exactly the question that you are asking here:

The scope of monetary policy would be more limited under the Bitcoin standard than
under the gold standard. The ability to issue fiduciary currency would give central banks
limited ability to act as lenders of last resort. However, virtually costless arbitrage of Bitcoin across countries would prevent central banks from implementing interest rate policies to affect their domestic economies.

An empirical examination of countries’ experience with the gold standard leads to the
following conjectures about how the Bitcoin standard might perform:

In the long run, there would be moderate deflation that would increase over time until
reaching a rate of deflation equal to the negative of the rate of growth of world output
around 2026.
Price levels of the various countries would be highly, but not perfectly, correlated, much
as they were under the gold standard.
Exchange rates among the fiduciary currencies of various countries would be fixed at
par, because the cost of Bitcoin arbitrage is essentially zero.
There would still be financial crises, because they can occur under any fractional reserve
financial system.

The paper concludes by speculating that even if the Bitcoin standard were to come into
existence, it would not last long, for two reasons: (1) The payments world is changing so
rapidly that there will be a technological innovation that provides a potential medium of
exchange with the same or greater benefits of Bitcoin or with lower costs. Such an innovation
could come either from the private sector or from the government. (2) There would be
pressure to return to a fiat money system so that a more activist monetary policy could be
pursued.

In a nutshell, it would be pretty similar to gold standard but with some extra strings attached that would just additionally constrain monetary policy making it even slightly worse. As a consequence, if Bitcoin standard would ever become adopted it would likely perform even worse than Gold standard did (which is saying something), and would likely go the same way.  You can find more detail on the workings of such standard in the paper itself.

Response to Edit:
The above still applies but let me also respond to the new infographic that was added to the question.

Scarcity - This is exactly why Bitcoin would perform worse, and it is connected to what was written above.
Durability - Given that gold has very long half-life and under gold standard it was mostly stored in vaults not actually used (hence no wear & tear) this never was issue with gold standard.
Portability - Same as above, under gold standard people mostly moved claims to gold, actual gold moved from vault to vault only occasionally. Also note in both Bitcoin and Gold standard people would not pay with Bitcoins or Gold respectively, they pay with banknotes that are backed by either Bitcoin or Gold respectively (and which would be on fixed exchange with banknotes e.g. 1USD=0.1 Bitcoin for example).
Divisibility - This is moot point. You can have 0.000001 troy ounce. In fact gold is for all practical purposes infinitely divisible (up to the scale of individual atoms of course).
Storage - this was never significant issue with gold standard, in addition people still store investment gold in vaults its just not tied to money.
Counterfeit - Again completely moot point. Under gold standard gold would mostly just sit in vaults. People would not pay with gold coins. Banknotes backed by either Bitcoin or gold would be equally difficult to counterfeit as regular fiat banknotes since that is what people would be using as money under Bitcoin standard.
Adoption - Again not relevant, if we talk about Bitcoin standard adoption requires fixed exchange between a currency and Bitcoin - to my best knowledge no country did this to the date. Also, I never heard of use of market capitalization as measure of adoption when it comes to monetary system so the metric does not provide any argument either in favor of gold or Bitcoin.


What are the best books for developing a solid understanding of fundamentals of Economics? Recently, Raghuram Rajan, a former chief economist at the International Monetary Fund and current Governor of central bank of India, while addressing undergraduate students of Economics, said:

  ... In this country there is a tremendous need for capable economists. I see that every day in my work. There is a need in Delhi, in Mumbai and all over the country. We have lost a generation of economists...The kind of economics we need is based on a good understanding of the fundamentals of economics, such as price theory and general equilibrium, which is the hardest concept to understand. A lot of policy-making is done without an understanding of general equilibrium which is often the key contribution that an economist can make to the dialog. The kind of economics we need is based on rigorous fundamentals – blood, sweat, tears, and toil. ...

I am a student of public policy in India, aiming to achieve a key position in public policy making. As much as his above statements make me worry at many levels, they also set a a goal for me to achieve.

In this context, given my background, what do I read to gain "that expected level" of understanding? How should my learning path look like?

EDIT: I'm asked to provide my mathematical background. I have done following undergrad math courses:

Algebra
Linear Algebra
Real Analysis
Complex Analysis
Calculus
Analytic Geometry
Ordinary Differential Equations
Partial Differential Equations
Linear Algebra
Vector Analysis
Linear Programming
Numerical Analysis and Computer programming
Dynamics & Statics
Mechanics and Fluid Dynamics

You can say, I can solve most of the problems from undergrad textbooks on above subjects. I dealt with statistics only at my Senior High School level.

Read Hal Varian's textbook "Microeconomic Analysis". It's brief, yet a standard text in a 4th year or graduate course in advanced micro.  Then grab a good book on mathematical economics that's actually well written, and includes suggestions on how to develop good mathematical intuition, not just a bunch of recipes on how to solve problems.  For example, you can learn how to use determinants in matrix algebra, but how many actually know what a determinant is, both algebraically and geometrically? That's the blood, sweat, and tears bit, I think.   I suggest the two volumes by Knut Sydsaeter (check Amazon)

You may also want to learn some advanced macroeconomic theory, and some spatial, urban and resource economics.

Take a good course in econometrics, and learn a programming language like Python or Julia so your are not always beholden to other people to provide you with data, which may be dirty or faulty, but you won't know it.

Watch lots of Youtube videos on economics, esp. controversial topics. Take some cool courses on Coursera or other MOOCS. They are often from some of the top universities in the world, and they are free.

OK, so now you have some basic tools; if you enjoy using them, and find that real work gets done, why not go to graduate school?

Then go practice for 20 years, and keep in mind that some aspects of economics may just be bunk anyway, so stay modest, don't get too overly seduced by beautiful models.


Strong sequential equilibria and the existence of others I am working on the following game

and I have to find all strong sequential equilibria here.
I determined that here any belief derived from a fully mixed strategy gives a distribution (1/2, 1/2) over the nodes in Player 2’s information set. Given this, player 2 will chose r and player 1 will chose y. I believe that this is the unique sequential equilibrium. But is it strong?
And are there any other Nash equilibria and if so why they are not sequential?
Thanks!

There are three classes of equilibria of this game.

The first class is sequential:
\begin{equation}
(s_1,s_2)=(y,r)
\end{equation}
and the beliefs are
\begin{equation}
\mu_1(a)=\mu_1(b)=\mu_2(a\mid y)=\mu_2(b\mid y)=\frac12.
\end{equation}

The second class is not sequential, but weak perfect Bayesian:
\begin{equation}
(s_1,s_2)=(x,l)
\end{equation}
and the beliefs are
\begin{equation}
\mu_1(a)=\mu_1(b)=\frac12,\quad\text{but }\mu_2(a\mid y)=1-\mu_2(b\mid y)=p>\frac58.
\end{equation}

The third class is actually a boundary case of the second class, which permits P2 to use mixed strategies. This equilibrium requires P2's off equilibrium belief to be
\begin{equation}
\mu_2(a\mid y)=1-\mu_2(b\mid y)=\frac58,
\end{equation}
so that P2 can play a mixed strategy that puts sufficiently high probability on $l$ ($\sigma_2(l)\ge\frac35$). It is also necessary that P1 does not play $y$ with positive probability, because if they do, Bayes rule would kick in, requiring that P2's belief be $(\frac12,\frac12)$ instead of $(\frac58,\frac38)$ which rationalizes P2's mixed strategy.


Find Price Elasticity of Demand for p = 0 Given a linear demand curve $q(p) = a - bp$, how would one find the price elasticity of demand at $p = 0$? The quantity that would be demanded is given: $Q_0 = a$

The formula for the price elasticity of demand then dictates:

$\epsilon_{p=0} = \frac{dq}{dp} *\frac {p}{q} = -b * \frac{p}{a} = -b * \frac{0}{a}= 0$,

this would mean perfectly inelastic. Thus, no matter the change in price there should be no change in quantity. This does not seem to make sense as at this point demand should be the most elastic. Where did I go wrong?

As an example one could think of a free good (e.g. straws), the demand for which can be observed. Then a levy is imposed and the new demand is being observed, allowing one to derive a linear demand function. How would one find the price elasticity for straws when they are free ($p=0$)?

The Answer can be found in the comments by user brunosalcedo:

"Remember that elasticity measures percentual rates of change. How does q change per unit of percentual change of p? If $p=0$, then any percentual change of p results in no change at all because 0 multiplied by any number is 0. The elasticity is not just 0 at p=0, it is also continuous at $p=0$. If you compute the elasticity for small but positive prices, and then take the limit as p goes to 0, the limit is 0."


How to measure home value distribution in a city? I would like to know how I can measure and compare the distributions of home values across cities. I have collected the following data for each city:

a) median price in the city;

b) number of housing units by value range, such as
500 units between \$100k-200k,
300 units between \$200k-300k,
600 units between \$300k-400k, etc;

c)Lower value quartile of housing units;

d)higher value quartile of housing units.

I know some of these cities have a lot high-end homes but few low-end homes while others have a lot of low-end homes but few high-end homes. Can I develop an index to measure that?

When it comes to constructing indices, the axiomatic approach is the standard approach in the economics literature.

An axiom is a property you would like your index to satisfy. For instance, in your example, you would probably wan your index to increase when the distribution in b) changes from $X$ to $Y$ and $Y$ first order stochastically dominates $X$.

You can require your index to satisfy the above property, as well as others, and hope that as you impose more and more desirable properties, you will narrow down the class of acceptable indices to a single index.

Now, such axiomatic characterization (i.e. proving that index $I$ is the only index that satisfies a set of properties) is typically not an easy task. As a matter of fact, some very fine researchers have made their whole career out of these kinds of characterization results.

These characterizations are also very much context dependent. Although there are some general results out there characterizing price indices (see https://scholar.google.be/scholar?q=axiomatic+price+index&btnG=&hl=nl&as_sdt=0%2C43) they might not be directly amenable to your problem .

(I don’t know enough about the topic to tell you whether something like an axiomatic theory of housing price indices already exists. It’s not impossible that it does, but I just don’t know.)

Depending on how much time you want to put into this, here is what I would do if I were you:

Learn about axiomatic price index theory ( again see https://scholar.google.be/scholar?q=axiomatic+price+index&btnG=&hl=nl&as_sdt=0%2C43 as well as Afriat, S. (2014). The index number problem: construction theorems (1st ed). Oxford ; New York: Oxford University Press. and
Diewert, W. (1988). The early history of price index research. Retrieved from http://www.nber.org/papers/w2713)
If you learn about an already existing theory of housing price indices, just pick the index you like best among the ones in the literature.
Otherwise, try to see if you can adapt some of the general price indices in the literature to your housing case.
In last resort, develop an axiomatic theory of your own.

If you have the time and ability, you can try to obtain characterization and publish nice research papers on the topic.
Otherwise, you can still use the axiomatic approach to craft an index that satisfies some of the properties you think are the most important. Just list those properties, and start looking for an index that does the job.
If you can’t find one, don’t disappear. It may be due to a lack of creativity, but it may also be that you have imposed so many properties that there does not even exist an index satisfying all of them (this is called an “impossibility result” in the axiomatic literature).
Just start relaxing or dropping properties one at the time up to the point where you find an index that works. Then if you still have the time and energy, start re-adding some of the properties you dropped, one at the time, and see if you can find a new index that works.


What did the Swiss National Bank use to purchase EUR while pegging the Franc to the Euro? To peg its currency (CHF) to the Euro (EUR), the Swiss National Bank (SNB) made purchases of EUR to the tune of several hundred billion.  By reducing the supply of EUR, the SNB made the EUR relatively valuable, achieving the peg.

But how did the SNB fund its EUR purchases?  My original assumption was that the SNB simply printed CHF to buy EUR.  Is this correct?

The reason I ask is (a) I have not been able to find explicit documentation of this and (b) a colleague suggested that the SNB may have been using other means to purchase EUR, such as tapping into gold reserves or other kinds of reserves.

This quotation by Michael Bordo, Owen F Humpage, and Anna J Schwartz (2012) was the richest description I could find on how the SNB achieved the floor:

  In March 2008, the Swiss National Bank eased monetary policy in
  response to expectations of deflation, deteriorating economic
  conditions, financial-market distress, and a Swiss franc appreciation
  that resulted from the global financial crisis. In conjunction with
  this action, the Bank aggressively bought euros in the
  foreign-exchange market in 2009. Throughout March and April 2009, the
  Swiss National Bank did not seem to sterilise its substantial
  foreign-exchange purchases; the Swiss monetary base rose by more than
  the value of foreign assets on the Bank’s books. In response, the
  Swiss franc depreciated. By April 2009, however, the Swiss monetary
  base had more than doubled from a year earlier, and the Bank – now
  concerned about latent inflation – began to sterilise the liquidity
  resulting from its huge interventions. The Swiss interventions
  continued through June 2010, but the Swiss monetary base either grew
  by less than the Swiss National Bank’s holdings of foreign assets, or
  the monetary base actually declined. The Bank was clearly sterilising
  the operations, and the franc appreciated by nearly 10% between April
  2009 and June 2010. On balance, from May 2010 to August 2011, the
  Swiss monetary base contracted and the franc appreciated, reaching an
  historic high on a real trade-weighted basis.

  In early August 2011, the Swiss National Bank announced a series of
  new measures to inject liquidity into financial markets with the
  objective of stemming the Swiss franc’s appreciation. The operations
  included foreign-exchange swaps in which the Bank sold francs spot and
  repurchased them forward. The franc depreciated sharply, but undertook
  a stunning reversal late in the month. The Swiss National Bank then
  announced that it was prepared to buy foreign exchange in unlimited
  quantities to maintain a floor of SF 1.20 vis-à-vis the euro. The
  Bank’s holdings of foreign exchange increased substantially, but the
  Swiss monetary base increased by even more. Since September, the Swiss
  National Bank has maintained an exchange-rate floor, by giving up
  control of its monetary base in conformity to the fundamental
  trilemma.

Foreign-exchange intervention and the fundamental trilemma of international finance: Notes for currency wars

If they are not controlling their monetary base they probably be doing standard currency interventions. That is, they credit their own accounts at banks with CHF, then using those credited accounts to purchase Euro denominated assets. Or perhaps, they enter into spot Euro-CHF FX transactions and use the proceeds to buy Euro denominated assets. If they were selling gold then they'd sell gold for dollars and buy euros with dollars. That might modestly move the Euro-USD  exchange rate but would affect the Euro-CHF rate only indirectly. But the Swiss monetary base shouldn't be increasing.


In the long run, would a production-possibility curve expand outward if the country preferred more consumer goods than capital goods? PPC will not expand outward if the country preferred more consumer
  goods than capital goods.

  The total amount of resources in an economy at any given point of time
  is fixed. If a country preferred more consumer goods, more resource
  has to be allocated to produce the consumer goods. It will lead to a
  sacrifice of the production of capital goods. In a long run, the
  production of consumer goods is difficult to expand since the capital
  goods’ restriction.

This is my answer to the question. But I'm not sure if it's good enough. Any suggestion would be appreciated.

To keep things simple, let's assume that inputs to production other than capital goods are constant over time, and that production technology is regarded as one of those inputs (ie there is no technical progress).  Let's also assume that the production function is such that output (across the whole range of the production possibility frontier) is an increasing function of capital when other inputs are constant: in symbols $\partial{Y}/\partial{K}>0$.

The question then is whether capital and therefore output can increase given the country's "preference for more consumer goods than capital goods".  If this simply means that its chosen output combination includes a higher proportion of consumer goods than capital goods, then that is certainly possible.  Suppose for example that output consists of $80\%$ consumer goods and $20\%$ capital goods, that the annual capital-output ratio is $2$, and that $5\%$ of capital is lost each year due to wear and tear.  Then the annual loss of capital due to wear and tear is $2 \times 5\% = 10\%$ of output, and capital goods increase each year by $20\% - 10\% = 10\%$.  Thus the production-possibility frontier would expand outwards.

If however the country's preference implies that output contains less than $10\%$ of capital goods, then (on the above assumptions) the production possibility frontier would contract inwards over time.

Note that the above takes no account of the fact that, in practice, capital goods are not infinitely malleable, that is, the production of different goods requires different sorts of capital goods. One might pursue that point by considering how a country's preference for consumer goods might influence its choice of what sort of capital goods to produce (if indeed it produces any).


Coase theorem study material I'd like to read a more detailed/mathematical analysis on the subject of Coase's theorem. Could you perhaps suggest any advanced textbook/paper on the matter?

The Public Choice III by D. C. Mueller has whole chapter with mathematical exposition of the Coase theorem. His exposition includes both the general case and practical examples. Also I think Mueller strikes very good balance between rigor and simplicity.
You will also find some treatment of the theorem from Game Theory perspective in Game Theory: An Introduction by Steven Tadelis or the Tirol's Game Theory but only relatively briefly when compared to Public Choice III. Also Tirol's The Theory of Industrial Organization has some treatment but again relatively short. Nonetheless despite that these other texts only deal with the theorem briefly expositions of the theorem in different situations which itself has wide application may help you.
If you would prefer some paper then for example you can see application and exposition of Coase Theorem here, but papers are rarely written with didactic motive in mind so if you are self-studying I would recommend the textbook sources above.


Interpeting equivalent annual cash flows So i have this question:

RainMan Inc. is in the business of producing rain upon request. They must decide between two investment projects; a new airplane for seeding rain clouds or a new weather control machine built by Dr. Nutzbaum. The discount rate for the new airplane is 9%, while the discount rate for the weather machine is 39% (it happens to be higher risk). Which investment should the company select and why?

Cash flow of airplane= -900,500,600 (life span of 2 years)
Cash flow of weather machine=-900,550,600,685 (life span of 3 years)

I proceed calculating the NPV of the airplane=63.72 and the NPV of the weather machine=61.29.

I calculate the annuity factor of the airplane which is 1.759 and the annuity factor of the weather machine which is 1.60935.

Then the annuity payment of the airplane is 36.38 and the annuity payment of the weather machine is 38.08.

It would appear to me that since the annuity payment (or the equivalent annual annuity) of the payment is lower, then it should be chosen

HOWEVER! Thesere are the possible answers to the question :

A) Airplane, because it has a higher equivalent annual cash flow

B) Airplane, because it has a higher NPV

C) Weather machine, because it has a higher NPV

D) Weather machine, because it has a higher equivalent annual cash flow

The answer on the sheet states to choose D. It says that since they have different life spans the weather machine has a higher EAA and should be accepted.

My current knowledge has taught me to choose the project with the lowest equivalent annual annuity . Other questions on my text book had answers that preffered projects with lower equivalent annual annuities.

Then what am i doing wrong ? Am i confusing the equivalent annual cost principle with the equivalent annual annuity approach which states to choose the project with the highest equivalent annuity ?

I am quite confused since the methods used to calculate the EAA and the EAC appear to be the same on my answer sheet ( different questions obviously ) but yet this question tells me to choose the highest annuity payment and some the lowest?

The other question in which the answer was to choose the project with the lowest EAC is this:

Two machines, A and B, which perform the same functions, have the following costs and lives. Machine A has a PV of costs of 6000 and its life is equal to 5 years. Machine B has a PV of costs of 8000 and its life is 7 years. Which machine would you choose? The two machines are mutually exclusive and the cost of
capital is 15 percent.

Yet again i would still do the same process (other than calculating the NPV which is already states) and i would come to the conclusion that the EAC(A) is 1789.89 and the EAC(B) is 1922.88.

The possible answers to this question are:

A) Machine B, because it has longer life

B) Machine A, because it has lower PV costs

C) Machine B, because the EAC is $1,922.88

D) Machine A, because the EAC is $1,789.89

Then obviously I would choose D (which is correct since the EAC of machine A is 1789.89 which is indeed lower than B)

Please explain in the simplest way possible what i am not understanding. Thank you !

You're missing the distinction between costs and benefits. In your first probem you have positive NPVs and therefore the equivalent annual value is the equivalent annual cashflows that comes in.

In your second problem you have costs only. Converting that that to an EAV means converting it to an annual cash flow that goes out. Obviously you want the former to be as large as possible and the latter to be as small as possible.


Meaning of Additively Separable, Linear in X Often I see both in micro and macro two common terminology :

Additively separable.
Linear in price or linear in probability.

I understand exactly as they sound  by looking at the functional form of the object.

But can someone provide why these structures or assumptions are sensible or unreasonable and why they are "convenient" or "useful"? The context can be anything consumer, producer, choice under uncertainty, game theory or GE. But trying to see why it is repeatedly coming up and why it is important or mathematically useful in many parts both in micro and macro.

A utility function is additively separable if it can be written as:
$U(x,y) = u(x) + v(y)$

Examples:

*$U(x,y) =ax + by$ is additively separable by inspection.

*$U(x,y) = ax + bx2 + cy$ is also.

*$U(x,y) = x^a y^b$ is additively separable, because you can write it as  $U(x,y) = log(x^a)+log(y^b)=alog(x)+b log(y)= u(x) + v(y)$

*$U(x,y) = \frac{xy}{x+y}$ is not additively separable because there's no way to transform it into an independent sub-function of $x, y$. Even if you take logs, you're down to $U = log(x) + log(y) - log(x+y)$ - notice that the third term can't be 'split'. Generally, mixing addition, multiplication and exponentiation will destroy additive separability.

And so we can see, The actual definition of additive separability is:

A function $f(x_1,...,x_n)$ is AS if it can be rewritten as $f(x_1,...,x_n)=f_1(x_1)+...+f_n(x_n)$

The assumption is usually one of mathematical convenience. For example, when utility is additively separable in $x,y$, then the marginal utility of $x$ does not depend on the level of $y$, and vice-versa. And so anything requiring the use of partial derivatives is made easier. Is it a reasonable assumption? Sometimes. For example, if your utility depends on apples and horses, we can probably assume additive separability. If Instead your utility depends on two closely related things, it might be a bad assumption.


Name of a certain economic fallacy I remember seeing a fallacy mentioned concerning the different valuations you put on something just because you own it. I would like a link to the discussion of that fallacy. Thanks.

The endowment effect is the hypothesis that people ascribe more value to things merely because they own them.


Is net neutrality not important in a competitive market of internet providers? In my understanding, allowing ISP to throttle sites that use a lot of traffic is just price discrimination. The ISP will charge sites like Netflix, which will then pass the cost to Netflix consumers. So basically people who use a lot of data will get charged more--seems perfectly fine to me.

I understand the argument that in practice, the ISP won't build new infrastructure but simply put up roadblock to slow down the current speed. However, this seems like a problem only in the oligopolistic market of US internet providers. In a competitive market, putting up roadblock will cause an exodus to competitors.

So, am I correct in thinking that preserving Net Neutrality is not important in a competitive telecom market? Instead of fighting to preserve Net Neutrality, may be the correct fight is to encourage more ISP to enter the market.

Yes, if there were more competition then net neutrality would not be such a big issue. Any throttling would cause an ISP to lose customers to competitors.

Competition is a main assumption behind why markets work. However, in this case an ISP has market power which breaks the assumption. The market power allows them to easily put smaller ISPs out of business.

Here is a link to a rather long article on how ISPs get this market power. Essentially, the reason is that starting an ISP is entering an economy of scale, which requires a large amount of capital to start: http://arstechnica.com/business/2014/04/one-big-reason-we-lack-internet-competition-starting-an-isp-is-really-hard/


Data on Individual Performance of Franchises I am doing a research project on the effect of market sharing agreements on the profits of franchises, and I would like to get some empirical data to guide my analysis. Are large franchises required to publish data on the individual performance of their franchisees? I looked on the McDonald's website, and found a huge amount of legal information, but I am not sure which documents, if any, are relevant to me. What would be the best place to look for this kind of data? I would like anything possible, but especially data on sales, profits, etc. over time. Thanks!

It depends on how detailed you your data want, but in the case of McDonald's or Wendy's, you can find some data in their annual reports. They split their total revenues and costs into company-operated and franchised restaurants.

Hope that helps you


Non-trivial steady state Consider the growth model with inelastic labor supply, full depreciation, log utility and CRS technology with the Bellman equation be defined as follows:
$$V(k)=\max(log(k^\alpha-k')+\beta V(k'))$$
st $$k\geq0\ \text{and}\ \theta k^\alpha-k'\geq0$$
As a guess I have used the usual $V(k)=a+bln(k)$ substituted on the Bellman and have derived $k'=\frac{k^\alpha\beta b}{1+\beta b}$. From this I have found the $k_{ss}=(\frac{1+\beta b}{\beta b})^{1/(\alpha-1)}$ called the non-trivial SS
This is the first SS while the other is $k_{ss}=0$
My question is how can we use the policy function to show that the system converges to the non-trivial steady steady state given any $k_0 > 0$

Let's guess that the value function is of the form $a + b \ln(k)$.
Then substituting for $V(k) = a + b \ln(k)$ in the Bellman equation gives:
$$
a + b \ln(k) = \max_{k'}\left(\ln(k^\alpha - k') + \beta(a + b \ln(k')\right)
$$
The first order condition is given by:
$$
\begin{align*}
&\frac{-1}{k^\alpha - k'} + \beta b \frac{1}{k'} = 0,\\
\to & k' = \beta b (k^\alpha - k'),\\
\to & k' = \frac{\beta b}{1+ \beta b} k^\alpha
\end{align*}
$$
If we plug this  into the objective function of the Bellman equation, we obtain the following identity:
$$
\begin{align*}
a + b \ln(k) &= \ln\left(k^\alpha - \frac{\beta b}{1 + \beta b}k^\alpha\right) + \beta\left(a + b \ln\left(\frac{\beta b}{1 + \beta b}k^\alpha\right)\right),\\
&= (\alpha + \beta b \alpha) \ln(k) + \ln\left(1 - \frac{\beta b}{1 + \beta b}\right) + \beta a + \beta b \ln\left(\frac{\beta b}{1 + \beta b}\right)
\end{align*}
$$
As this holds for all $k (> 0)$ we can equate coefficients on both sides:
$$
\begin{align*}
a &= \ln\left(\frac{1}{1 + \beta b}\right) + \beta a + \beta b \ln\left(\frac{\beta b}{1 + \beta b}\right),\\
b & = \alpha + \beta b \alpha
\end{align*}
$$
The second one gives a closed form expression for $b$:
$$
b = \frac{\alpha}{1 - \beta \alpha}.
$$
Then substituting this into the first order condition gives:
$$
\begin{align*}
k_{t+1} &= \frac{\beta \frac{\alpha}{1 - \beta \alpha}}{1 + \beta \frac{\alpha}{1 - \beta \alpha}}k_t^\alpha,\\
&= \beta \alpha k^\alpha_t \tag{1}
\end{align*}
$$
This shows that:
$$
k_{t + 1} > k_t \iff \beta \alpha k_t^\alpha > k_t \iff k_t < (\beta \alpha)^{\frac{1}{1 - \alpha}}
$$
So the capital stock will rise as long as $k_t$ is below $(\beta \alpha)^{\frac{1}{1 - \alpha}}$ and it will decrease if $k_t$ it is above this threshold.
According to the dynamic equation (1) above, it would appear that $k = 0$ is also a steady state. However, for $k = 0$, the first order conditions are not satisfied and in fact the value function does not exist. Anyway, for $k_t$ very close, it's value will be below $(\beta \alpha)^{\frac{1}{1 - \alpha}}$ so the stock of capital should increase to the unique steady state.


In Diamond's OLG model, why is capital equal to saving by the young in previous period? In Diamond's OLG model, why is capital in the next period equal to total savings by the young in the current period?

What happeend to the pre-existing capital? Surely it doesn't just cease to exist?
I know it belongs to the old who die, but just because they die doesn't mean the capital disappears?

Property rights and assuming away bequest motives (the Old do no care about the Young).

Capital of the previous period belongs to the Old, and since they will die at the and of old age, the finite-horizon transversality condition for utility maximization requires that either all assets have been consumed at the time of death, or that they have no utility-enhancing potential. Since the utility function reflects the "more is better" property, assets do have value as consumption down to the last bolt, and since there is no bequest motive, no utility from "leaving something for your children", it follows that the Old will consume all their capital, being utility maximizers.


Why does one have to ask for a quote to get a price for some things? When ordering items from some companies, they don't have their prices listed. One rather has to ask for a quote to get a price, having to provide information to do so. Why is this? Why do they not just show a price? Is the only point to get customer information or are there other reasons? This is with the product model number and quantity already known.

I believe that prices are typically available for well-defined products that dont vary between customers (e.g. groceries, cars, etc.). Whereas some products are customer specific (more so on the business to business side) and depend on quantity and quality simultaneously. I think of the example of a landscaping job (a service) that would depend on how much time the job would take (labour inputs) as well as the type of machinery (capital inputs) that would be needed to get the job done. Another example would be buying paper for an office, the cost would depend on how much you are buying and what quality and every companies needs would be entirely different.


OLS bias in demand estimation: the bias always underestimate the demand's elasticity? Some papers argue that OLS can produce less bias than IV estimation depending on the quality of your instruments. Suppose we consider a demand estimation equation.

Suppose the demand elasticity is negative in OLS. By my intuition weak instruments should produce biased estimates towards OLS, but no less negative. Can you guys produce an example? I cannot really grasp how it could lead to a more biased estimation with IV estimation.

Usually, $\hat{\beta_1^{IV}} = \beta_1 + \frac{cov(z,u)}{cov(z,x)}$.  The denominator will go to zero.

That is true unless there is some correlation between the instrument and the error term, and the nominator is the strength of the relationship between the instrument and the endogenous variable. The smaller the denominator gets, the greater the bias $\left[\frac{cov(z,u)}{cov(z,x)}\right]$.

In addition,  weak instrument will have no precision, so that the variance will have a big upward bias.
\begin{eqnarray} var(\hat{\beta_1}) &\to_p& \frac{\sigma^2}{n \sigma^2_x} \nonumber \\
\hat{\beta_1^{IV}} &=& \frac{\sum (z_i - \bar{z})y_i}{\sum(z_i - \bar{z})x_i} = \beta_1 + \frac{\sum (z_i - \bar{z})u_i}{\sum(z_i - \bar{z})x_i} \nonumber \\
var(\hat{\beta_1^{IV}} &=& var \left( \frac{\sum (z_i - \bar{z})u_i}{\sum(z_i - \bar{z})x_i} \right) \nonumber\\
var(u | z) &=& \sigma^2 \nonumber\\
var(\hat{\beta_1^{IV}}) &=& \frac{\sigma^2 \frac{1}{n} \sum (z_i - \bar{z})}{n[ \frac{1}{n} \sum (z_i - \bar{z})(x_i - \bar{x})]^2} \nonumber
\end{eqnarray}

As $n \to \inf$
\begin{eqnarray} var(\hat{\beta_1^{IV}}) &\to_p& \frac{\sigma^2 \sigma_z^2 }{\sigma^2_{zx}} \nonumber\\
var(\hat{\beta_1^{IV}}) &\to_p&  \sigma^2 \frac{1}{n \sigma^2_x} \frac{1}{\rho^2_{xz}}\nonumber \\
\rho^2_{xz} &=& \frac{[\sigma^2 _{xz}]^2}{\sigma_x^2 \sigma_z^2} \textit{for} \rho \in [0,1]\nonumber
\end{eqnarray}

That is why if your instrument is weak, then you  may be better off running an OLS regression.


Normalizing comparisons of corporations and countries When publicly-traded corporations reach record valuations, articles in the media often compare such valuations to the GDPs of countries throughout the world, typically in the form "Company X's valuation of Y is now larger than the GDP of all but Z of the world's countries..."

For example, a Fortune article from Nov. 2014 states:

  At this point, Apple’s market cap is higher than the gross domestic
  product of all but 19 of the world’s countries, coming just behind
  Saudi Arabia (GDP of \$745 billion) and ahead of Switzerland (\$650
  billion), according to data compiled by the World Bank.

This doesn't seem like a meaningful comparison to make, given that GDP and market cap are very different metrics.

Similarly, a Business Insider article compares corporate revenue to countries' GDPs. This is intuitively a better comparison than market cap to GDP, but wouldn't comparing profits to GDP be a more accurate measure?

In summary, what are the best metrics for comparing the performance of companies to the performance of national economies?

GDP is a flow (of goods and services) while market capitalization is a stock measure. So I agree, this is not a great comparison. If we want to compare stocks, we'd compare total enterprise value (sum of equity and debt) to national domestic assets. But that's imperfect because much of what makes a country rich is labor income and that's not going to be in domestic assets. So we'd like to add in some measure of human capital. That's going to be imperfect at best. So I prefer to compare flows.

Consider how GDP is a value added measure. If you import steel for 150 and export cars you make out of that steel for 250 the GDP contribution is 100. Some of that 100 went to capital and some to labor. What's the value added of the corporation? Think of the company as "importing" the goods it buys and "exporting" the goods it sells. The difference is paid out to three sources, equity capital, debt capital, and and wages paid to labor. So to make a number comparable to GDP, add together corporate profits, net income expense, and labor costs. This is the value added of the firm and much more analogous to GDP than firm value.


Converting word definitions of Pareto-Optimal into math symbols I'd like to have a mathematical version of the following two definitions just because I remember symbols better than words. But I lack the math prowess to convert them from words to symbols. Can someone assist me?

Def 1:

A feasible allocation is weakly Pareto-optimal if there is no alternative (feasible) allocation such that everyone prefers the alternative to the original.

Def 2:

A feasible allocation is strongly Pareto-optimal if there is no alternative (feasible) allocation such that at least one person prefersthe alternative, and everyone else is indifferent.

Let $\Omega$ be the set of all feasible allocations with an element $\omega \in \Omega$.  Consider $I$ agents such that the utility of agent $i$ is described by $u_i(\omega)$.

Definition 1: $\omega \in \Omega$ is weakly Pareto-optimal if $\nexists \omega' \in \Omega$ such that $\forall i$ $u_i(\omega') > u_i(\omega)$.  Weak Pareto-optimality is basically just saying that for any other allocation, $\omega'$, in the set of feasible allocations that not everyone can strictly prefer the alternative.

Definition 2: $\omega \in \Omega$ is strongly Pareto-optimal if $\nexists \omega' \in \Omega$ such that $\forall i$ $u_i(\omega') \geq u_i(\omega)$ with strict inequality for at least one $i$.  Strong Pareto-optimality is a little stronger in the sense that your allocation must be strictly preferred by some to all other allocations and everyone else can be indifferent.

I hope that is helpful.


Why will these steps NOT fix the problems with LIBOR? I am new to finance and recently came across the LIBOR scandal that happened some time in 2008. From my limited understanding of finance, it looks like a scandal that was obviously going to happen and the fix also seems obvious. Clearly, the fix I suggest has issues, or else they would've already been implemented. I want to understand why my proposed solutions will not work.

Here's some background on LIBOR and the scandal. LIBOR is an index maintained by Thomson Reuters on behalf of the British Bankers' Association that attempts to track the interest rate at which world's major banks are borrowing and lending from each other on a daily basis. It is calculated by asking 18 main banks the question "At what rate could you borrow funds, were you to do so by asking for and then accepting interbank offers in a reasonable market size just prior to 11am?" and then taking the average of the numbers reported after removing the top 4 and the bottom 4. Some time in 2008, the people responsible for answering the question started collaborating with each other and reporting incorrect interest rates in order to manipulate Thomson Reuters' calculations. This was good for the participating banks but bad for the world in general since several financial products traded throughout the world are defined in terms of the LIBOR rate and thus misreporting could potentially lead to harmful effects worldwide.

From what I understand after reading many articles, the two main incentives that lead a bank to misreport its borrowing rates are: 1) reporting a higher borrowing rate is bad for your own reputation since if everyone is charging you high rates on loans then it means they don't trust you, 2) if you are one of those 18 banks that are polled for calculating LIBOR and you also happen to be dealing in a financial product that is defined based on LIBOR, then you might be incentivised to manipulate it.

Here is my proposed solution. Following things can be done to handle #1:

Anonymize the answers. Thomson Reuters doesn't need to know exactly which bank reported what. All it needs is the 18 numbers from 18 different banks. Anonymizing should be easy to do with the help of technology. Or law, i.e., Thomson Reuters can promise to not reveal the data to anyone. The technological solution will probably be less prone to future scandals than the legal one.

Instead of asking what rate a bank can borrow at, ask them what rate they will lend at. Of course you will need to specify "to which bank". So do this for each pair of banks. Ask each bank A what rate it will lend at to each bank B. You can't manipulate your own image by answering incorrectly. The only thing you can potentially do is manipulate another bank's image. But with roughly 18^2 numbers to look at, I am sure you can detect a lot of manipulation attempts. For someone to make one specific bank to look bad, they will have to collaborate with several banks at once and ask them to report poor lending rates for that specific bank.

To handle #2, the obvious way is to take the median instead of the mean. Median is much more resilient to manipulation than mean. All 18 banks will have to collaborate to be able to manipulate the median. Is it possible that all of them want LIBOR rate to move in the same direction? Even if it is, I imagine it will be much harder for all of them to collaborate at once.

Finally, one solution to all these problems is to base LIBOR on the actual rates at which trades are being made as opposed to the estimates of those rates. I guess this one will be hard to implement because if the trades are happening over the counter then the records will not be public. And there is probably no way to force the banks to trade on some sort of exchange without invoking law, which as we have seen, is always open to manipulation.

Rather than answer regarding your specific proposal, as that would be of less use generally than providing the current state of thought about interest rate benchmarks, I will provide a quick review of the literature, allowing you to think more generally about the issue.

Regarding LIBOR specifically, the Wheatley Review of LIBOR was the foundational document outlining the general issues with LIBOR and setting a path for reform. After this review, the International Organization of Securities Commissions (IOSCO) published a report, "Principles for Financial Benchmarks" that addresses general issues surrounding benchmark governance, quality, methodology, and accountability. You will find that this report is particularly important in thinking about benchmark calculation approaches, as it provides a framework for evaluation of benchmark proposals, yours included.

Since then, the Financial Stability Board's Official Sector Steering Group has issued specific recommendations relating to LIBOR reform; this document relates the general IOSCO principles to the specific issues that arise in interest rate benchmarks.

Finally, two academic articles may prove of interest to you.

Duffie and Dworczak's "Robust Benchmark Design" discusses the design of robust estimators in situations where a benchmark is based on transactions and agents attempt to manipulate these transactions to profit on derivatives based on the benchmark.

Finally, Duffie and Stein discuss LIBOR reform and alternative reference rates in "Reforming LIBOR and Other Financial-Market Benchmarks."


Was the average person no better off in 1800 than in 100,000 BC? I was somewhat surprised by the following claims by Gregory Clark in A Farewell to Alms, A Brief Economic History of the World (2007):

  the average person in the world of 1800 was no better off than the
  average person of 100,000 BC. Indeed in 1800 the bulk of the world’s population was poorer than their remote ancestors. The lucky denizens of wealthy societies such as eighteenth-century England or the Netherlands managed a material lifestyle equivalent to that of the Stone Age. But the vast swath of humanity in East and South Asia, particularly in China and Japan, eked out a living under conditions probably significantly poorer than those of cavemen. ... for the majority of the English as late as 1813 conditions were no better than for their naked ancestors of the African savannah.

So, would most economic historians agree with the above claims? Or have any openly disagreed with the above claims?

In a detailed review of Clark's book, concluding that its "central theses ... are contradicted by well-known evidence" (p 969), Robert Allen addresses the claim about 1800 and 100,000 BC in a section headed "Malthus in the Very Long Run" (pp 951-5). His criticisms of Clark include:

That he has no evidence of living standards in 100,000 BC, but relies on an assumption that living standards at that time were the same as those of modern foragers (p 951).
That he draws inferences about diet (a key aspect of living standards) from male heights (from skeletons) but ignores evidence from female heights and from other skeletal features, which some have claimed to support different conclusions (p 952).
That his argument that humans of 100,000 BC had more leisure time (another aspect of living standards) because of their forager life-style is not supported by skeletal evidence comparing (more recent) foragers and agriculturalists (p 955).

Some other criticisms in this section are hard to summarise briefly. In conclusion of this section, Allen states: "Economic growth before the Industrial Revolution was not rapid, but it did generate a higher standard of living for most people than that enjoyed by ancient foragers".


Do the stock performances of various companies have a measurable correlation with exchange rate? For example if the values of big companies in a country decrease, will the value of that country's currency measurably decrease?

A company valuation is merely in paper. It is similar to  economist eating shit jokes. When the stock price of a big company drops, it "suppose to" hurts the shareholder who bought it on high.

When I say "suppose", because intervention does happens to "too big to fail" company. In worst case, government hold too much "interest" in big company that might issue bonds(AKA print money) to bails out the entity, as what happens to Asian financial crisis, and USA subprime loan financial crash.

IMHO, details real world example falls under TL;DR; category. There is countless global example.

A large company stock can be jack up by speculation. Say a company issues  10 millions stock with $1 face values. If a willing buyer trade 100 stocks with $1.50, and subsequent buyer keep buying 100 stocks and jack it to $50, it doesn't mean the company "values" sudden shoot up from $1 x 10 millions = $10 millions  to $50 x 10 millions($500 millions). This WILL NOT create extra $490 millions to the economy, nor to the money supplies.

Without government money supplies and cheap loan rates, it is impossible to create such speculation. In addition, without increase money supplies, not hot money flow into a country, foreign exchange will always stay in a stabil level.

Example of high stock values and insane inflation

Zimbabwe stock market compare stock value.

Examples of bubbles crash and NO bailout made, no apparent inflation

Dot Com bubbles.
Enron, Worldcomm scandal.

Example of bubbles crash. Country bail out cause higher inflation

Asia pre 2007 economy crisis stock value

Example of crash and bail out inflation flow to other country.

USA QE. Speculator borrow cheap money and speculate outside US. Hot money cause many Asian country company stock shoot up without fundamental.


Is the dictator game studied by game theory or by decision theory? Is the dictator game/dilemma studied by game theory or by decision theory? I'm not sure because of the lack of other interactive agents.

I would say that the dictator game is of interest to a decision theorist more so than to a game theorist, although the dictator game can be formally modeled in a game theoretic framework.

Decision theory studies how behavior, especially those that deviate from the rational ideal assumed by standard economic theory, can be modeled, as well as the implications of these behavioral models.

Game theory, in contrast, focuses more on the interactive aspect of decisions. The fact that the dictator game can be formalized as a game has more to do with the broad applicability of game theory than the dictator game's intrinsic game theoretic value.

Based on the purpose of your research, you should be looking up references in the behavioral/experimental literature.


Monopsony diagram curves Why is the marginal cost curve not the same as the supply curve?

My personal explanation is that since the marginal cost curve is cost of producing each new product, the supply curve just represents the break even point of selling a certain number of these products. The seller can sell some at a profit, and some at a loss, and as long as the loss and profit cancel out, he's on the supply curve. Thus the supply of producing x goods is just the average of the marginal cost curve from 0 to x.

This explanation seems logical to me, but I have been given an alternative explanation - the supply curve is that of the market, whereas the marginal cost curve is intrinsic to the firm. However, I am unsure as to why the market supply would be related to the marginal cost curve as the average of its integral.

There are two assumptions in your explanation that require change

1st of all, regading the seller

  The seller can sell some at a profit, and some at a loss, and as long
  as the loss and profit cancel out, he's on the supply curve.

The supply curve theoretical logic is that the seller will produce as much products as possible, at a rising cost, as long as the market price that he sees is higher than the last product he produced - the marginal product
Based on that, the seller will always sell at market price. the profit comes from the gap between the market price and the entire cost of production, which is cheaper than the marginal cost. he's initial products cost less

The supply curve is the average MC of all firms, which, in a competitive market model, share the same technology, since open information is available, so the average should be of identical firms


Books for microeconomics and macroeconomics for selected topics I am a mathematics undergraduate trying to self-learn some economics. I have no background in economics. I wish to know from which chapters of Hal Varian's "Intermediate Microeconomics" (7th edition) should I study for the following topics:

Microeconomics: Theory of consumer behaviour, theory of production,
market structure under perfect competition, monopoly, price discrimination,
duopoly with Cournot and Bertrand competition (elementary problems) and
welfare economics.

Macroeconomics: National income accounting, simple Keynesian Model of
income determination and the multiplier, IS-LM Model, models of aggregate
demand and aggregate supply, Harrod-Domar and Solow models of growth,
money, banking and inflation.

Regarding the macroeconomics part, I still do not know which book to follow and which chapters to read. It would help me a lot, if someone can guide me in this. Since the headings of the chapters differ from the names of these topics, I am unsure which portions to read without any expert's help.

P.S.: I am unsure if this is the right place for me to ask such a question.

From Varian (7th edition):

Consumer behavior: at least chapters 1–6; preferably also chapters 7, 8, and 12.
Perfect competition and Theory of production: chapters 15, 16, and 18-23.
Monopoly price discrimination: chapter 25 (you might want to look at chapter 24; it seems a bit odd to study price discrimination without first looking at a non-discriminating monopolist).
Bertrand/Cournot duopoly: chapter 27.
Welfare economics is a bit tougher, because this could mean a number of things. I would suggest chapters 31 and 33 (and maybe chapters 32, 34 and 36).


Indirect changes in Marshallian Demand Suppose we have a Cobb-Douglas utility function: $$U(x,y)=x^\alpha y^\beta$$ and a budget constraint: $$p_{x}x+p_{y}y=I$$ where $\alpha+\beta=1$.

It can be shown that the Marshallian demand for $x$ and $y$ is $x^*=\frac{\alpha I}{p_{x}}$ and $y^*=\frac{\beta I}{p_{y}}$ respectively.

Does a change in $p_{y}$ affect the quantity of $x$ demanded? By looking at $x$'s Marshallian Demand, it seems as though such a change will not affect the quantity of x demanded but $p_{x}$ and $p_{y}$ are related by the budget constraint which makes me not quite sure.

You correctly derived the Marshallian demand function for Cobb-Douglas utility, you notice that the optimal level of consumption of $x$ or $y$ is a function only of the individual's income and the price of said good.  This is an interesting feature of CD-utility, that when the price of good $y$ changes the demand for $x$ doesn't change.  This means that $x$ and $y$ are neither substitutes nor complements to one another. Econport has a nice figure of this:

$\hskip2in$

The first figure shows that as the price of good $x$ changes the quantity of $x$ changes but the quantity of $y$ does not change.  The second figure shows that as price increases the amount demanded decreases and vice-versa when price decreases.

As a side note, CD-utility further implies strict quasi-concave utility so that the indifference set is strictly convex, hence $\vec{x}^* (\vec{p},I)$ is single-valued.  With constant prices for $y$ and prices $p_a, p_b, p_c$ for $x,$ we choose the optimal consumption level of each commodity at the points $a = (x_a, y_a) ,b = (x_b, y_b) ,c = (x_c, y_c)$, such that the slope of the budget hyperplane and the tangent slope of the indifference curve are equal.


Free Data Source for Credit Spreads? Credit spreads are a key economic indicator. They are the difference between yields on corporate and government debt. They are a measure of confidence in the private sector, they provide insight into economic culture.

Where can I find a free and reliable online daily historical data source that indicates how credit spreads are moving by region?

CDX and iTraxx quotes provide exactly this information but as an individual, you struggle to even pay Markit to provide them - they generally only have corporate clients.

Quandl.com has databases of bond yield by credit rating which could be used in conjunction with government interest rates to get an indication of how spreads are moving but the data is not reliable and there is little explanation of what regions/markets the databases cover.

Yes, there's daily data available on the St. Louis Fed's FRED.


Jordi Gali Book First Edition Page 47 (need help for derivation) The below image is from P.47 of Monetary Policy, Inflation, and the Business Cycle by Jordi Gali. My question is "how can we derive the equation (15). If (15) is a correct equation, my guess is that $E_t[\hat{mc}_{t+k}] = 0$ for all $k \not= 0$ and $E_t[\pi_{t+k}] = 0$ for all $k \not= 0,1$. But, on what basis can we ensure these results?
Notation: $\theta \in (0,1)$ is the probability that the firm can change the price level. $\hat{mc}_{t+k} = mc_{t+k} - mc$ where $mc$ is the marginal cost at the steady state.
It is hard to put all relevant information to my question in this post. Here is the link for this book:https://perhuaman.files.wordpress.com/2014/06/gali_polc3adtica_monetaria.pdf (please look at page 47)

This simplification of the infinite sum is commonly made by a differencing approach. You can see here an example of this approach in this kind of models.
Regarding with the assumptions mentioned by you, for $\hat{mc}_t$ since it's a deviation from the levels variable steady state, in the equilibrium there's no expectations and therefore $mc_t=mc\implies \hat{mc}_t=0$ for all $t$ in the steady state. In other words in the steady state the value of this variable is deterministic and zero, but by no means the short term expectancy of this value $E_t[\hat{mc}_{t+k}]$ has to be zero, nor this is the way the series is simplified.
With respect to $\pi_t$, something similar happens, since by definition $\pi_t=(1-\theta)(p_t^*-p_{t-1})$ (Galí, 2008, p.57) and again, in the steady state $p_t^*=p_{t-1}\implies \pi_t=0$, but as with the marginal cost there's not a reason why log-linearized inflation is expected to be zero, apart from being in the steady state.


Math basics for Macro&Micro economics and econometrics I have just been admitted to a graduate school for studies in economics and I major in public administration during my undergraduate time. I have learnt linear algebra, single variable calculus, probability theory and mathematical statistics by myself(Otherwise I will not be admitted). After all I am a amateur in economics, and I have another 5 months to go before register to the graduate school.

So, I think I'd better to equip myself with solid mathematical knowledge to deal with the courses in the first year, which are showed in the title.

ps. The books I will use in these courses are:

  Microeconomic Theory, Andreu Mas-Colell

  Advanced Macroeconomics, David Romer

  And there is no prescribed textbook for econometrics.

Any ides are going to be appreciated, and if I didn't make a clear expression of my question, please tell me to edit my question.

I recommended familiarity with the following topics:

partial differentiation and optimization of multivariate functions
study fixed point theorems. Kakutani and Brower are good ideas.
Set theory is very important
analysis (especially sequences, sub-sequences, convergence of sequences, etc.)
Topology (basics is good enough. For example, understanding the open ball for local non-satiation)
Contraction mapping theorem (For Bellman equations in Macro)
Value functions / Bellman equations
Envelope Theorem
Be very comfortable with calculus (so...do some review if you aren't)
Familiarize yourself with the simplex
basic ideas of function properties like concavity, convexity, quasi-concavity, quasi-convexity, continuous, differentiable, discontinuity etc.
Take a look at point-to-set mappings

Edit:

I'll add for point to set mapping that upper, lower-hemicontinuity and hemicontinuity are necessary as well
Taylor expansions around a point c for multivariate and log functions
glance over methods of log-linearization
This isn't too hard but very important: binary relations over finite and infinite sets. To be a bit more specific - completeness, transitivity etc.
I also recommend being familiar with cyclicity etc.
The separating and supporting hyperplane theorems

This may sound silly, but also make sure you are ridiculously comfortable with algebra. Sometimes I feel like the unending onslaught of algebra is the thing that slows me down the most during exams etc.

Edit: I'd like to recommend a book for math prep that covers almost everything I've listed: The Foundations of Mathematical Economics by Michael Carter

It's a solid book with good exercises and readily available solutions to confirm your answers.

Alright - I tried to give you some specific things rather than provide the broad strokes. I figure it is easy enough to know that you should study a subject and so I've tried to highlight what I remember being the important little bits of math that we use most often.

Good luck with graduate school.


Are there strains of economics that are "no (political) economics"? To support my belief in the arbitrariness of economic theory and thought, since different economic systems have their own rules, theories etc., which contradict the rules of other systems and which most of I think are authoritarian (because they're enforced over groups using politics),

does there exist school(s) of economic thought that is about "no economics" or "no economic theory"? Or perhaps no economics in the sense that "all economic theories (e.g. capitalist, communist ...) at the same time".

Or in other words, is there economic theory that's non-political, i.e. does not require politics for functioning?

Government behavior/actions play a big role in economics, but economic study certainly isn't constrained by "arbitrary" political forces.  As @dismalscience pointed out in his comment, the existence of black markets points towards the drive towards a market-based system no matter the laws or political systems of a given country.  Rather than picture economics as a derivative of a set of laws, picture the laws and political systems as being constructs to help shape the underlying economic system (to correct market failures, etc.).  The goal and job of those that study economics is to help explain how all of these moving forces interact with one another.

Also, in the comments it is asked why we need economic theory to set prices if it is achievable through "common sense."  We don't need economic theory necessarily to set the price, but rather to understand why the price is set, what led to a given price, and how might the price change in the future.  The example used of grocery store prices was used for simplicity, but certainly you could imagine far more complex economic interactions where a solid economic theory would come in quite useful (think international trade, wall street, the labor market of the EU, etc.).