Are rational expectations in economics purely forwards looking, or can they have backward looking components? Are rational expectations (Muth, Lucas, Kyland and Prescott) in economics purely forwards looking, or can they have backward looking components?

Depends on what exactly you mean by backward looking component. When people talk about agents being 'backward looking' they often mean adaptive expectations, if that is what you have in mind then answer would be no.
However, rational expectations really just require agents to have model consistent expectations (see Snowdon, Vane, & Wynarczyk,(1994). A modern guide to macroeconomics). So if by 'backward looking components' you mean that agents utilize past information in some way answer is yes. This is especially true if the underlying model predicts that expected variable has some structural relationship to its past realizations. This being said there are not many situations where this occurs.
There can also be mixed expectations models that assume that portion of agents follows adaptive expectations for example and rest rational expectations, but these would not strictly be called rational expectations models.


A question about Nash Equilibrium I have some trouble with Nash Equilibrium. The specific question as follows.

Suppose that there are $2N$ people in the village, of which $N$ residents live in the first district, and each person chooses to raise $q_1$ sheep, and the cost of each sheep is $c_1$. In addition, n people live in the second district, and each person chooses to raise $q_2$ sheep. The cost of a sheep is $c_2$. The income brought by each sheep is $200-q$, where $q$ is the total number of sheep in the village.

Q: Find the number of sheep raised by each resident in the two regions under the Nash equilibrium of this game.

Here is my thought. For simplicity, let $I$ denotes the index set of individuals in the first district, similarly, $II$ for the second district.
For $\forall i\in I$, the profit maximization problem is
\begin{equation}
\max_{q_i} \pi_i=(200-q_i-\sum_{k\neq i,\\i\in I}q_k-\sum_{l\in II}q_l)q_i-c_1q_i\\
F.O.C\qquad \frac{\partial \pi_i}{\partial q_i}=200-2q_i-\sum_{k\neq i\\k\in I}q_k-\sum_{l\in II}q_l-c_1=0\\
BR_{q_i}(q_{-i})=q_i=100-\frac{1}{2}\sum_{k\neq i\\k\in I}q_k-\frac{1}{2}\sum_{l\in II}q_l-\frac{1}{2}c_1
\end{equation}
Similarly, for $\forall j\in II$, we have best reaction function
\begin{equation}
BR_{q_j}(q_{-j})=q_j=100-\frac{1}{2}\sum_{k\in I}q_k-\frac{1}{2}\sum_{l\neq j\\l\in II}q_l-\frac{1}{2}c_2
\end{equation}
Since every individual belonging to the same area is in the same situation, we can assume that
\begin{align}
\begin{cases}
q_i^*=a, &\forall i\in I\\
q_j^*=b, &\forall j\in II
\end{cases}
\end{align}
and then substitute it into the best reaction function, we have
\begin{align}
\begin{cases}
(N+1)a+Nb=200-c_1\\
Na+(N+1)b=200-c_2
\end{cases}
\end{align}
\begin{align}
\begin{cases}
a=\frac{
\begin{vmatrix}
200-c_1 & N\\
200-c_2 & N+1
\end{vmatrix}}{\begin{vmatrix}
N+1 & N\\
N & N+1
\end{vmatrix}}\\
b=\frac{
\begin{vmatrix}
N+1 & 200-c_1\\
N & 200-c_2
\end{vmatrix}}{\begin{vmatrix}
N+1 & N\\
N & N+1
\end{vmatrix}}
\end{cases}
\end{align}
I don’t know if I’m doing it right, and I’m going to solve it under the assumption that there is an interior point solution. I think if it is strictly proved, the cost $c_1,c_2$ may be considered.

From symmetry we can say that for each player $i$ in $I$, $q_r=q_k$ $\forall r,k \in I$. Similarly for $II$. Let this be $q_I$ for producers in $I$ and $q_{II}$ for $II$.
So profit function for individual $i$ in $I$:
\begin{align}
\max_{q_i} \pi_i&=(200-(N-1)q_I-Nq_{II}-q_i))q_i-c_1q_i\\
\text{FOC: }\,\,\frac{\partial \pi_i}{\partial q_i}&=200-(N-1)q_I-Nq_{II}-q_i-q_i-c_1=0 \\
\implies q_i^*(q_I,q_{II})&=\frac{200-Nq_{II}-c_1-(N-1)q_I}{2}
\end{align}
Similarly, we will get for individual $j$ in $II$:
$$q_j^*(q_I,q_{II})=\frac{200-Nq_I-c_2 - (N-1)q_{II}}{2N}$$
At NE, we know that $q_i^*=q_I^*$ and $q_j^*=q_{II}$. Using this:
\begin{align}
q_I^*&=\frac{200-Nq_{II}^*-c_1-(N-1)q_I^*}{2} \\
&=\frac{200-Nq_{II}^*-c_1}{N+1}
\end{align}
And so, $$q_{II}^*=\frac{200-Nq_{I}^*-c_2}{N+1}$$
Solving for $q_I^*$:
\begin{align}
(N+1)q_I^*&=200-N\frac{200-Nq_I^*-c_2}{N+1}-c_1 \\
\implies q_I^* &=\frac{200-c_1+N(c_2-c_1)}{2N+1}
\end{align}
Similarly, $$q_{II}^* =\frac{200-c_2+N(c_1-c_2)}{2N+1}$$


Is Canada a country of high taxation in international comparison? Looking through Canada's culture section on wikipedia, it's described as having:

  Government policies such as publicly funded health care, higher taxation to redistribute wealth, the outlawing of capital punishment, strong efforts to eliminate poverty...

However, looking into taxation in Canada their income tax of 31.6% (if single with no children) and their corporation tax seems fairly lower then, for example, the higher rate of tax in the UK (45%).

Why is Canada regarded to have policy in high taxation to redistribute wealth when their taxation actually appears to be fairly low?

Because they are high in comparison. Take a look at the data from the OECD here, for 2015. I have plotted them below:

(The red is the personal income tax set by law, and the blue is the one adding tax credits, as far as I understand).

As you can see, rates in Canada are quite high in comparison with other OECD countries like Estonia or Poland, and also higher than the UK.

Also, in international comparison, Canada is quite good in redistributing income. You can see that by comparing the Gini index before and after taxation:

Property taxes are quite high too:

The final evidence comes from this index of progressivity of both personal income tax and social security:

Conclusion

Canada is quite a progressive country in terms of taxation, redistribution quite a lot, and lowering market inequality considerably. Even more, it seems to be better than the UK in almost every comparison.

Source: OECD (2012).


Present Value Analysis For my exmaple, we have machine A with an initial cost of 15K and O&M of 2k per year for the next 4 years. After 4 years, the O&M rise to $2.7k per year. No salvage value and life span of 20 years. 10% interest. What's the present worth of machine A?

It is easier for me to understand the problem by first stating that all cost out of pocket is negative. Since we do not have any salvage value in this problem, it will all be negative.

Here are my thoughts:

The cost of purchase the machine is out of pocket. 2k per year of O&M for first 4 year, at an uniform rate which is annual. 2.7k after the 4 years.

My equation came out to :

Present (A) = -15k - 2k (P/A, 10%, 4) - 2.7k (P/A, 10%, 16)

However at the solution, they added one more variable that I do not understand why.

Present (A) = 15k + 2k (P/A, 10%, 4) + 2.7k (P/A, 10%, 16) * (P/F,10%,4)

Please explain to me why do we need the last part (P/F,10%,4)? to get the present value of machine A.

thanks

You need the last part because you want the present value. If you were to only use the 16 you‘d get to 4 years in the future, or you‘d be calculating the PV for 4 year operating cost of 2000 and concurrent 16 year cost of 2700. without the last part you‘d basically have two operating costs (one of 2000 and one of 2700) for the next four years and then 1  operating cost of 2700 for the next twelve years.

This is the way you can think of the cost in more granular terms

Purchasing cost: $15k$ no discount because purchased today.

1st four years overhead:
$
\sum^4_t{2'000\over(1+r)^t}
$

2nd 16 years of overhead: $ {\sum^{16}_t{2'000\over(1+r)^t}}\over(1+r)^4 $

The first part gives you the PV of the 16 periods, but because this would only start 4 years in the future you'd need to take the PV of the PV in a way.

The total of the cash flow is then the following:
$15'000 + \sum^4_t{2'000\over(1+r)^t} +{{\sum^{16}_t{2'000\over(1+r)^t}}\over(1+r)^4}$

Alternatively you could write
$15'000 + \sum^4_t{2'000\over(1+r)^t} +{{\sum^{20}_{t=4}{2'000\over(1+r)^t}}}$

Hope this helps.


Perfect complement graph and isoquant $f(x_1,x_2) = min \{x_1,x_2\} + x_2$ if that was the production, what would the isoquant be?
Would it simply follow $x_1 = x_2$? I'm not entirely sure what it the graph would look like.

An isoquant is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs.

Having production function: $f(x_1, x_2) = min \{x_1, x_2 \} + x_2$ for $x_i \in [1, 10]$

We can produce isoquants for varying number of inputs. Below you will find 10 isoquants for quantities ranging from 1 to 10 (keep in mind that $Q = 1$ and $Q = 2$ are overlapping). I hope it helps to visualize the problem.


Value vs. Price and its relation to tariffs I’m naturally against tariffs as they impede on free trade, and end up hurting the consumer by inadvertently becoming a tax on imports as well as raising the cost of goods. So I'm trying to challenge my natural assumptions as best I can.

I know the Hayekian school of thought is that the cheaper and more widely available products/materials are the better for the consumer, but I wanted to pose the question that if cheaper doesn't necessarily equal quality why is cheaper always being preferred ? For instance with Steel, I've read numerous publications citing American Steel & Aluminum to be of far greater strength and quality than overseas Steel. Does it all boil down to the freedom to choose as Milton Friedman says ? What is the cost / benefit analysis on something like a Tariff on Steel & Aluminum if its a far better product which might require us to buy less of it over-time ?

I remember growing up my father would say that he didn’t care that he could buy a microwave for 30$, and that he would gladly pay triple or quadruple for a superior product that would last a lifetime. Do we rely too heavily on affordability ?

Sub-Question : I’ve noticed prominent speakers like Victor Davis Hanson say that these Tariffs are so minuscule no one will notice them. Apparently 70% of steel used in the United States is American Steel and China is actually 11th on the list of steel & aluminum providers. Is there too much hyperbole that a steel & aluminum tariff will cause a trade war ?

You asked "why is cheaper always being preferred". Well, it's not. People routinely pay more for quality. Cheaper is almost always preferred for identical products. But cheaper is not always preferred for goods that are only partial substitutes. For example, a well-made pair of shoes that will last ten years, will cost more than an equally-comfortable pair that will last one year. But will cost less than ten times as much, and many people who can afford the well-made pair, will buy them.

"I've read numerous publications citing American Steel & Aluminum to be of far greater strength and quality than overseas Steel"

There are many different grades of steel. These guarantee certain proportions of metals, that in turn guarantee certain physical properties. And they come at different costs, and thus different prices. It doesn't make sense to say "this country's steel is better than that country's steel" - that's jingoism, not economics, not materials science. What matters is the grade of steel being produced, and its price.

"these Tariffs are so minuscule no one will notice them": if that was the case, there'd be no point in flouting international agreements to implement them. The big issue is that this signals an administration that is willing to cause itself and other countries economic harm, in the interest of pursuing an ignorant, silly ideology.


rotating and exchanging x for y's in regression I was just wondering what happens generally if i send all my x points to y's and y's to x's (i.e reflect along the y=x line) - if I change the x's and y's will my old error minimizing line still be the error minimizing line after reflection? How about if I rotate points?

Many thanks

This is a somewhat "dated" subject in introductory econometrics, I suspect because, in econometrics the models come from theories and arguments that try to a priori establish causality and not just association.

Anyway, the issue is analyzed in Maddala's Econometrics textbook.

In the 2001 3d ed. the issue for simple regression is presented in ch. 3. inside section 3.4, under the title "Reverse Regression".

Writing

$$\hat y = \hat a + \hat b x,$$
and

$$\hat x = \hat a' + \hat b'y$$

one can quickly find that

$$\hat b \hat b' = r^2_{xy}$$

i.e. the product of the two is equal to the squared correlation between $x$ and $y$. If this correlation coefficient is close to unity then the two regression lines will be close.

One can also establish a relation between the two constant terms easily.


Are markets inherently short sighted? If markets are types of "information systems", how do they assist in the attainment of a future common objective that is beneficial or even necessary to a society?  Since markets are driven by individual needs and wants, are such future planning objectives beyond the scope of markets?  So, if markets are inherently short sighted, does that mean we are at the mercy of fate when it comes to large scale global problems that evolve over decades?

Of course markets can be shortsighted. The same problem can apply to any institution though. In order to correct a market failure using government it's necessary to appeal to the self interest of various interest groups, which may end up putting you back in square one.


Monetary Policy and the Yield Curve PART ONE As I understand it the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations.

I'm trying to understand how the yield curve is affected:

The Fed Fund rate is the overnight rate at which reserve balances, held by banks at the fed can be lent to each other. The shortest maturity that the treasury yield curve has is 1 month (no overnight). Are expectations regarding overnight fed funds rates reflected in the 1 month yields? I would suppose so, because if the government raises fed funds, their intentions are to influence and increase interest rates in general. Thoughts?

The discount rate is the interest the Fed charges other banks to borrow money. Does the 'discount rate' relate to the commercial paper listed here?. Am I correct in thinking that the discount rate refers to short term borrowing < 1year and that changes in the yield curve at maturities greater than 1 year may not be directly correlated to changes in fed funds or discount rates? (because these are not tools for influencing long term rates)

Finally I understand that changes in the curve at longer maturities may reflect the governments 'open market operations' and their buying and selling of US securities.

Any help solidifying this understanding would be much appreciated.

PART 2 TO THIS QUESTION HERE

You've asked a lot of questions, so I will have to keep my answers rather brief.

  As I understand it the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations.

This is incorrect in a few ways:

The discount rate is a tool, but it's not a tool that is used to conduct monetary policy in normal times. It is, instead, a "penalty rate" in the sense used by Walter Bagehot.
The Fed Funds rate is not a tool, it is a target. The Fed Funds rate is calculated from market transactions, and the Federal Open Market Committee will often instruct the Federal Reserve Bank of New York to engage in open market operations to move the Fed Funds rate toward a particular level.
These are not the only tools at the Fed's disposal. It also has, for example, the reverse repurchase program, which enables it to set a floor under short-term secured borrowing rates.

  Are expectations regarding overnight fed funds rates reflected in the 1 month yields?

Yes, they are related, though the yield on a  1-month Treasury bill will in practice differ from the compounded Fed Funds rate for a number of reasons. One notable reason is that the Fed Funds rate, being a market rate, does vary, while the yield on a 1-month Treasury is effectively fixed at the time of purchase. The relationship between the expected values of a fixed rate and a floating rate is expressed through Overnight Indexed Swap values, and 1-month OIS on the Fed Funds rate is the best direct indication of the expected value of compounded overnight borrowing in the Fed Funds market.

  ...stuff about the discount rate...

No, as I said above. On an average day, bank borrowing from the discount window should be zero. Commercial paper represents medium-term borrowing by private companies.

  Finally I understand that changes in the curve at longer maturities may reflect the governments 'open market operations' and their buying and selling of US securities.

Yes, but that's also true of the short end of the curve. In fact, sometimes the Fed has sought to change the relationship of the short and long ends of the curve, as in "Operation Twist".


How are payoff values in game theories calculated / estimated? In game theories such as Nash Equilibrium, exactly how are each of the players' payoff values for each of their potential strategies created?  In the common 2x2 matrices I've seen in academic papers, the various payoff values seem to just "appear" in the matrices without an explanation of how they were derived / calculated / estimated, whether or not those values have (or need) a confidence level associated with them, etc.  Is it possible, for example to have a range of payoff values rather than a single number for a given player/strategy choice?

Though I'd ask for a bit more clarification which papers you are referring to for a more specific answer, overall the answer depends a bit on what the purpose of the paper/game and payoffs being proposed is.

Papers like Selten's 1978 Chain Store Paradox use payoffs that are important in their relative magnitude (not their absolute value) as a means of creating a perceived disconnect between Industrial Organization and Game Theory. Similarly, in the classic Prisoner's Dilemma game, the actual values for "fink/tattle" and "mum/don't" aren't as important as the fact that the dominant strategy is for both players to tattle. That payoff can be (0,0) or (-10,-10), so long as that payoff makes tattling the dominant strategy, it works for the game.

One of the larger reasons why "exact" values are given instead of confidence intervals is because of how strategies are calculated. Indifference is the key to defining mixed strategies, which is a much simpler feat if exact values are given.

That being said, there is a variety of games of imperfect information and, perhaps most important for your question, games with imperfect monitoring which do exactly as you suggest- allow payoffs to be dependent on some random variable not observed by one (or more) of the players.

I'm sorry if that wasn't very direct, or didn't really fully answer your question- please let me know if I can improve the answer. Confidence intervals can be difficult to use because they are so dependent on the statistical results as opposed to the theoretical model. However ranges of values are a relatively common phenomena in certain types of game theory models (for example, see auction theory). Usually it is assumed that players know the relative likelihoods of different payoffs, but even that can be relaxed in certain circumstances.


In today's money, what was the value of a 1492 Spanish maravedí? Satava (2007) estimates that the costs of Columbus's 1492 voyage was 1,765,734 maravedís.
In today's money, what was the value of a 1492 Spanish maravedí?

Walsh (1931):

The author of this work has translated maravedis into dollars of 1929 by reference to statistics on purchasing power in wheat, corn and other staples. Hence his opinion that the maravedi was worth about two American cents of 1929.

According to the BLS inflation calculator, \$1 in 1929 is about \$15 today (2020).
So, if we accept Walsh's estimate, then one maravedi in 1492 converts to about \$0.30 today.
(And if we also accept Satava's estimate, then Columbus's voyage cost 1,765,734 $\times$ \$0.30 $\approx$ \$529,720 in today's USD.)


Why will the holder of a broad-based index fund, by definition, achieve the average return for the market? A Random Walk Down Wall Street (2015 11 ed, but an 2019 ed. is upcoming). pp. 271 Bottom – 272 Top.

    All “smart beta” strategies represent active management rather than indexing. Capitalization-weighted portfolios are the market. If you believe a subset of securities will give you superior returns, you are counting on some “dumb” investors to hold portfolios producing poorer returns. Some “smart beta” advocates have been quite explicit in suggesting who these dumb investors might be. They claim that the investors in traditional capitalization index funds are the dumb beta investors, since by holding the broad index they will be holding a number of overvalued growth stocks. But that argument must be false. $\color{red}{\text{The holder of a broad-based index fund will by definition achieve the average return for the market.}}$ If “smart beta” funds generate above average returns, it can’t be at the expense of traditional index-fund investors—it must be at the expense of all active managers who do not hold the market portfolio.

For simplicity, suppose that a country’s economy has only 2 types of ETF:

i. 1 broad-based, whose return I'll call $r_B$ +

ii. 1 Smart Beta one that's a subset of securities without some (overvalued) growth stocks, whose return must be higher than the broad-based fund's (say $2\% + r_B$).

Then the average return of ETFs is $1\% + r_B$, which nobody achieves (as my imaginary economy has only 2 types of ETF).

So how's the red sentence true?
How's the bolded sentence true? Wouldn’t fund ii's higher return 'be at the expense of traditional index-fund investors'?

1. The Red Sentence

Because it is market-weighted, the market portfolio is the average of what's going on. It is the default scenario, in which you don't need to trade to maintain your asset allocation.

As soon as someone trades and diverge from this default scenario, one of the two parties will lose, relative to the market (they can both be better off, but one of them will underperform).

In addition, your setup with two funds cannot work. The smart beta index is going to trade. With whom? Not with the market-weighted fund: he does not need to trade (the weights basically adjust all by themselves with the price changes, he only needs to reinvest dividends). Therefore if there are two funds only in your universe, and one of them holds the market portfolio, then the second either holds nothing, or he holds the market portfolio as well. If he holds any other security, then the market portfolio funds cannot hold all securities with market-weights.

2. The Bold Sentence

I think this sentence is wrong. It confuses return and performance. Performance is the efficiency of the process which generates return from risk. Basically, you input risk, and you output return. That's what investing is all about.

The claim behind smart betas is that the market portfolio is not correctly diversified. Basically, you get exposure for some risk without being paid for it. This can be shown quite intuitively : equally-weighted portfolios overperform market-cap weighted portfolios (Platen and Rendek, 2010, Platen and Rendek, 2012). That's because it gives you exposure non non-rewarded risks!

To sum up: the market-weighted portfolio does give you the average return. It can be outperformed by other strategies. Your example is too simple to work.


Help improving this definition of a "game"? My professor defined a game as follows:

a set of $n$ players
a set of strategies $s_i$ for each player $i$
a set of payoffs $p_i$ for each player $i$
turn-taking: sequential or simultaneous
repetition: $k$ rounds, where $k\geq1$ and $k \in \Bbb{N}$

I have three problems with this definition:

He didn't define turn-taking mathematically, so I feel like it's a vague definition. There should be like an index of possible turns with max value $n$. But I'm not sure how to write it formally.
He doesn't define how we map from strategies selected to payoffs. Presumably, the set of payoffs should include a value for every possible combination of strategies selected. But there should be a way to state this formally as well.
He doesn't define what a strategy is. I suppose one could simply say that a strategy is the object we map from in the domain to an element in the set of payoffs (ie codomain). In that sense, anything that can be valued is a strategy, ie a possible action.

My Question:

Can someone offer a more complete definition than the one given? Specifically make sure it improves upon the concerns I mentioned.

Your question is a little bit vague, but I'll do my best.

Your professor was motioning in the correct mathematical direction, but I think that what you're asking for is a more complete formalization.

Any game can be thought of as a tree (i.e. a non-cyclic graph). So to answer your first point about turn-taking, you might think about a function which maps nodes of the tree to some $i\in\{1,2,...n\}$ In the picture below, you might be able to define a formula to characterize the turn taking, but you can't necessarily do this in general. In this example $P_1$ and $P_2$ take alternating sequential turns. $P_1$ can choose $L$ or $R$, then $P_2$ can see which he chose, and then also choose $L$ or $R$.

Before going on to your second point, I need to take a moment to define information sets, which it doesn't sound like you've gotten to yet. Colloquially, an infoset is a set of vertices that represent uncertainty. The root of a game tree is always a singleton infoset, for example. Consider the game where you and I simultaneously choose heads or tails. When $P_2$ chooses whether or not to play heads or tails, she doesn't know if I have chosen to play heads or tails either. Thus while the game tree will have 3 internal vertices (1 that is the root for $P_1$, and 2 for $P_2$, reflecting $P_1$'s choice) there will only be 2 infosets because both vertices for $P_2$ will be contained in the same infoset. In games where turn-taking is sequential, all infosets should be singleton.

Now back to your question about strategies. Each player has a set of strategies. In the example tree provided above $S_1 = \{LLLLL,LLLLR,...,RRRRR\}$. This might seem a little bit confusing at first as it seems like each element of $S_1$ goes above and beyond defining a path. Each player's strategy is defined in terms of infosets. Therefore, the element $LLLLL$ should be read as, when $P_1$ finds herself at the top, she will choose $L$, and when she finds herself at the vertex that is farthest on the left and 1 down from the top, she will also choose $L$. It then also says that if $P_2$ were to choose $R$ instead, that $P_1$ would choose $L$. Thus a strategy is the set of all possible actions a player might take under all possible contingencies.

Finally, how do we state the mapping from strategies to payoffs? First we note that ever player has a strategy set $S_i$, and then form the cartesian product $S=S_1 \times S_2 \times ... \times S_n$, which characterizes all possible strategy combinations for all possible players. Then our payoff will be $\pi:S\to\mathbb{R}^n$. In our example $\pi(LLLLL,LLLLLLLLLL) = (4,2)$.


General equilibrium effects of affirmative action policies I am interested in the debate about affirmative action in college admissions and I would be happy to read some theoretical economic investigations of the effects of these policies. I would be glad if someone could point out a good and recent survey of this literature, or some papers addressing this issue. The following two questions are of particular interest to me:

the general equilibrium effects of affirmative action (say, in college admissions) on labor market outcomes (acquisition of human capital, wage differentials, etc.)
the welfare analysis of affirmative action policies, with some discussion of the appropriate social welfare criterion (e.g., fairness vs efficiency)

Any reference would be appreciated. Thanks in advance.

I found one survey which corresponds to what I was looking for: Theories of Statistical Discrimination and Affirmative Action: A Survey by Hamming Fang and Andrea Moro, in the Handbook of Social Economics (2011 edition).


Solving Utility Maximization with Lagrangian I know how to solve the 2 variable constrained optimization problem using MRS = MRT, but I also want to make sure I understand how to do it with the Lagrangian method.
So if I have the following problem
$U(x) = \alpha\ln(x_1) + (1-\alpha)\ln(x_2)$
with $p_1x_1 + p_2x_2 = w$
I got the answer using the MRS = MRT method as $x_1 = \frac{w\alpha}{p_1}$ and $x_2 = \frac{w(1-\alpha)}{p_2}$.  I am a bit confused on how to set up the Lagrangian.  Here's what I did
So $L = \alpha\ln(x_1) + (1-\alpha)\ln(x_2) + \lambda(w - p_1x_1 - p_2x_2) + \mu_1x_1 + \mu_2x_2$
$\frac{dL}{dx_1} = \frac{\alpha}{x_1} + p_1\lambda + \mu_1 = 0$
$\frac{dL}{dx_1} = \frac{1-\alpha}{x_2} + p_2\lambda + \mu_2 = 0$
$\frac{dL}{d\lambda} = w - p_1x_1 - p_2x_2 = 0$
$\frac{dL}{d\mu_1} = x_1 = 0$
$\frac{dL}{d\mu_2} = x_2 = 0$
Here is my issue here.  If I assume $x_1$ and $x_2$ cannot be 0 and I somehow assume $\mu_1$ and $\mu_2$ are 0, then I can solve it pretty easily.  I then just equate the $\lambda$ in the first two equations and then plug into the budget constraint like in the MRS = MRT case.

However, what gives me the right to make $\mu_1$ and $\mu_2$ equal to 0?  Is this the correct approach?  When are they not 0?

I heard in order to use the Lagrangian method, some "conditions" need to be satisfied.  What conditions need to be satisfied?  How do I verify this?  Is this related to differentiability?

Is there some restrictions on what $\lambda$ and $\mu$ can be?

Thanks!

You have added inequality constraints $x_1 \geq 0$ and $x_2 \geq 0$.
Hence, you now have Kuhn-Tucker conditions for complimentary slackness:
$$
\mu_1 x_1 = 0 \text{ and } \mu_2x_2 = 0
$$
So whenever $x_i > 0$, by the complimentary slackness condition, $\mu_i = 0$.
See Karush-Kuhn-Tucker conditions. It also contains regularity conditions you ask for.


Why does the European Central Bank use the 5y5y rate to measure inflation I cannot understand why the 5y5y swap rate measures inflation. I can see how the floating rate somewhat measures the rate of interest rates which are related to inflation. However I cannot understand why this swap rate is the preferred way to measure (medium term) inflation expectations.

For more information see here.

In an interest rate swap, two parties swap with each other the obligation to pay a fixed rate for the obligation to pay a floating rate. Because it concerns a simple swap of obligations, the rates must have equal present value for both parties. The market quotes the fixed rate, so this is the variable of interest.

Draghi may have been referring to one of two types of swap contracts: the 5-year/5-year interest swap or the 5-year/5-year inflation rate swap. The case of the 5-year/5-year inflation rate swap is simplest. Because the contracts trade at equal present values, a lower fixed rate implies lower expected inflation.

The case for the interest swap requires an additional assumption. Consider that interest rates consist of two components: a compensation for inflation rate risk, and a compensation for default (and possibly other) risks. This latter part is called the risk premium, and it also affects the quoted fixed rates. So in order to draw any conclusions about market inflation expectations on the basis of interest rate swaps, it is simplest to assume that the risk premium is constant. Of course this is not necessarily the case, and this assumption could be investigated by looking at the difference between the two different swap contracts.

Finally, I cannot be certain about why the ECB prefers this measure to any other measure of inflation expectations. But besides the fact that it is a market measure, the timing adds up: the 5 year swap starts in 5 years, so it is an indicator of inflation 5-10 years in the future.


An easy GDP growth question A woman pays her gardener £60 per year and later married him. The gardener continues to work in the garden but unpaid. The woman earns £1000 before and after the marriage. Statement: the marriage decreases GDP by £60.

My question is why the decrease? The economy still has £1000 regardless of whether it's consumed separately or combined (herself and her husband)?

You are confusing money supply with GDP. GDP is defined as the total monetary value of all goods and services produced within the economy. For this case,

GDP =  Woman's Earning + Gardeners Earning

Before Marriage = 1000 + 60 = $1060

Even though the woman has $940 she was still compensated $1000 for whatever service she provided. The money supply is 1000 but GDP is not.

Post Marriage = 1000 + 0 = $1000


SPNE of a normal form game If we have a sequential game which is equivalent to a simultaneous move game because of its information structure, then the NE we find are also SPNE?

If you draw the corresponding game tree, you will see that "equivalent to simultaneous move game" implies that the game has no proper subgame and the only subgame is the whole game.
This is because the information set of the second player covers every move of the first player.
Therefore, every Nash equilibrium is trivially also subgame perfect.


The Household Production Function I was wondering whether someone can explain the household production function (HPF). Specifically, the variant presented in Patanayak et al (2005). The paper uses the HPF to determine household willingness to pay for improved water supplies. The HPF model theorizes that averting expenditures (coping costs) are lower bound to willingness to pay (WTP). However other people (e.g. Orgill-Meyer et al (2018)) talk about how including sunk costs (expensive tank assets, pumps, etc) when calculating coping can reverse this relationship causing coping costs to be upper bound to WTP. However, Patanayak et al, 2005 includes amortized sunk costs in his coping cost calculations and the HPF premise still holds.

This is confusing me a bit.

I know the question is elementary but I am really not an economist. Can someone please clarify this?

I have only read the abstracts, but the two statements aren't conflicting.

From Wikipedia, a production function gives the technological relation between quantities of physical inputs and quantities of output of goods. A household production function is a form of that idea that looks out how households combine inputs to get outputs that they consume such as water.

Under the HPF model, water is considered as an output that households consume. However, there are many ways to combine inputs to obtain water: you can use utility based water if the infrastructure for that exists or non-utility based water (involving personal tanks, pumps, etc). The assumption is that households will be willing to pay for the utility based water infrastructure at least the amount that it takes to upkeep their non-utility based water that they currently own accounting for the sunk costs of the upfront purchase of the tanks and pumps. And hence that is the "lower bound to WTP". But this assumes that the utility based water is higher quality than what households already have. As noted in the abstract of the latter paper, "[w]e attribute this departure from the traditional relationship between averting expenditures and contingent valuation to the lack of household confidence in the quality of utility-provided water." Hence, current coping costs become an upper bound to WTP. To put it differently, if households believed utility based water is exactly equivalent to what they currently have, then the WTP would be exactly equal to current coping costs.


Increased production costs associated with increased output produced? Why do firms have prices increase with the SRAS or Supply Curve? In my textbook, it said (this is for SRAS and AD, but I'm also going to apply this a bit fo microeconomics.. sorry for mixing, but my question applies in both ways, I believe) "The average price level will need to increase too, from P1 to P2, to allow firms to cover the increased production costs associated with increased volumes of output"

In my opinion, the price does not need to increase to make up for an "increased cost associated with increased quantity supplied/output"

When I was doing some math regarding all of this I realized that for a firm to "cover its cost" (maintain the same amount of profit as before) it could actually lower prices and then maintain the same amount of profit (due to the increase in quantity counteracting my hypothesized lowering of prices)

Here is my math, which has allowed me to come to this conclusion:
A firm sells 10 tomatoes for ¥10. Revenue is (¥10x10) = ¥100. Each tomato costs ¥5, so I do (¥5x10) to get ¥50 as a cost. Thus, profit is ¥100-¥50= ¥50. Farmer wants to maintain his profit of ¥50.... let's say now he increases his quantity supplied or output to 20 tomatoes. the cost is now (¥5x10)x2 = ¥100 (I did x2 cuz its 20 tomatoes now). For the farmer to maintain profit of ¥50 he prices the 20 tomatoes at ¥7.50 (less than previous price of ¥10), so that Revenue(¥7.50x20=¥150) and Cost(¥5x10x2=$100). Thus ¥150-¥100 is ¥50 for profit. profit maintained, but price was lowered to ¥7.50
I know I'm wrong, but I'm not able to understand the logic behind this. If anyone could help me with my specific questions or direct me to any online resources, that would be awesome. Thank you!

this is for SRAS and AD, but I'm also going to apply this a bit fo microeconomics.. sorry for mixing, but my question applies in both ways, I believe

You are applying market equilibrium logic to the supply function. When aggregate demand shifts for some reason while the supply function is unchanged the equilibrium price will change.
If the short-run aggregate supply (SRAS) function is upward sloping then there are no economies of scale (in the short-run). This does not give you detailed information on what a firm is able to do long term.


why not use $Ap - p$ instead of $p - Ap$? I am watching this video about the Leontief input-output model: https://youtu.be/hlaBURtSDO8?t=12m26s

One thing I don't understand is: why not use $Ap - p$ instead of $p - Ap$? It seems to make better sense to measure net production by output - input. Maybe I am missing something?

$p$ represents total production.

$Ap$ represents the intermediate goods and services used in production, i.e. intermediate consumption.

So $p-Ap=(I-A)p$ represents net production, i.e. output minus input.


Matlab code example for piecewise linear approximation and Euler Equation Iteration Where I can find a good Matlab sample code that performs Euler equation iteration with piece-wise linear approximation of policy functions?

The Projection method I have in mind is something like described in the Finite Elements method in Aruoba, Fernandez-Villaverde, Rubio-Ramirez (JEDC 2006) or more generically Chapter 4 in Heer and Maussner "Dynamic General equilibrium models" (the examples in the cited references are either Fortran or Gauss).

Two suggestions:

First, try some of the sample code at this website. It builds simple Euler equation iteration methods from scratch in Matlab.

Second, try the sample code here. You will need to read the associated notes, also. The code makes use of the CompEcon toolbox in Matlab, by Miranda and Fackler (associated with their book:  Applied Computational Economics and Finance).


What does the vertical axis of the Kuznets curve depict (mathematically)? I do not understand what does the word "inequality" means on the vertical axis of the Kuznets curve. Can someone please explain?

Kuznet talked about income inequality. In this context it is often measured by the Gini coefficient or the Kuznet ratio, but basically any measure of income inequality would do, since Kuznet's hypothesis is merely a qualitative one.


What is it about certain business types that seem to restrict how much large they can grow? For example, I've never heard of a large lawn-mowing corporation. Phone and computer repairers seem to consist mostly of 1 or two man operations. Wedding planners and photographers seem exclusively to be home businesses.

Why is it that certain types of businesses seem never able to grow into a large company? I'm assuming if it were possible, at least some percentage of lucky or savvy businessmen or women would have found great success.

That's a very interesting question and there are multiple potential reasons for this.

One reason is that production is simply not efficient at a larger scale. There are diminishing returns to scale: i.e. doubling inputs will result in less than twice the output. This means that two smaller production facilities can be more efficient than one large one.

One way to think about this are kids shoveling snow in winter. Beyond a certain number of kids with shovels they're just going to get in each other's way shoveling the same driveway. Now they could of course split up into two or more groups, these two groups could be one firm or these could be two firms. But what's the rationale for combining these two firms into one? They probably will not economize on any fixed expenses. They need to ring the doorbell, bring their shovels, and ask people whether they wish their driveway to be shoveled. Sure one kid could specialize in negotiating a price and ringing many doorbells and scheduling appointments, but
the gains from specialization are probably not such that it's worthwhile. It's not how that "industry" works. You ring, you shovel, and you move on. So there is no good reason for combining. The kid ringing and making appointments is an unnecessary overhead. It's better that he shovels too.

Another reason are the fixed costs of certain regulations. You're probably familiar with the fact that in some jurisdictions firms above a certain size need to provide certain services to their employees. If you're a small firm, then you will incur that fixed costs all at once if you expand over that threshold. You'll have to get your existing employees those services and the new people. These additional fixed costs might not make it worthwhile to hire extra people unless you can be certain that you can expand your business well beyond that.

A third reason is that many people do not want to expand their businesses. They enjoy the work that they do and the extra income is not worth it. They'd have to spend less time doing the work that they enjoy and more time on administrating the work done by others. Effectively this is a change of employment. So you might as well ask why do some people do work A and not work B?

These are three reasons. The reasoning is the same each time though. The benefits of expanding do not justify the costs of expanding in that particular situation. Given that there are many different situations there will be many different reasons why people choose not to expand their business.

Does this answer your question?


What is the purpose of multiple regression? For instance, consider the following regression equation
$College Score=\beta_0+\beta_1HighSchool GPA+u$. We interpret this $\beta_1$as the effect of a higher High School GPA holding all other variables constant.
The second regression model adds a new term  and becomes $College Score=\beta_0+\beta_1HighSchool GPA+\beta_2ACTSCORE+u$. The interpretation of $\beta_1$ is still the effect of a higher High School GPA holding all other variables constant. So what is the difference?(and the values in two regressions are different). The textbook explanation is that, in the first equation, ACT score is assumed to be fixed. In the second equation, however, ACT score is explicitly controlled. I don't quite understand the real difference between 'assumed fixed' and 'explicitly held fixed'.

The difference is that the first regression is unbiased only if you can assume that high school GPA and ACT score are orthogonal on each other $cov(x,z)=0$ where $x$ is shortcut for high school GPA and $z$ for ACT score. Or if you can assume the second variable ATC score does not affect the dependent variable at all $\beta_2=0$. This is because in simple regression the $\beta$ coefficient bias is given by:

$$\hat{\beta_1} = \beta_1 + \beta_2 \frac{\text{COV}(x,z) }{VAR(x)} $$

where $\hat{\beta_1} $ is the estimated beta effect of GPA on col. score (beta reported by your statistical program like R), $\beta_1$ is the true unobserved coefficient, $\beta_2$ is the true unobserved effect of ACT on score, and the fraction is just covariance between $x$ and $z$ over variance of $x$.

So unless you know that the two variables are completely unrelated you will have bias. Now an example of variable that is completely unrelated to another is variable thats hold fixed. For example if in $z(x) =100$ no matter which $x$ we examine then we can be confident that $cov(x,z)=0$. Regressions should be applied only if you think they are unbiased so the first equation implicitly assumes that the second variable is hold constant given $x$. However, once you include the second covariate explicitly you can calculate both expected beta coefficients conditional on each other which is equivalent to actually keeping the other variable constant.

So there is actually a great deal of difference between the two regressions (except for special cases where $cov(x,z)=0$ or $\beta_2=0$).


Why is economic growth measured exponentially rather than linearly? If economic growth is indeed highly desirable (see this question), why must this growth be exponential? With finite resources, exponential growth might hit limits rapidly (or be impossible?). Why not express growth in linear rather than exponential terms?

Growth as is meant here "must" be nothing in particular. It is a specific metric, the percentage change in yearly GNP/GDP, and it is what it is.
In Blanchard and Fischer 's "Lectures on Macroeconomics", in the introductory chapter 1, page 2, Figure 1.1, the logarithm of USA GNP 1874-1986 is graphed: and it is impressively linear , bar a disturbance around World-War II (a dive before it that was roughly equally compensated immediately after). But this means that

$$\ln Y \approx at \Rightarrow Y \approx e^{at}$$

(for the US Economy, $a \approx 0.030\;\; \text{to} \;\;0.037$ for the period).

It is the data that told us that "growth was exponential" during this period.
(Note that "exponential growth" usually includes the concept of constant growth rate, while  in informal language, "exponential" may also refer to exploding paths, paths with increasing growth rate).
And so economic models were deemed relevant if they could replicate to a respectable degree the observed data.

The question "can this go on forever?" is an altogether different issue, starting with the meaning of the word "forever".


What did "18/9", "25/", and "30/" mean in this 1800 British document? In "The Petition of the Master Taylors of London and its Vicinity, December 1800" (reproduced in Galton, 1896), it is stated

the wages and allowances ... were accordingly settled at the rate of 18/9 per week ...
the wages the journeymen now receive is 25/ per week ...
have refused to work unless their respective masters will raise the wages they now receive to 30/ per week

I'm guessing that "18/9" means 18s9d, while "25/" and "30/" mean 25s and 30s?

Yes your guess is correct.

In fact, the forward slash punctuation mark "/" actually comes to us through its being the abbreviation for the English shilling.

From Humez and Humez (2008):

  ... forward slash (/), which is also variously known as a solidus, virgule, or just plain slash, when the deletion of a single character is to be marked. The solidus was a Roman coin and is ultimately the basis for English soldier, the idea being that a soldier is someone who fights for money, or, as we might say today, a mercenary (from the Latin merces ‘wages.’) The solidus as slash is historically a straightened-out S, the abbreviation for the English shilling (as in 2/3—two shillings thruppence), the step from one coin to another being relatively easy. How we get from shilling to slash in its various other uses—as proofreader’s strike-out mark, arithmetical sign of division, general separatrix, and so on—is rather more murky.


supply demand question beginner I am learning about shifts in supply and demand. Things that shift supply include things like improvement in production technologies. But why would a firm want to increase their supply if they are just going to sell more product for less at the new equilibrium ?

The new "equilibrium" would have been at a lower price on the assumption that the firm has full Monopoly over the market (and hence cannot instead just compete with some other firm for a larger share of market demand) and demand remains constant.

Moreover unless you know about the elasticity of demand (how sensitive people's wish to buy is with regards to commodity price) you cannot be certain if selling a significantly larger amount at a slightly smaller price might in totality fetch the producer a larger sum of money.


What is Production Possibility Frontier (PPF) diagram drawn on consumption-leisure? When explaining basic macroeconomics model involving consumption-leisure tradeoff, often diagram showing production possbility frontier (PPF) is drawn with leisure on x-axis and consumption on y-axis. But what exactly is the meaning of this production possibility frontier?

Production Possibility Froniter diagram is often drawn on two-goods basis (for example, like butter on x-axis and milk on y-axis) but I am confused on what PPF might be on consumption-leisure basis.

Reference: http://newmonetarism.blogspot.com/2014/02/rbc-and-nk-in-nutshell.html

Edited because wrnog answer, did not took the time to read the page.

Without maths

So your PPF would just be the link between leisure and consumption set by technology : the amount of leisure you choose give the time you can spend working, so the wage you earn and therefore the consumption you have (since there is no saving, all you earn is what you consume).

With a bit of math

You have a fixed amount of time, which we normalize to $1$. You can spend it either in leisure F (fun) or in work L (labour) so that
$$1=L+F$$
Then you get a wage $w$, that is related to $L$ in some way : $w=\psi(L)$, and you consume $C=w=\psi(L)$, so that $L=\psi^{-1}(C)$

Then your PPF is
$$F+\psi^{-1}(C)=1 $$
It is a relation between leisure $F$ and consumption $C$ set by technology (the way wages are fixed).

Then the program is to maximize the agent utility $U(C,F)$ subject to this contraint. You can visualize it by the common tangent between iso-utility curves and your PPD.


How does a bank convert one currency to another? Say for example I sell ZAR and buy USD. What happens behind the scenes so that the local ZAR bank is able to deposit USD into my account?

Does the bank require some sort of USD cash reserve?
How do the banks interact/negotiate with each other?
What if the bank selling ZAR cannot find a bank/trader selling USD who wants ZAR?
If the bank does find a source of USD, is any physical money like notes/bills/gold ever moved from one bank to another to settle the account?
How are these transactions regulated or monitored to
avoid fraud?

Yes, a reserve is needed to ensure the integrity of the money issued (as always).

On the international foreign exchange market, many millions are traded at a time. Otherwise, with smaller amounts of money, the costs of transferring that money (e.g. via SWIFT) would be too high for the amount transferred. That is why investors and small businesses do not trade in the forex market themselves—they go through the financial intermediary.

Banks communicate with each other using computers and telephones. If you collectively put all these many communications together, you get the concept of an international interbank foreign exchange market.
Prices are offered for foreign exchange deals. If the price is fairly high, the bank may not get a sale quickly—they will have to wait, or lower their price. If the price is lower, they will be more likely to find a buyer.
This question is related to the reserve requirement. If banks need to increase their reserve, they will buy securities denominated in that currency (government bonds, stocks, and other financial instruments), as these securities can easily be transferred from other locations. Vice versa: If the financial institution has too many illiquid assets (giving a lower leverage), they could choose to then sell these assets to other financial institutions who need them. So, buying and selling currency is not inextricably tied up with buying and selling reserves, as there is some play between the two. You asked about physical cash—cash is related to the demand for currency (so, yes, some cash is transferred, but not much as not everybody wants to draw cash). And you asked about precious metals—well, those are transferred even less, and only really serve as a 'reserve' to give integrity to fiat money generally.

The rest of my answer is copied from https://kevinkotze.github.io/if-2-forex/ , which comes from Kevin Kotzé's web page https://www.economodel.com/international-finance

1.1 Communications and funds transfers
The enormous volume of trade in the foreign exchange market requires an extensive communication network between traders and a sophisticated settlement system to transfer payments in different currencies between the buyers and sellers of different currencies. Traders are able to obtain information that is provided by major commercial distributors such as Reuters and Bloomberg. The traders are then able to contact each other, to obtain actual prices and negotiate deals. In addition, they could approach a foreign exchange broker to broker a deal, or they can trade on an electronic brokerage system, where quotes on a screen are transactable. When a trade is agreed upon, banks communicate and transfer funds electronically, using systems such as the Society of Worldwide Interbank Financial Telecommunications (SWIFT), which confirm trades and facilitate payment.
As Cross-Currency transactions may involve the simultaneous exchange of currencies, there is a risk that only one leg of the transaction may be completed, due to the possibility that parties use different systems in different countries that operate out of different time zones. This is known as cross-currency settlement risk, or Herstatt risk. Recently, foreign exchange dealers, encouraged by the BIS, have developed a number of practices to limit settlement risk. These measures include: firstly, banks now have strict limits on the amount of transactions they are willing to settle with a single counterparty on a given day. Secondly, banks have started to engage in a variety of netting arrangements, in which they agree to wire the net traded amounts only at the end of a trading day. Thirdly, settlement risk is eliminated if the exchange of the two monies occur simultaneously in a process known as payment versus payment (PvP).
More recently, we have witnessed the foundation of the Continuous Linked Settlement (CLS) Bank, which is owned by the world’s largest financial groups. CLS is the largest multi-currency cash settlement system, eliminating settlement risk for over half of the worlds foreign exchange payment instructions and its members include central banks, large commercial banks and other large corporations. The CLS daily settlement cycle operates with settlement and funding occurring during a five-hour window when all real time gross settlement systems are able to make and receive payments. This enables simultaneous settlement of the payments on both sides of a foreign exchange transaction. Each member holds a single multicurrency account with CLS, which has a zero balance at the start and the end of trading day. The settlement of the payment instructions and the associated payments are final and irrevocable.


confusion regarding elasticity of a demand curve The following question is on a quiz at Marginal Revolution University:
https://mru.org/practice-questions/calculating-elasticity-demand-practice-questions

The elasticity of demand is 2.0. Is the demand curve relatively steep
or flat? Will a fall in price raise total revenue or lower it? Note:
we present the elasticity in terms of its absolute value.

The official answer is "relatively flat; raise total revenue".
I can't understand this; isn't it true that elasticity > 1 means higher responsiveness of demand to changes in price?  And isn't 1.0 defined as neither steep nor flat, and anything above 1.0 being steeper?
I can understand that a fall in price will lead to a huge surge in demand, because of the high elasticity, and therefore more profits.
I missed another question on the quiz that, for me, should be explicable in terms of the same reasoning as above.

The elasticity of demand is 1.1. Is the demand curve relatively steep
or flat? Will a fall in price raise total revenue or lower it? Note:
we present the elasticity in terms of its absolute value.

Again, the official answer is "relatively flat; raise total revenue".

It is correct that the higher the elasticity is the more flat the demand curve will be. A higher elasticity means that demand responds disproportionately more to change in prices. In fact an example of demand curve where elasticity $ | \epsilon|  = \infty$ would be a flat horizontal demand curve.
The reason for this is that elasticity of demand tells you how much quantity demanded (plotted by convention on x-axis) changes in response to change in price (by convention plotted on y-axis). In order for a small price change (small distance 'traveled' across y-axis) to have large impact on quantity (distance 'traveled' across x-axis) the curve has to be relatively 'flat' since the slope which will be the rise/run of tangent line at a given point must be relatively small.
For example if elasticity $| \epsilon | = 2$ that means that $1\%$ decrease in price increases quantity demanded by $2\%$. Since total revenue is defined as price times quantity $P*Q$ if $P$ decreases only by $1\%$ but $Q$ increases by $2\%$ the total revenue has to increase.  So the answer provided is correct.
To actually showcase how the demand becomes more 'flat' I generated 3 constant elasticity of demand functions ($P=Q^{1/\epsilon}$) using R for natural numbers $Q = 1, ..., 10$. The blue demand curve has constant elasticity of $0.5$, the orange one $2$ and the red one has constant elasticity of $5$ (all expressed in absolute value). You see as the elasticity increases the demand graph becomes more 'flat'.


Papers with insignificant results There are a few papers that I have seen that publish insiginficant results, such as responses (see Easterly's response published in the AER to Burnside and Dollars World Bank paper titled 'Aid, Policies and Growth). The aim of these papers, however, is to negate a positive claim which they do by producing insignificant results (in the hypothesis testing sense) using the same idea as the original authors, but using new data.
However, I have yet to come across a major paper in its own right published in the top 5 journals that publishes results that are insignificant. This is a scary thought because when I do my own research, I always shudder before entering the regress y x command.   Are there well known papers that publish insignificant results?
Thanks!

This does not directly answer your question, but I will try to explain why I don't think that such well known papers exist.

If submitted I don't think that such a paper would be accepted by the top five journals. This is because the journals also compete to stay relevant, to give surprising information. The phenomenon is known as publication bias.

This was also a big problem for the medical community. The solution they arrived at is that they only accept trials if the trial and its hypothesis is reported to the authorities at the beginning of the trial. Because of this the result will be stored no matter what it is. Even though unsurprising results are unlikely to get much publicity, a researcher looking for them can find them. The same solution cannot work for economic regressions because running a regression on the same data always gives the same result. Hence false positives are not a result of lucky samples, but of tweeking the model to particular data.


Timeline of comprehensive NIPA revisions I have been fruitlessly searching for a list of dates of comprehensive National Income and Product Account revisions.  Clues I have found so far: The Bureau of Economic Analysis  website says the 1999 revision was the 11th one, and there have been three more since then - 2003, '09, and '13.

From the Philadelphia Fed's vintage datasets it looks like there were comprehensive revisions in 1975, 1985, 1991, and 1995.  This still leaves several unaccounted-for revisions.  Is there an online source for this information or should I hunt through old print copies of the Survey of Current Business?

Thanks

edited to remove acronyms

You can read what looks like the entire collection of back issues of Survey of Current Business on the BEA website but the old issues seem to be PDFs that are not indexed by the site's search engine. You can see the 1995 revision discussed there. This seems to be the 1965 and 1980 revisions. The seem to have changed the termenology on the major revisions at one point. In 1980 the called it The National Income and Product Accounts of the United States: An Introduction to the Revised Estimates for 1929-80 instead of Preview of the Comprehensive Revision
of the National Income and Product Accounts which they called in since at least 1995.

That still leaves five more still to discover. I set my DownThemAll to download the whole archive and then I'll see if can get anywhere with searching the pdfs.


Effect of government debt on tax rates? Is there any well known study that links government debt to tax rates? I have been searching the literature for some time now and haven't found any.

More importantly, could government debt track tax rates?

Looking across countries, there is not much of a relationship.

The following chart is taken from the latest IMF World Economic Outlook database, comparing General Government Gross Debt as a percentage of GDP (you could look at net debt) and General Government Revenue as a percentage of GDP (which includes more than taxation) both in 2014.

The extreme debts are for Japan and Greece, while the extreme revenues are for Tuvalu, Kiribati, and Micronesia (foreign aid related), and Kuwait (oil revenues/taxes).  Hong Kong, Brunei, and Saudi Arabia have small gross debts while Nigeria and Bangladesh have the lowest revenues.  But even without these special cases the relationship is weak.

You could instead look at individual countries over time, but some of the relationship may be cyclical (either political or economic) as lower debt encourages lower future tax rates, but lower tax revenues can lead to higher future debt rates.

Of course the true relationship also involves government expenditure rates and GDP growth rates among other significant factors.


Why Turkey's president thinks that by cutting interest rate it will lower inflation? Recently, President Erdogan sacked the head of Turkey’s central bank because he didn't want to cut interest rates. He even said: “We said that if rates fall, inflation will fall. He didn’t do what was necessary.”

From my understanding of economics, this is the opposite of how things work. If we want to lower inflation, we should raise interest rates even further. So why President Erdogan is conviced of the opposite? Is there a sound economic theory that would agree with Erdogan's initiative?

I'm gonna start this off by saying this is speculative, so take this answer with a grain of salt.

In order for a counter intuitive measure like this to work, there must be something else going on that over-shadows it. (Inflation topics tend to be riddled with things like this). I admit I don't know what the economic climate in Turkey is like currently; but I can think of a way that it would make sense to lower rates and expect lower inflation.

In light of recent events, Turkey has been the focus of some very negative media coverage as of late, and some of it for good reason. The last couple years for Turkey have been rough to say the least; but that's not the macro-trend of Turkey.
Turkey is an emerging market economy, they have urbanized dramatically from 2000-2015, maintained strong macroeconomic and fiscal policy frameworks, opened up to foreign trade and finance, harmonized many laws and regulations with European Union (EU) standards, and greatly expanded access to public services. It also recovered well from the global crisis of 2008/09.

Tying this back to your question now, it could be the case that Turkey's government spends too much money and is the biggest factor in the inflation numbers. If President Erdogan can better enable the people of Turkey to replace the effect of government spending organically (enable the people via lowering interest rates), then he can purposely scale back government spending (which would lower inflation b/c it's the bigger factor).

In summary: Erdogan may be trying to stabilize Turkey's economic climate via lower government spending which will reduce aggregate demand, leading to lower growth and less demand pull inflation. The macro trend of Turkey and forecasted growth expectancy is very high, and probably over heated, despite the recent negative issues in the micro economic climate.


Finding Optimal Consumption Bundle Suppose u(x,y)=min{x+y,4(x)^1/2,4(y)^1/2} , Px=1, Py=2, M=5 . Here, Px, Py and M are the price of x, price of y, and the Income.

Give an example of the optimal consumption bundle of x and y for this consumer.

I know to plot the Indifference Curve given a value of Utility,however how could I know what is the maximum utility that can be obtained in this case?

In this case the optimal choice is $(x^*, y^*) = (3, 1)$. Here is the picture :


Norway inflation and exchange rates I am looking at Norway's economy, and I'm trying to make sense of some of the data I see. Norway's economy has a very close relationship to crude oil, and in 2014 crude oil had a massive drop. Looking at the inflation, exchange rate (USD/NOK, EUR/NOK) and interest rates, my questions are the following:

Is it a correct assumption that the the central bank started decreasing the interest rate, so that the damage to the economy (coming from the low crude oil price) is minimized?
Is it correct that a lower interest rate led to a weaker currency and thus higher inflation (2015, but mostly in 2016)?
What could be the reason that inflation has dropped significantly recently? (I am asking this since the interest rate has remained the same, though the currency has strengthened a bit).

I do not know Norway's economy. BTW, based on what you report, I would first rearrange your points into a more chrono-econo-logical order. Briefly,

3 - Facing the loss of income due to the massive drop in the crude oil price, --
depending on the impacts that this drop may have in term of income redistribution -- Norway's economic agents may have increased their saving rates $\iff$ economic agents consume less. Less demands means weaker upward pressure on prices, which in turn means less inflation.

1 - Facing the increasing masses of savings, Norway's central bank may have started to decrease the interest rate so as to disincentive agents to do so. Indeed, lower interest rates $\iff$ lower rates of return on savings -- if commercial banks propagate this rate change, which is very likely.

2 - Finally, since these lower interest rates tend to attract less foreign investments -- and since, to access to Norway's lending market, those must first buy home country's currency -- this exerts a downward pressure on the value of Norway's currency, which in turn causes a relative price increase of imported goods $\iff$ imported inflation.

To conclude, I would say that your points 1 and 2 are as correct as they are incomplete.


Why debt/equity ratio is limited to between 0 and 9 Is there any economic reason that debt/equity is limited to between 0 and 9 as in the picture below?

This research examines the impact of the law on firms' financial flexibilities.

When a company is in near-bankrupt state, it's equity $\rightarrow0$, meaning that D/E goes $\rightarrow\infty$. Including such observations would make the resulting mean D/E meaningless. This is why boundaries are needed


Advanced economies tend to slide down to zero interest rates and stay there. Why? Advanced economies (e.g., Japan, USA, Europe) tend to slide down to zero interest rates and stay there. Why? Are there any theories which explain this tendency?

Recently I read an interesting paper on this subject from the Bank for International Settlements:

Juselius, Mikael and Takats, Elod, Can Demography Affect Inflation and Monetary Policy? (February 2015). BIS Working Paper No. 485. Available at SSRN: http://ssrn.com/abstract=2562443

The abstract:

  Several countries are concurrently experiencing historically low inflation rates and
  ageing populations. Is there a connection, as recently suggested by some senior
  central bankers? We undertake a comprehensive test of this hypothesis in a panel of
  22 countries over the 1955–2010 period. We find a stable and significant correlation
  between demography and low-frequency inflation. In particular, a larger share of
  dependents (ie young and old) is correlated with higher inflation, while a larger
  share of working age cohorts is correlated with lower inflation. The results are
  robust to different country samples, time periods, control variables and estimation
  techniques. We also find a significant, albeit unstable, relationship between
  demography and monetary policy.

As I'm not an expert on the subject, it is probably not the main explanation in literature but it's in my opinion an interesting research path.


Maximal Allais paradox The Allais paradox, is an  experiment set up as follows, where you are free to chose between gambles $A$ and $B$:

(the table on wikipedia is much more readable if you prefer)

  Experiment 1

  Gamble 1A

  \$1 million, 100% Chance

  Gamble 1B

  \$1 million, 89% Chance

  \$0, 1% Chance

  \$5 million, 10% Chance

  Experiment 2

  Gamble 2A

  $0, 89% Chance

  \$1 million, 11% Chance

  Gamble 2B

  \$0, 90% Chance

  \$5 million, 10% Chance

The paradox arises when one chooses both Gamble 1A and Gamble 2B.

This paradox is portrayed as a proof, or evidence of inconsistency in von Neumann–Morgenstern utility theory with it's status as a "rational" decision theory. In particular it is intended to show inadequacy of the independence axiom of that theory.

However, while I find that while {Gamble 1A, Gamble 2B} is an acceptable and even desirable set of choices (which would be logically inconsistent with the theory), this observation doesn't seem strong enough to show the theory is absurd -- it seems fair to argue that if one refused to accept 1% chance of gaining nothing, one would desire a 10% greater chance of winning anything (versus gaining nothing) to be the correct choice in Experiment 2. In other words, both choices {Gamble 1A, Gamble 1B} and {Gamble 2A, Gamble 2B} seem perfectly logical. In fact, if all choices were approximately the same utility, the inconsistency would disappear (which seems entirely plausible to me).

Is there another set of parameters, or another example entirely, which more convincingly shows an absurdity of the independence axiom, or are the parameters above as strong as it gets?

One must first distinguish two different senses in which the Allais Paradox can be seen as a "contradiction" of vNM independence; these correspond to the two different interpretations which can be given to any model in Decision Theory. (von Neumann-Morgenstern (vNM) utility theory is one such model.)  According to the descriptive interpretation, a model in Decision Theory is supposed to provide a description of how real, actual human beings actually make decisions.  According to the normative interpretation, the model is supposed to tell us how an "ideal rational agent" should make decisions.   To put it another way, the descriptive interpretation matters to you if you are trying to construct a predictive model of insurance markets or financial markets or some other social phenomenon where people make risky decisions;  the normative interpretation matters to you if you yourself are making risky decisions, or if you are trying advise someone who is making such decisions.

The Allais Paradox certainly falsifies the descriptive interpretation of the vNM model; this simply means that, as a matter of empirical fact, most people (including, apparently, many economists) will choose 1A and 2B, which cannot be explained as maximizing the expected value of any possible vNM utility function.  Whether the Allais Paradox falsifies the normative interpretation of the vNM model is a more subtle and controversial question. Basically it depends whether or not you think that {1A, 2B} is really the "correct" answer.  Some people strongly feel that {1A, 2B} is correct;  for them, this is evidence that vNM is not the correct normative model of decision-making under risk.  Other people are initially tempted by {1A, 2B}, but once they recognize that it is inconsistent with vNM, they are willing to "bite the bullet" and reject their own intuitions in favor of the theory;  their ultimate position is that the normative implications of vNM are counterintuitive, but correct.  (The fact that a theory has "counterintuitive" implications does not make it wrong;  modern physics is full of theories like this.  Indeed, there are even mathematical theorems which are "counterintuitive", but evidently they are correct as a matter of logical necessity.)

In your post, you wrote:

  In fact, if all choices were approximately the same utility, the
  inconsistency would disappear (which seems entirely plausible to me).

I don't think "approximately the same utility" is good enough ---as long as the agent has any nontrivial vNM utility function, the choice pattern {1A, 2B} is impossible.  Perhaps what you mean is that the choice pattern {1A, 2B} can be reconciled with vNM theory if the agent's vNM utility function is trivial (i.e. constantly zero); in this case, the agent would be indifferent between all possible lotteries.  As a purely mathematical point, this is correct. But it is not consistent with people's preferences; most people experience a strict preference for 1A over 1B, and a strict preference for 2B over 2A.  So we cannot "explain away" the paradox by positing trivial utility functions.

Your post ends with the question:

  Is there another set of parameters, or another example entirely, which
  more convincingly shows an absurdity of the independence axiom, or are
  the parameters above as strong as it gets?

Perhaps you will be interested in the Ellsberg Paradox.  (I won't bother including a complete description here, since there is a very nice Wikipedia article about it.)  The Ellsberg Paradox differs from the Allais Paradox in that the probabilities of certain events are left unspecified;  the decision-maker must construct her own "subjective probabilistic beliefs" about these events.  But the interesting fact is that there is no set of "subjective probabilistic beliefs" which can explain the pattern of choices most people make in the Ellsberg Paradox.  So it definitely falsifies the "descriptive" validity of expected utility (EU) maximization as a model of human decision-making.  More importantly, it presents a strong challenge to the "normative" validity of EU-maximization;  even many economic theorists who "bite the bullet" in the Allais Paradox are willing to acknowledge that in the Ellsberg Paradox, the choice pattern which is inconsistent with EU-maximization is much more compelling than a choice pattern which is consistent with EU-maximization.

However, I should acknowledge that the Ellsberg Paradox is properly understood as a challenge to EU-maximization in a setting of "ambiguity" (where probabilities are not known a priori), whereas the Allais Paradox is already a challenge to EU-maximization even in a setting of "risk" (where all probabilities are known).  It is a perfectly consistent position to accept the vNM axioms in a setting of risk (and hence, "bite the bullet" in the Allais Paradox), while rejecting EU-maximization (i.e. rejecting the Savage Theorem) in a setting of uncertainty.

Another, entirely different normative challenge to vNM independence arises in a setting of social choice.  Suppose that you have an indivisible resource (e.g. a hard candy), which you must allocate to one of two claimants (e.g. two children, Alice and Bob).  Suppose that, a priori, both claimaints have an equal claim to the resource (they are equally deserving, equally hungry, etc.).  The resource is indivisible, so you can't "split" it between the two claimants.   Question:  should you allocate the resource by some random mechanism (e.g. by flipping a fair coin)?  Or should you allocate it by some deterministic mechanism (e.g. give it to the older child, or the one whose name comes first in alphabetical order, or the one who is standing further to the left at the moment the decision is made)?   Most people have a strong intuition that a random mechanism is more "fair" than a deterministic mechanism.  So they prefer to randomize.  But at the same time, they are indifferent between giving the resource to Alice and giving it to Bob (recall: Alice and Bob are equally deserving of the resource).  So if A is the outcome "give it to Alice", and B is the outcome "give it to Bob", then we have a situation where the decision maker is indifferent between A and B, but strictly prefers the lottery (1/2 A, 1/2 B) to either A or B.  Clearly, this normative position cannot be explained by the vNM theory.  This is sometimes called the Diamond Paradox, since it was originally pointed out in a 1967 article by Peter Diamond.


Understanding IMF statistics I teach Politics and I've been asked to prepare a course which includes a lot of financial data because it covers recent international financial crises.
I've been trying to use IMF statistics, but I find them rather confusing. For instance, if I want to know a country's deficit, I find three different options:

And when I look up GDP, I have a bewildering number of options to choose from (I've highlighted the one that makes more sense to me):

Is there any rule-of-thumb method for a lay person to use these statistics? Alternatively, is there any other source in which the data is comprehensive but simplified?
Thank you so much in advance!

This is a general problem with anyone who comes face to face with official statistics for the first time.
Official statistics of a particular country comes from an institution of that country. However, there is something called the System of National Accounts that contains guidelines on pretty much every aspect of national accounts data. This is maintained by UN, IMF and World Bank, among others. Thanks to this you will find data definitions and compilation methods across countries to be largely consistent.
Rule 1: So if you have to use cross country data make sure that you select comparable datasets, i.e. choosing same variables.
Rule 2: Unless you are doing a deep data data analysis, it is okay to chose the variable which is seems most common. What is most common? The variable that you see easily available for any country.
Rule 3: Just keep in mind the difference between real and nominal variables. In most scenarios, you'd need real variables, especially, if you are doing cross-country comparison.
If you still get confused about what to use, the best way is to just read about the variable on wiki and you'll get some sense. Going into more details than what is easily available on wiki is only going to confuse you further as official statistics get fairly complex as you start peeling the layers.
Finally I'd recommend to give CEIC database a try, if you have access to it (through your institution). It is one of the best place today to find any data related to official statistics (I have seen even the officials from IMF using it).


Cointegration in stock market between different market places Hi guys im interested in cointegration in stock market between Brazil, USA, London, China, India, Argentina and Hong Kong.
Since I want to  compare each country’s index to the BR index, how do i do to to convert all prices into BRL?  Should i use the variation, close or adjusted close?

Your question is not particularly clear - but let me try to give some elements that may help:

Think about why do you want to convert prices into the same currency? Pure stock market performance is usually evaluated using Local currencies. You can compute daily, weekly or monthly returns (that is % price increases) for each stock index and then do whatever analysis you wish to do: correlations, cointegrations ... you name it.
If you really need to convert indices into the same currency, you should take the close price in local currency and then convert that price into the currency of your choice (Bloomberg does this for you if have an acces, otherwise you will find exchange rates on the IMF website). Then you compute the returns as in 1.


Income Elasticity of Demand for Higher Education My model has been given as:
$$\ln (H_ed) = 18.08 -  0.53\ln Pop -2.01 \ln Distance + 0.47\ln RGD $$

Where (Hed) is higher education, pop is population, and RGD = Real GDP per capita.

I have been asked to find the "income elasticity of the demand for higher education".

As there are no income variables in this model, I am unsure of where to look for the income elasticity.

Real GDP is a variable for aggregate income. You might think of your model very loosely as an "aggregate demand function". Then, as the elasticity of a function $\varepsilon=\frac{\partial f}{\partial x}\frac{f(x)}{x}$ can be expressed in terms of logarithms $\varepsilon=\frac{\partial \ln f}{\partial \ln x}$, in your estimation it would amount to say that, ceteris paribus, the elasticity of (assuming average) higher education to real income per capita is $0.47$. This implies that the "demand" for higher education is inelastic ($\varepsilon \in (0,1)$), which kind of makes some sense.  Within that framework (aggregate average, not consistent with demand theory), I think a better model would come from adding ${(\ln RGD)}^2$ to your model, to let the "income elasticity" describe some nonlinearities as it would sound really strange that if RGDP would go up 1000x average education would go up 470x, as this would mean people would be living some centuries before completing their education...


Effect of population growth on Solow steady state My textbook says that:

  Ratio of capital per capita to income per capita in the steady state is a positive function of s and an inverse function of η and δ.  Thus, k*/y* is a constant.  This means when saving increase, the ratio does not change as both capital per capita and income per capita increase at the same rate.  However, both capital per capital and income per capital decrease at the same rate if the depreciation and population growth rate are higher.

It also says that:

  When you get to the steady state of output per worker, it means that your economy will still grow, just that it will only grow at the rate of growth of the labour force i.e. equals to the rate of population growth)

Doesn't both statement contradict each other?  I mean if the population growth rate grows, why could the capital and income per capita decreases which the first statement seems to state.  Am I reading the statements wrongly?

if the population growth rate grows, why could the capital and income per capita decreases

This is basically asking "why does higher population growth lower the steady state capital per worker"?

Mathematics

Let us assume a Cobb-Douglas production function with constant returns to scale. This is,

$$Y=K^{\alpha}L^{1-\alpha}$$

It can be shown that in the steady state optimal capital per capita is:

$$k^* = \left(\frac{s}{\delta+n}\right)^\frac{1}{1-\alpha}$$

(for example, see here)

Therefore, an increase in $n$ lowers $k^*$.

Similarly, in the steady state, output per capita is $y^*=k^*{^{\alpha}}$. Thus, a fall in $k^*$ leads to a fall in $y^*$, given that $\alpha \in (0,1)$.

Intuition

To start simple, think of an economy with a fixed level of workers ($n=0$). This economy has an exogenous saving rate $s$. Thus, for an initial level of output $Y$, workers save $s$ percentage of their income $Y$. These savings become investment, which then contributes to expanding capital. Meanwhile, there is a positive depreciation rate $\delta$, which in a given year renders a $\delta$% of the capital stock unusable. These two forces go in the opposite direction, moving capital stock up or down, depending on which force is stronger. Will there be a point in which these forces are in equilibrium? Necessarily there is one. Why? Because $\alpha \in (0,1)$ implies there is decreasing marginal returns to capital, case in which the Inada Conditions hold. In other words, if capital is very low, adding more capital will expand output and investment by very much. Conversely, when capital is very low, an identical increase in capital expands output and investment by very little. In the middle, there is a point where such expansion is equal to the depreciation (which is constant). In the Solow diagram with axes $K$ and $Y$ (in capital letters, not in per capita terms), that point is represented by the intersection between the depreciation function (a straight line) and the $sY$ line (concave, in line with the Inada Conditions).

Now, let us move to the case of positive population growth ($n>0$). Here, employment is increasing every period. Therefore, $Y$ is also increasing. In consequence, savings, investment and therefore capital is also increasing. In this economy, there is no steady state in terms of $K$ (unlike before), because $K$ is growing every period with the expansion of the population size. In terms of the same Solow diagram of above (with axes $K$ and $Y$, in capital letters, not in per capita terms), the function $sY$ is shifting upwards every period, pushing the never-reachable point where $sY$ intersects $\delta K$ further to the right.

Since there is no steady state in terms of $K$, the next question to ask is, is there a steady state in terms of $K/L$? Because of the same logic than before, necessarily there is one. To see this, notice that capital per capita terms has decreasing marginal returns in the production function (see the function above). This is, an increase in $K/L$ by 1% leads to an increase in $Y/L$ by less than 1%. Therefore, for a very low $K/L$, an increase in $K/L$ means a relatively large increase in $Y/L$ and therefore in savings $sY$ and in investment, and therefore in capital. Conversely, for a very high $K/L$, an increase in $K/L$ means a relatively small increase in $Y/L$ and therefore in savings $sY$ and in investment, and therefore in capital. The Inada Conditions ensure there is a middle point by which the forces that lower $K/L$ (in this case, depreciation and population growth) equilibrate the expansion of capital.

Finally, why does an increase in $n$ lowers that optimal $K/L$? On the one hand, the first force in the equilibrium (pushing $K/L$ up) is given by both the savings rate $s$ and the degree of marginal returns ($\alpha$). Neither of these have changed. On the other hand, the second force in the equilibrium (pushing $K/L$ down) is given by both the depreciation rate $\delta$ (which makes a certain proportion of $K$ obsolete) and by the exogenous increase in $L$, which itself depends on $n$. In consequence, an increase in $n$ makes the second force stronger. This pushes the equilibrium to a lower level of $K/L$.

Notice that a way to compensate this is to make the first force stronger, for instance, by increasing the savings rate. This can be easily seen in the Solow diagram, where it is possible to revert to the original $K/L$ steady state by increasing $s$.


How much of the Greece's public debt is created by its trade deficit? How much of the Greece trade deficit reflects into it's public debt?
Each year, Greece is importing about two times as much as it's exporting. In some years, even three times more. How much of that is converted into public debt?

Assuming that the Greek citizens and companies are not sitting on large amounts of cash reserves to afford to spend double the money they make and they can't make such huge credits to cover such expenses (and that looks very much to be the case), the only way to cover that deficit that I can think of is this: The government doesn't have enough money to pay the people working in the public sector, then it borrows money from external creditors, making public debt, then it pays the wages of those workers, and then the workers buy imported goods and at the end of the year, Greece imports more than it exports. And then it's the public debt that supports/fuels that huge trade deficit.

I can't imagine another way of having trade deficit than having reserves or by making private or public debt. But maybe there are such ways and that's why I'm asking.

Later edit: I managed to squeeze another example out of my brains: The Greek ship owners (who don't pay taxes) make such huge profits that they can afford to import materials and technology that's worth 35 billion Euro each year, so they can build more ships for their business. They build the ships and they keep them, doing a lot of imports and no exports. But that works only if their shipping services do not count as exports.

As an accounting identity, it is required that the current account surplus (deficit) +  capital account surplus (deficit) = 0. This is known as the balance of payments (BOP) identity . So if Greeks are importing more Euros worth of goods and services than they are exporting it must be that, consolidating across those outside of Greece, non-Greeks are buying more Euros worth of Greek assets than they are selling.

However, this accounting identity says nothing about who in Greece is selling and who outside of Greece is buying. It need not be that the government is involved at all. If the Greek government borrows more than before the household sector might offset this greater borrowing more than one for one with greater savings (BOP decreases), exactly offset (no change in BOP), partially offset it (change in balance of payments less than increase in government spending), or also borrow (increases in BOP more than change in government spending).


Does a strong exchange rate always mean a cheap holiday regardless of where you are from and going? As question title states, does going from one country with a much stronger exchange rate, or a moderately higher exchange rate, in comparison to a country you visit always mean you get more bang for your 'buck'?

If by "stronger exchange rate" you mean you get more units of the local currency for a dollar (or whatever currency your home country has) then no, not at all. In fact, in economics the term "stronger exchange rate" is not used in this context. People sometimes say that currency A is growing stronger compared to currency B, but this only means that the exchange rate is improving, it does not say if the number is large or small.

If you want to know whether you get more bang for your 'buck' then what matters is purchasing power: how many goods in the foreign country you can buy for the currency units you got for your dollar. Assuming an exchange rate of $E$ units of currency X per one dollar, and a foreign price $p^*$ for some good, you can buy $E/p^*$ units of said good. You can compare this number for different countries to see how far your money will go.

The comparison is made somewhat difficult by the fact that the ratio will probably differ for different goods. Economists usually construct price indices to go around this problem. However no price index is perfect, each one is made to suit a distinct purpose. Basically you would have to look at the price of the goods that you are likely to buy during your stay.


What is the tipping point for hyper-inflation? The recent injection of $2 Trillion into the US economy has prompted me to wonder: At what point does introducing money to a system cause hyper-inflation? (such as Venezuela or other hyper-inflation economies)

There is no set tipping point. In simple terms the relationship between money supply and inflation is given by the standard monetary model which shows that:

$$MV=PY$$

Where M is the money supply, V velocity of money P the price level (and change in the price level gives you the inflation) and Y is the real output.

Hence to get any inflation the changes of M must be such that they are not offset by changes in other variables.

If money supply changes by 10%, velocity of money stays constant, but real output also increases by 10% then there will be no change in prices and hence inflation will be zero. However, in the same example if the real output would not change and all other things remained as above the inflation would be 10%.

In normal times it is valid to say that inflation is a monetary phenomenon and depends mainly on quantity of money. The economy usually grows at steady rate of about 1-2% per year (I am talking about advanced economies at the technological frontier) and velocity of money does not change that much so in that case it is valid to say that relatively large increase in money supply causes inflation.

However, in situations like when interest rates are at 0 lower bound the velocity can actually easily offset any increases in money supply and relationship may break. Moreover, more complex models show that its expectations what matters. If money supply increases today but people expect this increase will be reversed in the future it might not affect inflation (you might want to look at this paper from Paul Krugman if you want to know technical details about that).

To go back to your main question:

  At what point does introducing money to a system cause hyper-inflation?

Following Cagan hyperinflation can be defined as an increase in price level exceeds 50% per month.

To get to that rate money supply would have to growth at the rate of 50% + the rate at which economy grows per month + at any rate that would offset changes to velocity in of money. Special conditions like no zero lower bound interest rates and assumption that people credibly believe the money supply increase is permanent (or at least long lasting) must be imposed as well. In US there would also be special issues since \$ is the world’s reserve currency which helps to reduce inflation pressure as portion of the US money supply is absorbed by other countries.

So to sum up, there is no magic rate of increase in money supply. Even if money supply remains the same but output collapses you can get inflation. Alternatively even large increases in money supply might not change inflation levels at all as recent Great Recession experience shows. You have to do some complex econometric analysis to see at which rate in a given year money supply increases start to affect prices. Since that requires some historic data it’s not possible to say for sure what the level is at a given point of time.

You can make forecasts of course and central banks do that routinely. This is the FED inflation forecast for 2020 which is also based on money supply changes (aside from other things). Although it does not mention money supply explicitly because FED does most of the operations through the funds rate they factor it in their models (the money supply also expands and contracts based on the funds rate). They do not expect hyperinflation so to the extent their forecasts are accurate the recent surge in US spending as response to the recent crisis as well as the increases in money supply seem to not be large enough to cause it yet.


What does my lecturer mean by "economic calculation"? We got this essay question

"It is argued that economic calculation should exclusively be based on individual utility maximization but include an altruistic concern for the common good and for other human individuals. In the perspective of such an ethical correction of economics we think of the economic actor as an individual, who makes an economic calculation which is extended to include the responsibility for other human beings and society integrating economic calculation in well-founded moral norms and ethical customs of society"...Rendtorff (2010)

Discuss the economics of the creation of a separate aesthetic medical industry, borne out of the technological advances in the health sector. Is the economic calculation based on 'well-founded moral norms and ethical customs' of our society? Support your answer with economic reasoning and ethical considerations for various stakeholders.

I'm not so sure what  she meant by economic calculation. Is some kind of economic reasoning such as with indifference curves.

The historical economic calculation debate, between Mises and Hayek on the one side and people like Oskar Lange on the other, was about the extent to which accurate trade-offs can be made in a world without meaningful prices, like the world the naive socialists seemed to envision.  For example, if I am looking to buy a car I observe the prices and characteristics of various models, I evaluate the utility I will expect to receive from the various packages of automotive characteristics on offer, compare that utility with the utility I'd expect to get from other uses of the money that I would spend on the car, and make my choice accordingly.

I assume that the question above is asking about the nature of my utility calculation.  It is usually, not literally correctly but not too incorrectly either, assumed that the in the above car buying scenario I am considering my utility exclusively, ignoring the way the utility of others might be affected by my choice in obvious (pollution) and not so obvious (how I would alternatively arrange my life based on my choice of car).

What "separate aesthetic medical industry" is supposed to mean is outside of my expertise.


Are equity prices and stock prices the same? Do we use in common language "equity price" as a synonym to "stock price"?

Stocks:

Stock (also capital stock) is all of the shares into which ownership of a corporation is divided

Equity:

In finance, equity is ownership of assets that may have debts or other liabilities attached to them. Equity is measured for accounting purposes by subtracting liabilities from the value of the assets