What Constitutes The Size Of An Economy?

Your book is correct.

To quote it

  Size of economy is measured in terms of value of goods and services.

Suppose the Netherlands had its current population of 16 million people but only 14th century technology. I hope you'll agree that the value of whatever they produced would be significantly less than the value of their current production.

Another comparison:
The Indian economy is currently smaller (in terms of value) than the US economy
despite the difference in population. The reason for this is that the US has much more capital in advanced technology.

To address the question whether value is a good indication of size is good question:

There are several arguments for this. Imagine that a country produces something that it consumes very little of (e.g. cash crops). In this case they will not care at all about the weight, volume etc. of their production, they will want to know how much they can sell it for so they can import other things. I would say in such a case value is much more relevant then other measures.

Another example:

Imagine that the A pill immunizes you against malaria for a day and the B pill immunizes you for a year. Would you say a plant producing 100 A pills produces more than a plant producing a B pill?  I would argue in some sense it does, in some sense it does not. There is no absolutely clear method of comparison. For reasons of international trade, value is used. Is the word size confusing? Perhaps. But not overly so.


Subjective theory of value applied to gross domestic product

Interesting observation, but I think the answer is partly explained by several factors:

First, any calculation of real GDP would eliminate the year-over-year variance that could be due to taste shocks leading to significant price changes.

Second, I think your observation is partially true, however. What makes an iPhone more valuable than an old Motorola smartphone? Sure, some inputs might be slightly different, but the "production technology" of the iPhone makes it such that we (in general) do value it higher. While some measures like CPI try to account for some of those issues by considering benchmarks for certain performance criteria (like processing power, memory, etc.), in the end, there absolutely is some taste-based component.

I think it's partly accounted for by aggregation, as you mentioned, but I think the third point is that there's a bit of a disconnect between what value is trying to measure, and what GDP is interested in. Theories of value attempt to explain why we attach certain "utility amounts" to different goods. But that doesn't mean the output of any particular "theory of value" is subjective: the observed prices and quantities are quite objective. GDP (like other macroeconomic indicators) is more interested in tabulating those objective outputs of the theory of value and observing their change over time.

For example, I know I value the green mechanical pencil in front of me at \$2, despite the fact I only paid \$1 for it. Assuming the production costs are negligible, GDP would observe that as \$1 of economic activity. It doesn't consider how much I would have paid for it, which is what different theories of value attempt to explain. Furthermore, why I value it at \$2 might be for any host of reasons- perhaps its a subjective value, or perhaps that valuation reflects what I think the pencil will be worth in a year's time. Regardless of what that reasoning is, the objective measurements that GDP considers are the price paid and quantity.


What economics theory explains changes in purchasing different types of goods?

If you research "discount rates", "time preference" or similar, you'll find all sorts of stuff about seemingly inconsistent decisions, some of which can in fact be explained quite well and some of which show some ways that people can be dumb sometimes. You'll find lots of approaches to modelling comparisons involving things like someone revealing an implicit interest rate of over 100% per annum in one situation while accepting 5% as a good return in another situation.

I wouldn't focus too much on any specific paper. Check the bibliographies and see the variety of what's out there, and maybe narrow in on a handful of most-promising conceptualizations afterwards.

As a point of contrast, you could introduce the lifetime income hypothesis of Friedman as discussed in many 1st and 2nd year textbooks.


Credible Threat in the Perfect Bayesian Equilibrium

I am going to assume that $F$ and $G$ are continuous distribution functions (I.e. players are playing properly mixed strategies). If this is not the case there is not enough information to answer your question. Given that assumption, player 1 and 2 must be indifferent among their actions in game 1 given the strategies of the other player.

In the second game, you are assuming that the node given by $x,k$ is never reached (since $j$ and $k$ give the same payoff and when indifferent, player 1 always choose $j$).

Under that behavioral assumption (which must be verified to be consistent with equilibrium), player 2 must believe she is at the node "$y$" with probability 1. Since Player 2's beliefs have changed with respect to game 1, the mixed strategy given by $G$ is, in general, no longer optimal (unless $a$ and $b$ give the same payoff regardless of the action of player 1).

In short, player 2 will, in general, not use the same strategy in the first and the second game; so threatening to use $G$ is not credible.

Btw all threats are credible in a PBE since strategies are best responses given some beliefs that are Bayesian.


Does the law of supply reject rise in total revenue for goods with elastic demand?

There is no contradiction.

The law of supply simply indicates a supply curve is upward sloping.  There is no prohibition against the curve itself moving so that it intersects demand in another location, so long as the slope remains positive.


How is it economically responsible to destroy proprty which has value?

The general answer would be that it is wasteful and selfish to destroy assets with value. I'm referring to assets as something you own, as property can be confused with land or real estate properties.
Still, I tried to list a few motives for destruction of assets
Responsible destruction
The only cases that come to mind as "responsible" destruction of assets, are when the assets in cause can harm others. Disarmament is a good example here: arms have value, but its destruction reduces the potential arm they can cause.
Destruction for personal gain
The case you provided goes more in the direction on "in which cases can you destroy value for self gain". The Art example you provide is a good one: increasing the scarcity could be economically profitable, when one is sure that the increase in value for the remaining asset is larger than the loss of value from the destroyed asset. If you consider fraud, burning your own house or car for claiming insurance is another example.
Irrational destruction
As many referred, you need to consider that humans don't always act "rationally", and in times of frustration and desperation people feel like destroying stuff. An historical example from the US: In the great depression in 1929, farmers were destroying their own production as the price of crops was below the cost of producing it. At the same time there was hunger around the whole US (source).
Creative destruction
As you tagged this question as reference-request, I believe that you might be interested to read the Wikipedia article on creative destruction, a term coined by Schumpeter, described as

The process of industrial mutation that incessantly revolutionizes the economic structure from within, incessantly destroying the old one, incessantly creating a new one.

Although this doesn't answer your question per se, is the only reference I could think of on the topic of "destruction".


Is there an equation for compounding interest while adding to the principle amount

Let $A_t$ be the amount of money at the beginning of year $t$ and let $r$ be the interest rate. Assume that each year, we invest an additional amount of $Q$ Then we can recursively write this as:
$$
A_t = (1+r)A_{t-1} + Q.
$$
So the amount at time $t$, $A_t$ is the amount last year $A_t$ plus a percentage $r$ of $A_t$ plus $Q$. We would like to find a closed form solution for this problem, i.e. remove the $A_t$ from the right hand side.
Notice that, by recursion, also:
$$
A_{t-1} = (1+r)A_{t-2} + Q.
$$
As such substituting for $A_{t-1}$ in our original equation gives:
$$
A_t = (1+r)^2 A_{t-2} + (1+r)Q + Q.
$$
Next, substituting out $A_{t-2} = (1+ r) A_{t-3} + Q$ gives:
$$
A_t = (1+r)^3 A_{t-3} + (1+ r)^2 Q + (1+ r) Q + Q.
$$
There's a pattern here. $A_{t-j}$ gets multiplied by $(1+r)^j$ and then terms are added: $Q$, $(1+r)Q, (1+r)^2 Q, \ldots, (1+ r)^{j-1} Q$.
We conjecture therefore that the solution will be of the form:
$$
A_t = (1+r)^t A_0 + Q \sum_{j = 0}^{t-1} (1+ r)^j
$$
We can show that this is indeed the solution by induction. For $t = 1$ we have:
$$
A_1 = (1+ r) A_0 + Q.
$$
which is true.
Also:
$$
\begin{align*}
A_t &= (1+r)^{t} A_0 + Q \sum_{j = 0}^{t-1} (1+ r)^j,\\
&=(1 + r)\left[(1+ r)^{t-1} A_0 + Q \sum_{j = 0}^{t-2} (1+ r)^j\right] + Q,\\
&= (1+ r) A_{t-1} + Q.
\end{align*}
$$
Now, to finish up we can simplify the geometric sum:
$$
\sum_{j = 0}^{t-1} (1+ r)^j = \frac{(1+ r)^{t}- 1}{r}
$$
As such:
$$
A_t = (1+ r)^t A_0 + Q \frac{(1+ r)^{t} - 1}{r}
$$


But perhaps this is not always the case. The price might have been so high that you would not have been willing to bid above it. In fact it might have been so high that the no one but the highest bidder would have given that bid. Knowing this the highest bidder could decrease his bid. In fact in English auctions (non-silent rising bid auctions) the final price is the second highest valuation of the unique good. In the auction you describe (a sealed bid first price auction) the final price is usually somewhat random based on what people believe about each others valuations and each others bidding strategies. It can happen that the final price is higher than it would have been in an English auction because one of the bidders overvalued what his competition would be willing to pay. So the English auction is not clearly advantegous.

It has been shown that given some rather strict conditions the English auction and the sealed bid first price auction have the same expected yield for the auctioner. This is known as the "Revenue Equivalence Theorem".

In practice it is somewhat agreed upon that in rising price auctions bidders experience something called 'auction fever'. Basically being outbid encourages them to raise their own bid. This is true even if the auction was designed in such a way that revealing the true highest valuation by all bidders would be an equilibrium move. (Auction by proxy, the auction system eBay and several other sites use is such an auction type.)

So it seems that in practice you might be right and rising price auctions might be better in expected value for the seller. This is just speculation but in your case you I think you might merely be experiencing remorse because you have undervalued your competitor's bid. I have been there :)
 (By the way this could encourage you to overbid on your next silent auction, to the benefit of the seller. Such overbidding might give him higher than English auction payoffs. Again, which system is better is not always clear.)


IS-LM - Effect of interest rate on price level

There are two different way to present the IS-LM model, one with a vertical money supply line, and one with a horizontal interest rate line. Consider the second one, as it represents better what central banks actually do nowadays.

If the r goes up, this means the central bank has increased its benchmark interest rate (it can mean a host of other things, but I am assuming your IS-LM model does not include risk premia and the like). The horizontal r line shifts upward. The point where this line intersects the money demand line implies that the real money supply is lower. This does not tell us much: it just tells us that the central bank, in order to achieve the higher interest rate it wants, has decreased the nominal money supply M, so that, given the money demand, the interest rate goes up. One could represent this equally well with a vertical line, as I mentioned, but that representation makes it seem as if the central bank targets a given level of money supply. It does not: it targets the interest rate.

Anyway, Patricio is right in saying that, to really track what happens to P, you need the AS-AD model. However, the basic mechanics can be understood intuitively in the IS-LM. The shift in money supply shifts the LM curve leftward, so Y decreases. We move upwards left along the IS curve, as the increased interest rate (endogenously) decreases I (the opportunity cost of investing is larger, so less people invest). The resulting decrease in demand lowers the price level (this is just basic S-D logic, no AS-AD needed). If the central bank wants to keep to its target interest rate, it further increases the M in response to the decrease in P, so as to keep M/P at the level conforming to its target interest rate.

There are some more dynamics in the AS-AD curves after this that have to do with wage rigidity and inflation expectations, but I will leave it at that, as I don't know if you've seen this already.


Can quantative easing be summarized as "The state prints cash to pay its debt to private sector"?

Altough you are correct saying that the state "own" central banks, they should be independent from their government. This gives freedom to monetary policymakers from direct political or governmental influence in the conduct of policy.

Given that, I would say that your interpretation is a bit exaggerated and maybe biased somehow.

Quantitative easing (QE) is a monetary policy in which a central bank purchases government securities or other securities from the market in order to increase the money supply. This is made with newly created bank reserves, but doesn't mean that new currency (bills and coins) has been printed. In theory, with more liquidity, the domestic demand would increase and eventually promote economic growth. Then, the excess of liquidity is absorbed by the growth and inflation would remain low.

The problem is if the economic growth don't happen, there will be inflation.

Using a more informal language, it's correct to say that the government is creating money in the present, hoping that this fresh money will increase economic growth in the future.


Indeed, their theory relates primarily household debt to net exports. This is the main focus of their working paper. However, as a referee, I would try to find out more and ask whether the change in net exports comes from imports or exports, or whether household indebtedness could also affect international transfers. A household may use debt to invest abroad and get dividends and interests in return. Are there no other margins that could be affected? This type of request is quite common from referees and may explain the differences between the working paper and the final version.


What properties must a utility function have such that we can define level sets and thus indifference curves?

Level sets are always well defined. No property of utility functions has to be assumed. For any utility level $\bar u$ just define the level set to be $\{x\in \mathbb{R}^n|U(x)=\bar u\}$. No property of $U$ must be assumed. This is well-defined regardless of the properties of $U$. Properties of $U$ are useful if one wants to derive specific properties of the level sets, but are not needed to define them.


Do Chinese tariffs on American goods make them more expensive to American consumers?

Well, due to Lerner's Simmetry Theorem, an import tax has the same effect of an export tax. When China makes its imports from the US more expensive, its exports get more expensive too.


Can the cyclicality of the real wage be used as a measure for the degree of competiveness in the labour market?

In general, no. The procyclicality of wages can also It could also be a measure of labor market frictions instead of the level of competition.

For an example that highlights the difference, consider an economy where only union electricians can do electrical work and where the union controls the members and their hours. If the union can frequently and costlessly adjust their total labor supply, then they don't have a lot of friction in their supply but they (by construction) have limited competition through their monopoly labor supply.  On the other hand, laws mandated costly separation processes for employees such as 2 years severance or, more extremely, lifetime employment make it very difficult to adjust the quantity of labor supplied but this isn't exactly a competition issue. There could be many employees, many employers, and no licensing restrictions and yet this could still significantly dampen the cyclicality of the real wage by making employment not adjust to cyclical productivity shocks.

This might be somewhat splitting hairs because both restrict the adjustment of labor demanded but conceptually they are quite different.

Additionally, there may be reasons related to other features of the economy or the way that the data is gathered for wages to be less procyclical in one place than another. For example, measurement error attenuates statistical relationships towards zero so in two otherwise identical countries, if one has wage measured with more error then the correlation between wage and your favorite business cycle measure will be shrunk towards zero in that country relative to the truth.


If Lebanon has a shortage of dollars, are USD donations meaningless?

Lebanon has had significant current account deficit (low level of exports versus imports). This was financed by capital inflows seeking to benefit from facilities given by the CEntral Bank. The Financial Times says:

Lebanon depends on imports and for years the central bank has helped to finance the trade deficit by offering high interest rates — sometimes more than 10 per cent a year — on dollar deposits from commercial lenders. The banks, in turn, passed those generous rates to their clients, helping to attract foreign currency from local depositors and the large Lebanese diaspora abroad.

The problem is that this suddently changed based on local instability. FT:

The system has helped Lebanese banks generate impressive profits. But last summer fragile investor confidence waned, the flow of dollars began to dry up and the system started to break down. Mass protests began in October, stoked by frustration with stark inequality, and eventually toppled the government.

The lack of USD means depreciation (in the black market particularly) of the local currency (which was overvalued).
Sending USD is equivalent to foreign capital inflow. It is one way to finance deficits and can help Lebanon. But it is clearly not a sufficieny nor sustainable solution. The problem is a depressed economy crippled with enormeous corruption (a problem running deep because of the ethnic and religious fault lines dividing society), lack of public investment and low productivity. It requires a deep clean of all the rotten political and elite class, which is on the "save yourselves" mode. Let's hope it doesn't descend into another civil war.


Why do many papers not write the actual utility function?

This is done in order to make the solution more general. If you use specific utility function you prove your result only for that specific utility function and not for other ones.
You can still derive Euler equation. For example in a simple 2-period consumption model where agents maximize their expected utility
$$E[u]=E[\sum_{t=1}^T u(C)_t]$$
where $t=1,2$. Given this, the Euler equation would be simply:
$$u'(C_1)=u'(E[C_2])$$
you could insert some specific utility function into the problem. For example, you could use quadratic utility $E[u] = E[\sum_{t=1}^T C_t-\frac{a}{2} C^2_t]$ (as in Romer's Advanced Macroeconomic handbook) which would give you Euler equation $C_1=E_1[C_2]$ and continue using that but in the first case you prove your result for whole range of utility function whereas in the second case only for single 1 quadratic utility. In science we like to make results as general as possible so usually the first approach would be preferred.
In a typical IS-LM model you will actually want to substitute some utility function because for derivation of the model its important to know what optimal consumption $C^*$ is. However, you might not substitute it right away. You are completely vague about your citation of Woodford (2003) which could refer to multiple sources. For example, in his 2003 book Interest and Prices, on PP 145 where he builds New-Keynesian style macro model he actually makes explicit assumptions about consumption and in these macro models utility is usually kept simple such as $U=C-\frac{1}{\gamma}L^{\gamma}$ (See for example again above mentioned Romer's handbook).


Optimization of Households' utility in " Rule-of-Thumb Consumers and the Design of Interest Rate Rules " (Gali et al., 2004)

In this case, the stochastic discount factor appears in equation (7), the intertemporal optimization equation. You can derive (7) by taking the first order conditions of the Lagrangean function with respect to consumption, and then investment (or capital, K_t+1, if you want to substitute out the capital accumulation equation). You then combine these two optimality conditions to yield (7).

The stochastic discount factor, then, is just the ratio of marginal utilities of consumption in period t+1 and t. The ratio of prices appears in the stochastic discount factor because this is a nominal model, and you need to discount future nominal payoffs by inflation between time t and t+1.


Is it possible to have a modern economy without a central bank?

It surely is possible: For a long while, Gold was the basis for the value of money in many "modern" countries, leaving central banks with little room for policies.


Lagrangian: How to understand the No-Ponzi Condition

The condition is mostly referred to as the No-Ponzi (-scheme) [NP] condition. It is one additional constraint, that prevents Ponzi-schemes: Paying debt with new higher debt, ad infinitum.

By the way: The NP condition is one condition, hence the associated multiplier should be $\psi$ instead of $\psi_t$. While certainly nothing is lost repeating the same condition over and over again (for any $t$), we don't need it more than once, and it is being imprecise.

Think about optimization for finite $T$ periods. Then, you have the condition that $B_T \geq 0$. The Lagrangian optimization gives you the local optimization between $0, 1, 2$... There are many solutions that are locally optimal, but you will only allow solutions that in the end lead to $B_T > 0$.

A simple example

Your example is much too messy to think about these core issues. Look instead at the problem

$$ \max_{\{c_t, a_{t+1}\}_t} \sum_t \beta^t U(c_t) + \lambda_t (a_{t+1} + c_t - Ra_t)$$

That is, a household that choses assets $a$ and consumption $c$ to maximize his utility. You can summarize the FOC as

$$ \beta^t U'(c_t) = \lambda_t \\
\lambda_t = R\lambda_{t+1}\\
\Leftrightarrow U'(c_t) = \beta R U'(c_{t+1})
$$

Look for a moment at the special case where $\beta R = 1$ (what does that imply?). With most preferences, this necessarily leads to $c_t = c_{t+1}$. This is the local optimization that I was referring to, which is what the Lagrangian gives you. There are, however, infinitely many solutions that satisfy $c_t = c_{t+1}$. Next, we try to use the budget constraint:

$$ a_{t+1} + c_t = R a_t\\
\Leftrightarrow R a_0 = \lim_{T\to\infty}\sum_{t=0}^T \frac{c_t}{R^t} + \frac{a_{T+1}}{R^T}$$

This is as far we get using the (infinite) set of local budget constraints, where I have used forward iteration (hopefully correctly), assuming any start date $t=0$.

Now, if the household also has to satisfy the NP condition, this boils down to

$$R a_0 = \lim_{T\to\infty}\sum_{t=0}^T \frac{c_t}{R^t}$$

which, as we showed $c_t$ to be constant, we can solve easily and receive a single budget constraint. The unique solution to the problem that satisfies the NP condition is the solution where $c_t$ is a constant and this last equation holds.


Can the supply curve shift while the PPF does not shift?

Edited.

PPF is the maximum potential output that a country could produce using its resources and technology. No, the PPF should shrink due to the loss of labour (from leg injury).

No, factory is a stock of capital, thus, ppf should shrink due to loss of capacity. It is also affected by the technology of production i.e. methods of production. It moves outwards due to technological progress.


Your question has been addresses in different ways. Kydland and Prescott (1977) argue that a central bank should follow defined policy rules instead of active stabilization methods because the latter contributes to economic instability. Barro and Gordon (1983) prove that under a discretionary regime, the central bank has an incentive to print money to improve the economic performance in the short run, but this doesn't happen in the long run. Walsh (1995) discuss the way central bankers incentives should be design in order for the central bank to follow a socially optimal policy.

On Central Bank Independence (CBI), Grilli, Masciandaro and Tabellini (1991) and Cukierman, Webb and Neyapti (1992) developed a methodology to assess CBI  from different countries, and how the degree of independence impacts on the economic performance of this countries. Alesina and Summers (1993) studied 16 OECD countries and they compared the countries CBI score against economic performance measures (GDP growth, unemployment rate, and inflation). Then, there are several papers that cite these researches and build upon them.

The CBI scores are based on multiple criteria, Grilli et al., have a different approach than Cukierman et al. Alesina and Summers used a combination of both, so for the case of Zimbabwe you'll have to analyze if the laws of its central bank have the characteristics that the researches take into account when they build their indices.


The concept which you should be looking it is called prime costs. Businesses use prime cost as a way of measuring the total cost of the production inputs needed to create a given output. Usually this would be e.g. material, working hours, machine time and so on; since in your case there are only materials they are the only components you should consider when calculating the price.

So in your example the prime costs would be cost of purchased material + cost of donated material at market price. After this you would have to add a profit margin which you feel comfortable offering to your members.

As you mentioned their might be cases when the prime costs are higher then prices on the open market. In this case the only thing you can do is sell your material and buy the product directly on the market this is classical make or buy decision. If you still want to offer these product at a discount to the market price your only option is to take a loss on every sold item.


You should always validate statistically your model, running various model diagnostics. It appears you work with time series (single country?).

Here, certainly autocorrelation may be an issue. After all, your series for capital is by construction an autoregressive equation with a forcing factor (investment).

Software packages usually warn for signs of multicollinearity.

Also, a serious issue could be that of endogeneity of regressors.


How to find the Utility Possibility Frontier when there are Perfect Substitutes?

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

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


The value of something, in this case money, is based on it's demand; and since you want the value based on it's efficiency, not what it can purchase, you are looking for the value of money based on how efficient money is.
I believe I have just the answer for you.

Your missing variable is the Velocity of Money.
The demand for money and the Velocity of Money are inversely related. (your question emphasizes this point, "in contrast to the value it represents?".

The velocity of money (or the velocity of circulation of money") is a measure of how fast money passes from one holder to the next. It is most commonly measured as the income velocity of money, which is the frequency at which the average unit of currency is used to purchase newly domestically-produced goods and services within a given time period. In other words, it is the number of times one unit of money is spent to buy goods and services per unit of time.

Vt = PT/M
where

Vt is the velocity of money for all transactions in a given time frame;
P is the price level;
T is the aggregate real value of transactions in a given time frame; and
M is the total nominal amount of money in circulation on average in the economy.
Thus PT is the total nominal amount of transactions per period.

Hope this helps.


Request of references regarding Friedman's Nobel Prize

The Royal Swedish Academy of Sciences has decided to award the 1976 Prize in Economic Sciences in Memory of Alfred Nobel to Professor Milton Friedman, University of Chicago, Illinois, USA, for his achievements in the fields of consumption analysis, monetary history and theory, and for his demonstration of the complexity of stabilization policy. [...]
  His major work, A Monetary History of the United States,1867 - 1960, is regarded as one of Friedman's most profound and also most distinguished achievements. Most outstanding is, perhaps, his original and energetically pursued study of the strategic role played by the policy of the Federal Reserve System in sparking off the 1929 crisis, and in deepening and prolonging the depression that followed. The critics agree that this is a monumental scientific work which will long stimulate the re-examination of the course of events during this epoch.

http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1976/press.html


The argument is based on the famous prisoner dilemma result. For example, consider the following situation. We have firm A and firm B. If they both collude and set high price (high P) they both can get profit $\\\$7$, If A sets high price but B undercuts A (note undercutting is not the same as engaging in dumping see end of answer) then A will earn 0 profit because everyone will want to buy goods from B and B earns $\\\$10$ profit. If A chooses low P and B high P the opposite will happen. If they both choose low price they both earn $\\\$5$ profit. Moreover, we will assume that they cannot enter into a contract that would allow them to make commitment to high prices that would be enforceable in law.
The situation can be visualized in the matrix below:

                             Firm B
                             High P    Low P
     Firm A       High P     $7,$7     $0, $10
                  Low  P    $10,$0     $5, $5

What will happen in this case? Lets start looking at the problem from perspective of firm B:

what happens if firm A chooses high price?  You can easily see that the most rational response for firm B is to chose low price - thats how they maximize their profit as getting profit of $\\\$10$ is better than profit of $\\\$7$.
What happens if firm A chooses low price? In this case again it would be most rational for firm B to choose low price because its better to get at least the $\\\$5$ profit than zero.

Thus setting low price is strictly dominant strategy for firm B and if firm B is rational it should always set prices low. The mirror argument applies to firm A as well. Hence, due to this collusion cannot be sustained.
Few caveats:
The simple prisoner dilemma model captures the core of the argument but also its not entirely realistic as in real life firms can be argued to 'play' repeated game of competition and in repeated games conclusions can be sometimes sustained depending situation. For example, if firm play the above game repeatedly they can collude because repeated games allow for richer amount of strategies such as trigger strategies where firms can try to punish each other for deviating from the collusion equilibrium.
You can learn about these more complex situations in some industrial organization textbooks such as Industrial Organization: Markets and Strategies by Martin Peitz and Paul Belleflamme.
Nonetheless, in real life also most countries set very high fines and penalties for colluding firms as well as rewarding any firm that 'snitches' on other colluding  firms. Thanks to the fact that these penalties are very strict it is incredibly hard for firms to sustain any explicit collusion which is why they are rare but still occur sometimes - see some EU cases here (although tacit collusion - i.e. collusion where firms set high prices without actually making some secret agreement can still occur).

Furthermore, note selling for price lower than your competitor is not called dumpling.  Dumping means selling products for less than it cost to produce them not less than others. Dumping is a separate issue altogether.


Why don't prices of USA labor and Mexican labor equalise?

The underlying reason for persistent wage differences is probably that Mexican workers are less productive than American workers.
It is sufficient that workers in some tradeable sectors are more productive to have persistent wage differences in all sectors. (a good explanation of this effect can be found here: https://en.wikipedia.org/wiki/Balassa%E2%80%93Samuelson_effect#The_effect_in_more_detail)
One would expect that unit labor cost in tradeable sectors converges, not necessarily wages.
Here is a graph that suggests this has already happened: https://fred.stlouisfed.org/series/CCRETT02MXA661N, for an explanation of real effective exchange rates see here: https://en.wikipedia.org/wiki/Effective_exchange_rate


Is a smartphone app(Non premium or subscribed service like Netflix) a public good?

Am I correct to say that the app is non-excludable?
I am sorry to say but this is wrong. Just assume google removes the application from the store. All android users would be excluded. There are many ways to exclude people from consuming an application. Access can be bound to a minimum age requirement, to a certain country (geo-blocking) or simply to a payment.
The possibility is important not the concrete situation.
Just because it is free now does not imply it is generally non-excludable.
Let’s ask the same question for a classic public good: Could you easily exclude someone from consuming air? Even if you wanted to this would be (nearly) impossible.


How do I calculate consumer surplus and producer surplus from this?

In equilibrium, we have supply equal to demand. So $Q_{s} = Q_{d} \implies 50 = 2p$, so $p^{*} = 25$ is the equilibrium price. Consumer surplus is defined as:

$$\int_{p^{*}}^{p_{max}} Q_{d}(p) dp$$

Here, $p_{max} = 50$, as $Q_{s} = 0$ when $p = 50$. So evaluate the integral.

Producer surplus is similarly defined as:

$$\int_{0}^{p^{*}} Q_{s}(p) dp$$


Why is it important to open up the economy before a cure for COVID-19?

This is not economics question
healthcare, helping sick people are economic activity.
This is example of false dilemma. Economy activity such as food and health equipment production are important to save many people lives.


Is the utility of money *actually* logarithmic?

"Essentially, all models are wrong, but some are useful"
George Box,  Empirical Model-Building and Response Surfaces

To what approximation would one like to know the utility of wealth?

To be guaranteed that a utility function representation of preferences exists you need a number of assumptions about preferences to hold. Usually, these are Completeness and Transitivity with Continuity, Monotonicity, and Convexity common additional assumptions to give the nicely behaved preferences we see in most economics settings. Levin  and Milgrom (2004) provides a technical, but short overview of the definitions and derivations in this branch of economics called "Choice Theory".

But that's just for ordinal utility functions (functions which rank bundles of goods but resulting the utils have no economic meaning beyond that a bundle with higher utils is preferred to one with lower utils) to exist. It turns out that the preferences of ordinal utility functions are preserved by any positive affine transformation. To get a particular functional form like $log(x)$ to matter you need cardinal utility where the values of the preferences matter (although even here they can be re-scaled by a positive constant and a constant added). Cardinal utility functions are more common in finance and macroeconomic settings even though more is required for such a utility function to exist. As Wikipedia says:

  The idea of cardinal utility is considered outdated except for
  specific contexts such as decision making under risk, utilitarian
  welfare evaluations, and discounted utilities for intertemporal
  evaluations where it is still applied. Elsewhere, such as in
  general consumer theory, ordinal utility with its weaker assumptions
  is preferred because results that are just as strong can be derived.

Cardinal utility

Given the findings of behavioral economics experiments, which provide evidence that preferences may violate completeness and transitive axioms, it is likely that no such "true" function exists. However, as Box's quote indicates, they may still be useful.

The log utility function has nice properties. The logarithmic utility function is a special case of constant relative risk aversion (CRRA) utility function. Roughly speaking, this family of utility functions views risks in percents of wealth as constant for all levels of wealth. That is, rich and poor alike worry the same about a 10% shock to wealth. Equivalently, the utility "pain" of spending 10% of wealth on something are the same at all wealth levels. This is an example of a function with a declining marginal utility of consumption.

Log utility is particularly easy to work with because it has simple derivatives and reflects a "low" but non-zero level of preferences over risk. Also, under log utility the wealth and substitution effects of interest rates cancel out in intertemporal choice problems, which further simplifies some models. In portfolio allocation, log utility maximization is effectively maximizing the geometric mean return the return in the long run, which feels intuitively sensible as an investment goal for the long run investor. Also, when working with shocks to wealth that are log-normal and a log utility function, there are nice closed form solutions to the values of expected  utility (they are slightly more complex in the CRRA case). Here is an example of trying to calibrate CRRA utility using experimental data:

  For this specification of CRRA, a value of 0 denotes risk neutrality,
  negative values indicate risk-loving, and positive values indicate
  risk aversion.  Thus we see clear evidence of risk aversion: the mean
  CRRA coefficient is 0.64. This distribution is consistent with
  comparable estimates obtained in the United States, using college
  students and an MPL design, by Holt and Laury [2002] and Harrison,
  Johnson, McInnes and Rutström [2003a][2003b].

Harrison, Lau, Rutstrom (2007)

If CRRA were the proper specification and the experimental point estimates recovered the true CRRA parameter, then we would be close to log utility which occurs when you take the limit of a CRRA utility function as the coefficient approaches $1$.

In conclusion, there is some empirical evidence that preferences can be approximated with a log utility function and it is very easy to work with.


Do the donated NFL losing team shirts destroy local economies?

My answer is no, it doesn't hurt the local economy. This seems like an example of the "Broken Window Fallacy":

Suppose, when nobody is looking, I break all of the windows in my neighbour's house. This creates a bunch of work for a glazier who might otherwise have been idle. So it seems like, by going round smashing things up we can provide a boost to the economy. Surely this must be wrong!?

Indeed, the problem with this logic is that we have to think what would happen if I had not broken the windows. My neighbour, not having to incur the expense of replacing his windows, would have some extra money to spend on a hair cut or a new bicycle, creating work for a barber or a bicycle maker. If the windows are broken then those guys miss out.

So the glazier earns some extra income and gains; the barber earns less income and looses. But these two things "cancel out": this is just a transfer of wealth from one person to another rather than the creation of new wealth. My neighbour, on the other hand, definitely loses because he doesn't get a hair cut any more. So overall, the broken windows are a net loss to society.

The reason I think this is relevant to your question is that we could reframe it as: "if we burnt the shirts [broke the windows] instead of giving them away for free, wouldn't that create work for a tailor and therefore make society richer?"

I think the answer is no because, freed from the need to buy a shirt, people have more income to spend on food, educating their child, taking care of their health, etc. All of these things create jobs in the local economy to replace the lost jobs in the clothing industry.

It is true that the tailors lose out at the expense of the farmer, teacher, or nurse. But over long time horizons people will adjust to this by training to do the jobs that pay.

tldr; Destroying real resources may create winners and losers, but is almost always bad for society overall.


Why US market is falling due to greece fear?

As dg99 mentioned the response has actually been relatively muted so far in the American markets  (SPX down 3% or so from its peak).  Generally, problems in major world equity markets cause cascading problems in their trading partners.  In this case there are many American companies that have European stores or otherwise sell into European markets that are affected by the turmoil.  There are secondary effects as well as companies that trade with affected companies feel the pain and so on.

As you mention the news out of the US has been fairly positive, but a melt down in the EU would likely overwhelm the tepid growth in the North American region.

The important thing to note here is that the investments do not necessarily need to go somewhere.  We can just all agree that the value of European investments is significantly less now because future earnings is likely lower (really for any reason) and the price will change even if no one sells and no money leaves the region.  In a very real sense billions of value just no longer exists.   However, it is true some people have been selling and investing elsewhere.  The main beneficiary is generally safer instruments like bonds which have rallied somewhat.


Are all country government budgets made up of taxes?

The answer to your first question is no.

For example in Saudi Arabia only foreign residents are taxed. The state can afford to do this because it owns the oil fields and receives a lot revenue from them.

In Russia the oil and gas companies gave 52% of the federal budget. Part of this is in the form of taxes, but it is mostly the profit of Gazprom, the state owned gas company. The Russian government also collects personal income taxes as well as other kinds, so taxes are also a source of their budget.


Measuring macroeconomic variables more frequently

Looking at the US Economy,  the US Bureau of Economic Analysis (BEA) and specifically ch. 3 p. 49 of the Handbok of NIPA (National Income and Product Accounts), we read

  "The data that BEA uses are collected from a variety of sources and are
  usually collected for purposes other than for incorporation into BEA's
  estimates. Data collected by federal government agencies provide the
  backbone of the estimates; these data are supplemented by data from
  trade associations, businesses, international organizations, and other
  sources. The Government data are from a number of agencies, including
  the Commerce Department's Census Bureau, the Labor Department's Bureau
  of Labor Statistics (BLS), the Treasury Department, the Office of
  Management and Budget, and the Agriculture Department.
  “Administrative” data are data that are tabulated by federal
  government and by state and local government agencies as a byproduct
  of administering their programs—such as processing corporate tax
  returns, regulating public utilities, and issuing building permits.
  “Statistical” data are data collected by the federal statistical
  agencies, such as the Census Bureau and BLS. These data consist of
  periodic economic and population censuses and a wide range of sample
  surveys, such as those that collect data on manufacturing and trade,
  employment, and prices. The relatively few surveys that BEA conducts
  cover international trade in services and international direct
  investment, both by foreign companies in the United States and by U.S.
  companies in foreign countries. The source data available to BEA are not always ideal for the preparation of the
  NIPAs. BEA must develop methods that transform the best available data into estimates that are consistent with the NIPA concepts and framework and that fill gaps in the
  coverage of the source data."

Macro-data are not just micro-data simply sitting out there and only needing adding up. So "collecting macroeconomic data" is a misleading term : "laboriously producing macroeconomic data", where collection is just a first step, moving on to selection, clean-up, adjustment, homogenization, and estimation, is more like it. This is a vast enterprise, even with today's Information Technology capabilities, even for smaller economies than US.

Increasing the frequency of macro-data amounts to increasing the total output from this data-production function, which looks convincingly like a huge increase in input factors absorption. So to do it, it would increase costs substantially.

Moreover, the "collected for reasons other than..." part, indicates that a lot of procedures should be disrupted and changed in order to achieve that. Also, the number of different primary sources implies too many people and institutions should change their way of doing things. These are significant barriers on their own, irrespective of cost-issues.

What could be the benefits?
One could think that it would permit a "better" fine-tuning of the economy? -to the degree that one believes that an economy can really be fine-tuned by its Government (it can certainly be affected, but fine-tuning is a whole different game).

What about the benefits to the private sector? It is indeed the case that, say, Gross Domestic Output is produced every day. Assume that in some magical way, GDP was recorded and published every day. So we could follow GDP as we follow the Stock Market. We will be able to observe the everyday variability of output. Would that be beneficial? No, on the contrary, it would be misleading. Why? Because, although GDP is produced everyday, it mostly is produced based on structural relations (contracts, technologies, customs, knowledge etc) that have a lower frequency of change -and for reasons other than lack of data. So its everyday variability would be mostly due to pure randomness or exogenous factors like the weather -and observing it would only torment us towards trying futilely to do something about it (at our own micro-level).

What about the benefits to the discipline of Economics? Presumably, more data is always better. Is it? By increasing the number of instances of "asking for" and recording data about an economic variable, we increase the instances for which we may have measurement error - and this may very well degrade the overall quality of our data. It is a standard wisdom departed in undergraduate statistics classes, that even if we could conceivably run a census than just collecting a sample from the population under study, it would be better to have just the sample, because the error of representability would most likely be smaller than the error of measurement we would have if we attempted to record the whole population.

That would offset the perceived benefits of having pushed the magnifying glass closer to the object of study. And sometimes, it is better to look from a certain distance, anyway.

Closing, by a "Laffer-curve" style of argument, one could argue that there must exist some optimal frequency to have available macro-data. I am not saying that what we do have now is this optimal frequency, but I doubt making the frequency higher is the way to go (my opinion is that modern economies of the western world at least would be tracked better under a three four-month cycle - Jan-Apr, May-Aug, Sep-Dec -it seems to me that this scheme combines better the seasons with the social aspects of life and economic activity).


Does different Base Year in Price Index affected conversion of nominal value to the real value?

This question might be better suited for a statistics group, but if I understand you correctly you're going to compare two prices from different price indeces and see if there's a difference in the growth? There's really nothing wrong with the reasoning, but you should take the results you get with a grain of salt as you'll be comparing two indeces with different samples.

The different base year is not a problem as long as the variables you're dividing are from the same dataset. When price indices are renewed, the sample is often changed, so this is why you should be aware what you're doing when comparing between different base years.


Why does lowering stock rate of returns increase stock prices?

In the part 1 there must be some omission. Just by itself a random Fed purchase would not reduce risk premiums. However, a targeted Fed purchase can reduce risk premium as non-trivial part of risk in any firm stems from liquidity risk. Through purchasing assets of illiquid firms Fed can provide them with liquidity that they need and thereby reducing the risk that they fail just due to illiquidity. Also as Fizz points out in his comment this is just one example, there are several other channels that can also lead to risk reduction as well.

The intuition behind this is that the stock prices represent present value of the future expected income streams you get from the stock and at lower interest rate the present value of this income stream becomes higher. To see why this makes sense consider practical example where the stock always pays dividend 10\$ in perpetuity. Then in order to actually calculate whats the present value of getting the stream of 10\$ at 10% you can use the Gordon formula which is just based on calculating the value of infinite sum. In simple Gordon stock pricing formula given as $P=\frac{D}{r-g}$ where $D$ is dividend and $r$ rate of interest and $g$ rate of growth which we can for sake of simplicity ignore and assume its zero so we get $P = \frac{D}{r}$.
At the 10% the infinite sum of 10\$ will be worth 100\$ because
although your are getting the dividend in perpetuity due to time
value of money money in future is less valuable than money now and
becomes less value the more you look into the future and hence this
infinite sum in present value terms becomes smaller and smaller
which allows us to actually calculate finite value even for an infinite stream of money. However, now if the interest rate drops to 1% the present value of those dividend streams becomes higher and the stock will now cost 1000\$ as now the future is discounted less heavily. To put it simply, at lower interest rate the money you receive in future have higher value today.


Slope vs elasticity of demand function - Is it the same thing?

No, slope of a demand function is $\frac{\partial q(p)}{\partial p}$ elasticity of demand is $\frac{\partial q(p)}{\partial p} \frac{p}{q(p)}$. So they cannot be same except in some special cases.


Why don't we count incomes of the government from taxation when calculating GDP using the income approach?

Actually you could use taxes because GDP formula using income approach can be also expressed as value added at basic prices + taxes less subsidies. However, you can’t do it at the same time when using the approach in your question as you would be double counting.

Using:

$$GDP= w+i + r+ \pi + o$$

Where $w$ are wages $i$ interest income $r$ return on capital $\pi$ profits and $o$ something you forgot in your question adjustments for things like net foreign factor income, capital consumption and revenue from some gov enterprise (not tax revenue) etc.

You would be double counting if you would include taxes, because taxes are subtracted from these. If you earn 100e and government taxes 10e then economy does not suddenly have 110e. The 10e is just transfer.

If government invests the money in some productive way it will show up as an gov revenue from those productive activities.

The value of public goods like army is already reflected in the income approach as soldiers earn wages, military contractors profits etc. The same holds for any other public good. Let’s say you build a road there are wages to be paid, contractors get profit etc.

Also, when government engages in pure transfers - for example redistribution this can’t show up on national accounts as it does not create more output in the economy, it’s just juggling output around.

However, this is not because government is viewed as parasitical. If you are Ralwsian or Utilitarian transfers from rich to poor are moral imperative. But economics is not moral philosophy it’s a science and GDP is a measure of output that is grounded in real production and fact of the matter is that transfers don’t create any additional output by themselves.


Question about Social Welfare Function and Social Profile

In its most general formulation, a social welfare function is just a utility function representing the preferences of "society as a whole" (or the preferences of a hypothetical "benevolent social planner" who makes decisions for the society).
Let $X$ be some space of "social outcomes".  (Social outcomes could be anything.  But if you want a concrete example, then suppose that social outcomes describe allocations of resources to individuals.  If there are $N$ individuals, and there are $M$ distinct types of resources, the an allocation is an ($N \times M$)- dimensional vector, so in this case $X$ would be some subset of $\mathbb{R}^{N\times M}$.)  A social welfare function is just a function $W:X \rightarrow\mathbb{R}$;  heuristically, if $x$ is some element of $X$ (some "social outcome") then $W(x)$ measures the "total welfare" or "social value" or "overall desirability" (or whatever) of $x$.  Thus, the benevolent social planner should aim for policies that maximize the value of $W$.
The key question, of course, is how to define $W$.  One way to do this is to somehow build $W$ out of the preferences or utility functions of individuals.  Suppose there are $N$ individuals, each of whom has a preference order $\succeq_i$ on $X$.  This collection of preference orders $(\succeq_1,\succeq_2,\ldots,\succeq_N)$ is an (ordinal) social profile.  (This partly answers your second question.)  A big part of the modern theory of social choice and welfare is about defining systematic, principled ways of defining $W$ based on the profile $(\succeq_1,\succeq_2,\ldots,\succeq_N)$.
Typically, purely ordinal preference information about the individuals is not sufficient. (This is one way of reading Arrow's Impossibility Theorem --I won't get into the details here).  So we might want to endow each individual with a utility function $u_i:X \rightarrow \mathbb{R}$ (which is more informative than just a preference order).  A collection of utility functions $(u_1,u_2,\ldots,u_N)$ is a (utility) social profile.  (This is the rest of the answer to your second question.) We  then seek to construct $W$ out of $(u_1,u_2,\ldots,u_N)$.
For example, given a social profile of utility functions $(u_1,u_2,\ldots,u_N)$, we could define $W(x):=u_1(x)+u_2(x)+\cdots+u_N(x)$ for all $x\in X$ ---this is the utilitarian social welfare function. Or we could define $W(x):=\min\{u_1(x),u_2(x),\ldots,u_N(x)\}$ for all $x\in X$ ---this is the egalitarian (or Rawlsian) social welfare function.  Or (assuming all utilities are strictly positive), we could define $W(x):=u_1(x)\cdot u_2(x) \cdots u_N(x)$ for all $x\in X$ ---this is the Nash social welfare function.
Different social welfare functions have different properties, which may be more or less desirable, depending on your beliefs about moral philosophy and social justice.  Much of social welfare theory can be seen as developing a mathematically precise way to think about moral philosophy and social justice, by understanding the properties of different social welfare functions and the tradeoffs between these properties.  For example, axiomatic characterization theorems begin with a list of axioms (each encoding a property corresponding to our intuitions about rationality, morality, justice, etc.) and show that there is a unique social welfare function that satisfies all of these axioms.


Question regarding General Equilibrium under non-convexities

You are right. Set of Pareto efficient allocations consist of all feasible allocations $((x_{11}, x_{21}), (x_{12}, x_{22}))$ satisfying the property that individual 1 consumes all of good 2 i.e. $x_{21} = 1$ and $x_{22} = 0$.

Competitive (or Walrasian) equilibrium in such an economy does not exist. At all price vectors $(p_1, p_2)$ satisfying $p_1 > 0$ and $p_2 > 0$, both the consumers will only demand good 1. As a result we will always have excess demand for good 1 and excess supply of good 2. When we consider a price vector $(p_1, p_2)$ of the form $p_1 > 0$ and $p_2 = 0$, then consumer 1 will demand infinite amount of good 2 leading to excess demand for good 2. Therefore, there does not exist a price vector that clears both the markets.

First Welfare Theorem holds because preferences satisfy Local Non Satiation. Second Welfare Theorem does not hold because no matter how we distribute endowments, competitive equilibrium in such an economy does not exist, but efficient allocations exist.

Also, please note that the lexicographic preferences are convex.


Why does a current account deficit contribute to making a country a "sitting duck" for currency speculators?

I do not think this answer is definitive, but want to point out that there are two very different regimes: pegged or floating currencies.
For a pegged currency, the central bank (or similar body) is attempting to keep the currency value pegged to an external currency or gold. (I am assuming this is a traditional peg, and not a currency board.) A current account deficit implies a capital inflow, and implies a drain on central bank reserves if the private sector is not acting to support the peg. Since the central bank cannot create whatever it is pegging at will, it would eventually be forced off the peg or to devalue. (It can absorb inflows indefinitely.) One can look at the history of the Gold Standard/Bretton Woods era to see this, or search for the literature on “rational currency runs.”
For a floating currency, the currency value can go up or down. The currency market is a market, and at least some weak version of the Efficient Markets Hypothesis applies - it is not easy to make money with simple rules based on public information (other than taking on risk premia, like owning equities for the long term). One cannot look at central bank foreign currency reserves and decide that the currency will move one way or another. Presumably, a country that loses export competitiveness will eventually have its currency lose value, but we can look at countries like the United States or Australia and see that they can support current account deficits for long periods without anything too interesting happening to the currency. That said, many people extrapolate the pegged situation to floating currencies in market commentary.
Since there’s not a whole lot of interest in articles that state “we cannot find a relationship between the current account deficit and the currency value,” it would be harder to find literature on the subject.


First off, I think it would be deeply against the rules here to give investment advice. Don't take this answer as investment advice.

For the answer to a) and b)

There is no reason why an index must return to the long term average, income or price wise. Whether it does or does not depends on the economic situation as a whole and as such relying only on historical statistics may not be productive. The western economy is going through difficult times right now, where growth and interest rates are low, and there are many structural problems to be concerned about. I would not be so sure that the market is undervalued to begin with (it might have been overvalued before - but possibly less so than some other western exchanges).

In general, you should not decide upon retirement savings based on bets on short term market fluctuation. Especially not, if you are not a professional investor.

As for the general retirement savings advice. Younger people should invest in stocks, since the investment has a long tail. As such the higher standard deviation of the investment is not as relevant as the higher expected return. When getting older, less deviation is preferred, as more certainty regarding the retirement savings is preferred. As such some nations with funded schemes have decided to invest overwhelmingly into stocks for young individuals, and progressively more to bonds for older individuals. This is a sound strategy.


Why does instrument exogeneity imply conditional mean zero?

No, you're right, $Cov[Z_i,u_i]=0$ does not imply $E[u_i|Z_i]=0$ in general. If the author defined "instrument exogeneity" as $Cov(Z_i,u_i)=0$ previously, he/she is being careless here.

"Instrument exogeneity" is often defined as $E[u_i|Z_i]=0$ too, in which case all you need to do would be to understand "implies" as "means". But since exogeneity is defined as uncorrelatedness (zero covariance), this issue has to be addressed. the author'd better fix it in a later version. How about "Instrument exogeneity usually means ..." instead of "Instrument exogeneity implies ..."?


Interesting!

A possible way to resolve this contradiction is by taking cost reducing technologies into consideration.

Perhaps (example with made up numbers follows) in 1960 a gallon of milk cost \$1 to produce, package and market. Due to strong competition, the consumer could get this for \$1.02, meaning a markup of only 2%. Today, due to technological advancements, the same gallon of milk's production, packaging and marketing cost could be lower, say \$0.80. However perhaps there is much less competition, and the markup is now 30%. This would make the consumer price of this gallon of milk \$1.04. The price jump from \$1.02 to \$1.04 seems negligible, something most people would call low inflation. (Especially if this took 60 years.)


When you say that a policy's objective is to "maximize well-being", presumably you mean "maximize collective well-being".  And presumably, by "collective" well-being, you mean some sort of aggregate or average of the individual well-beings of all members of society.  So your question breaks into two parts:

What is the right measure of individual well-being?
What is the right way to aggregate individual well-being into a measure of collective well-being?

Question #1 is really a philosophical question (although many of the more philosophically minded economists have thought about it).  Broadly speaking, there are three families of approaches to defining/measuring individual well-being:

Hedonic:   Well-being is an emotional state (e.g. happiness).  Different hedonic approaches differ as to whether well-being is a short-term or instantaneous phenomenon (e.g. pleasure, absence of pain) or a more long-term one (e.g. "overall life satisfaction").
Preference-satisfaction:  According to this approach, well-being is the satisfaction of the individual's preferences.  To the extent that people want to be happy, and to the extent that they are happy when they get what they want, this overlaps the hedonic approach.  But there are situations where they come apart.  Also, different preference-satisfaction approaches differ over whether we care about the individual's actual preferences, or her "ideal" preferences (i.e. those she would have if she was perfectly informed, perfectly rational, etc.).
Perfectionist (or "objective list") approaches.  These approaches propose to measure well-being in terms of some list of objective criteria, such as physical health, education, material consumption, participation in the community, etc.  Whereas the two previous approaches are "subjective" (it is is up to individual to determine her own level of well-being), this approach is "objective" (the individual's own opinion is only one part of the data, and perhaps is entirely irrelevant).   So in an objective list approach, an individual could have a high level of well-being even if she herself thinks she is miserable (and vice versa).

Turning to the second part of the question:  what is the right way to aggregate individual well-being into collective well-being?  This is also a philosophical question (indeed, it is the central question of the entire "welfarist" approach to moral philosophy).  But it has also been explored extensively by economists.  Economists refer to such an aggregator as a social welfare function or social welfare order, and there is a huge literature on the axiomatic characterization of various families of social welfare functions.

For a good introduction to these topics, I suggest the following books:

Handbook of Well-being and Public Policy, edited by Matthew D. Adler and Marc Fleurbaey,  Oxford University Press, 2016.
Handbook of Rational and Social Choice, edited by Paul Anand, Prasanta Pattanaik, and Clemens Puppe, Oxford University Press, 2009.
Handbook of Social Choice and Welfare, volume I, edited by  Kenneth J. Arrow,   Amartya K. Sen and  Kotaro Suzumura,  Elsevier, 2002.
Handbook of Social Choice and Welfare, volume II, edited by  Kenneth J. Arrow,   Amartya K. Sen and  Kotaro Suzumura,  Elsevier,
2011.

Each of these handbooks contains chapters written by different experts on different aspects of these questions.  The first two books are the most "philosophical".  The second two books are more focused on axiomatic analysis of social welfare functions.  The very first book (the Handbook of Well-being and Public Policy) is probably the best place to start.


What is the difference between a perfect foresight equilibrium and a rational expections equilibrium?

This is not a formal definition, but a useful piece of intuition. I  think that the best way to think about it is that when there is uncertainty in a model it arises mainly in two forms either there is information that some agents have, but not every agent has it (private information), or there are truly random events that no one knows (in game theory jargon, these are moves by nature).

This difference is key because private information affects agents' decisions. So for example, if the model predicts that people will act differently depending on their private information, a rational expectation equilibrium assumes that everyone understands this, and so by observing people's actions, they can infer their private information. If the "relevant outcome" that agents have to predict. depends only on all the private information dispersed among people, probably you can see how you can get people behaving as if they had perfect foresight.

Contrast the assumption of rational expectations with an assuming that agents are agnostic about how other agents use their private information to make decisions, or with assuming that agents predict the "relevant outcome" only using their own private information and past trends of the relevant outcome. In these cases, we should not expect a perfect foresight equilibrium.

How does that relate to stochastic models?

If the source of uncertainty is not only the existence of private information, but also "true randomness" then even a rational expectations equilibrium will not have perfect foresight (except perhaps by coincidence). Loosely speaking, if the model is stochastic, then it will predict many possible outcomes (each with some probability attached, perhaps), and agents will also expect these outcomes in a rational expectations equilibrium. Thus maybe agents make a decision based on the most likely outcome, however, this outcome may or may not occur (i.e. no perfect foresight).

(Further readings)

In the Wikipedia entry on this topic, here, you can see that rational expectation simply assumes that agent's expectations are the same as the model's predictions, so if the model is not stochastic (it has a unique prediction) agents anticipate it, hence the perfect foresight. But otherwise, these two concepts do not coincide.


There are sometimes cases where protectionist trade policies are a good thing. (note this is a big debate, so a bit of bias here).
Lets look at an example to make it clear...
Suppose I'm country A and you are country B.
I'm a small country, you are a large one.
My country is 100% agriculture based. Your country is completely diverse and strong in all sectors.
My country realizes it is time to diversify and become more integrated into the global economy/market. Instead of just agriculture based products, my country wants to also sell computer monitors.
Here is where the problem occurs, if my country just starts producing computer monitors and try's to sell them, people will just continue to buy your countries computer monitors because they are better quality and probably cheaper in price due to comparative advantage. So now what? What must my country do to compete with yours, and grow? Well if my country makes your products more expensive, (aka a tariff) less people will buy your monitors and more people will buy mine (only in my country). This would allow my computer monitor(tech) sector to grow on it's own, without a big bully competitor(your country in this scenario) forcing me out before I even get started.
Over time once my tech sector has grown enough to compete with yours, I would lower/get rid of the tariffs and be better off.

Hope this helps you understand.


I’ll try to succinctly explain bonding curves and then discuss benefits. Let’s look at a typical bonding curve where the buy price formula and the and sell price formula are equal:

 from https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5

The way the formula works is look at the current amount of tokens purchased (supply) and charge the price given by the formula for the next token. As people sell, the supply goes down and as people buy, the supply goes up. The total amount of money put into the token is the area under the curve.

At any point you can buy a token and sell it back and get your money. However, if you buy at $q_1$, wait and more people buy (not guaranteed!) then you can sell at a higher price at $q_2$. To make profit, you should only buy if you think others will buy after you as well.

At the end of the day, total money paid in will be total money paid out, but the smartest who buy early and sell at high supplies (buy $q_2$ and sell $q_1$) will make money while those who buy when it’s “hot” and sell when supply is low (buy $q_2$ and sell $q_1$) will lose money.

Now, sometimes the sell curve is below the buy curve:

In this case, the area between the buy and sell curve is revenue that will typically go to a company. There is money making opportunities, but because the sell curve grows slowly, it only really benefits the earliest buyers.

So what are these any good for?

The Buy curve equals the Sell curve:

This kind of market is good for content curation. It’s easiest explained by an example (borrowed from https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5):

  Meme Factory: A Game of Curation & The Trading of Dank Memes
  Meme Factory from District0x will be a game where users can create dank memes and bond tokens to each meme according to its own bonding curve. This becomes a game where users then bet on the popularity of each meme. Bonded early to a dank meme and got out at the top? You successfully traded a dank meme and just made a profit.

  The question each time is: do you think this meme is dank and funny enough that others will want to bet after you on this too?

  Ultimately, whilst this game is being played, these memes are also being curated themselves: more tokens bonded to a meme is a signal that is a funnier meme than a meme with fewer bonded tokens. This is an emergent outcome.

By people trying to make money, they will curate popular content as a byproduct (social surplus from private motives!)

The Buy curve > the Sell curve:

It’s very hard to start a community because the first members don’t have many people to interact with and it’s very laborious to create stuff that other people will want to join and see. It’s especially hard if you have to pay to join!

However, notice that if you enter early the sell curve is super close to the buy curve, so you have low risk of joining a community (because you can sell right back). And the upside is, if you work on the community to gather members and create fun content then more people will pay to enter. All of a sudden your share is worth a lot! This incentivized people to value their community and make money while doing so.


The global economy depends on growth, but growth can never be
  indefinite in a finite world with limited space and resources.

It is only partially correct to say that the global economy depends on growth, because an economy per se does not depend on it. But it certainly isn't wrong to say so, because a large part of the world's economic activity is funneled into investments. Without growth, there would be few investments and new enterprising going on.

Growth has certainly been one of the primary political goals of the 20th century and continues to be so, as the main technique for progressing the human race and bringing order to the global society. In our new century, it has much to do with continuous improvement of quality of life, and lifting millions (billions) of people out of poverty.

Furthermore, since the growth paradigm is so central to the way we order the economy, much of economic activity depends on it. We count on growth to make our pensions grow so we can afford to retire. Society counts on growth when investing in new expensive infrastructure, so that huge projects will pay for themselves over the long term. The financial system depends on growth of businesses in return for lending out their capital. And so forth.

  Moreover, growth always tends to decline over the long term due to the
  law of diminishing returns, as we choose opportunities which give the
  best returns first, leaving those which give lower returns for later.

Diminishing returns is used to refer to a point at which the level of profits or benefits gained is less than the amount of money or energy invested. This means that after a certain point, it is no longer profitable to invest more to extract more value out of a proposition, and it may be necessary to divert resources to other parts of the economy. For instance, in the early days of the oil industry, there were huge wells of oil to drill and a lot of oil was wasted due to early technologies. Since there was plenty of oil, the spill didn't matter so much. As oil became a scarcer resource and drilling became more difficult, new technologies were developed to counter diminishing returns. With modern efficient technology, we are producing more oil today than we ever have before, even though the oil has demonstrated diminishing returns.

Your assumption is correct in the sense that: the closer we come to the production possibilities frontier which is the current technological limit, we will see a decline in the growth rate. However, because growth is compounded, we have really seen an exponential growth of world GDP the whole time.

To answer your question: with current technology, we would undoubtedly run out of finite resources at one point. That doesn't automatically mean that there would be an 'economic collapse' – instead we would see ever more diminishing returns and a decrease in activity within that particular sector, while more profitable opportunities would emerge. Society would have to change and find a new way of living. There wouldn't be a sudden "energy catastrophe", but a slow and gradual decline over many decennia. It is plausible that we would see lower birth rates, not because people would die, but because it becomes more expensive to have many children while maintaining a certain standard of living.

With that said, as technology progresses, we become more apt at extracting resources efficiently. The big challenge of this new century is to become independent from fossil fuels and base our economy on renewable energy or other sources. There are also other potential shortages, as some rare-earth minerals have supply limits with practical implications for our way of life. Hopefully, there will be a replacement or recycling of these, and/or ways to locate and extract them more efficiently.

The challenges humanity face are certainly great, and no-one knows the solutions yet. But the hope is that we will be able to cope with the change via new technologies and/or changes to society. That doesn't mean that an economic collapse is inevitable, but it does mean that economic, and probably societal, reorganisation is inevitable.

Regarding your other questions, I hope someone else can elaborate on them in a more technical sense:

  Could the global economy survive indefinitely with zero growth, while borrowing more
  and more money to avoid decline?

  Under what scenario would the economy be indefinitely sustainable,
  without a huge collapse?


Estimate function expression for TC and MC

As the OP corrected in the comments, using $K=20, w=800$, and $r=500$, so $TC = 10000 + 800L$, we get , in the $\{Q,C\}$ space

This looks pretty text-book like. The fact that there are levels of labor for which output is reduced, tells us that for these levels we have to employ more of the "fixed" factor, capital (which thus stops being fixed).
The function as is, with capital fixed at $10000$, stops having economic sense after $L=9$.


Does the VCG algorithm work for any bundle valuation function?

In theory, the answer is yes.
In practice, the answer is no, because it is computationally intractable.
My take-away from talking to computer scientists was that determining a winner and computing the transfers are NP-hard problems. See, e.g., this write-up by Kirk Pruhs.


$a\geq 0$, $x\sim y$ implies $x+a\sim y+a$ so the preference is linear?

This is not true.

Let $n=1$ and define $u(x)=\min{\{x,0\}}$. Let $\succsim$ be the preference relation represented by $u$. This preference relation is continuous and convex. We also have $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R$. But let $x=0$, $y=1$, and $a=-1$. Then $x\sim y$, but $y+a=0\succ -1=x+a$, thus $x+a\nsim y+a$ and $\succsim$ is not linear.


Find Indifference curve/s and Marginal Rate/s of Substitution given only one point

In general, you are right to be mystified: specifying a point (consumption bundle) isn't enough to compute MRS and indifference curves.

However, in this problem, I would suggest you take the first sentence seriously as a description of her preferences.  She likes fries.  (She doesn't care about what box they come in!)

Let $v(f)$ represent her utility as function of $f$, the quantity of fries she consumes (in oz).

Mechanically, $f = 1R + \frac{1}{5} L$, where $R$ and $L$ are the quantities of regular and large orders of fries she consumes.  So, her utility as a function of these is:

$$u(R,L) = v(1R + \frac{1}{5} L).$$

Now you can compute marginal utilities $u_R \equiv \frac{du}{dR}$ and $u_L \equiv \frac{du}{dL}$ and the marginal rate of substitution $MRS_{L,R} \equiv \frac{u_L}{u_R}$.    You will see that in MRS, the $v'(\cdot)$ terms cancel out, and you are left with an MRS of $5$, at every bundle $(R,L)$.  These are linear preferences over bundles, and the indifference curves are straight lines with slope $-1/5$ (if you put $R$ on the horizontal axis).

This makes intuitive sense in two ways.

First, the canceling tells us that preferences are independent of the specific functional form of $v(\cdot)$, so long as it is an increasing function.  This is because utility functions only encode ordinal preferences.

Second, the MRS gives the rate at which she would be indifferent to  trading those two goods.  If you offered her five 1 oz boxes for one 5 oz  box, she wouldn't mind, since it's all the same to her.  (If you offered her a penny more, she would gladly make the trade, and if you offered a penny less, she would refuse.)

As an aside, we could say that the relationship $f = 1R + \frac{1}{5}L$ encodes the household production function: how she transforms things she can buy (boxes of various sizes) into the thing she really likes (fries).  This approach is associated with the work of Gary Becker and is commonly used in family and health economics.


It would be helpful if you could let us know the papers you found, some of the background experience you have, and some more specifics.

This might be a useful paper nonetheless.


Infinitely repeated games and real-world situations?

In most situations it is not clear when a game ends, it is just clear that at every point in time there is a probability that this is the last period of them game.

Just try to say what is this $T$ for the life of a human? 150 years? Even if you are 150 years old there is a (probably small) chance that you will survive another year. And the next year? There is also another chance to live another year, and so on.

As long as there is no fixed endpoint to the game, infinitely repeated games are, in my opinion, more realistic as long as there is some chance of ending the game included (i.e., as a discount rate).

Infinitely repeated games are also a way to resolve some problems backward induction (for example in the Chain-store paradox). You really have to know that there is a very last situation to use backward induction.


Which is safer in the long-term, diffuse debt or concentrated debt?

I do not think this question can be answered.

Firstly, the statement “ For example, entrusting asset management companies to take care of NPLs and free up bank resources so they may lend more.” does not follow. There are some administrative advantages to having concentrated borrowers, but this statement does not capture them.

We cannot choose the distribution of borrower size without choosing the distribution of firm size. So this question is: should societies aim for concentrated industries, or break them up? This is a large question, for example, the study of anti-trust law. I don’t think one can summarise that area without just posting an opinion.

If we just want to look at historical examples of debt crises, we can find crises both with distributed and concentrated borrowers. Qualitatively, they will look different, but it will be a matter of opinion which will be safer. E.g. concentrated firms pose the risk of a large planning error. However, it is easier to intervene into one firm. Which is “safer”?


Solving a two stage game by backward induction: which is the equilibrium notion?

It is called a subgame perfect equilibrium.


Are urban land (location) markets considered competitive even though the market price does not equal marginal cost (zero)?

Existence of rent has nothing to do with whether market is competitive or not. First there are different definitions of rent. As explained in the Palgrave dictionary of economics (Alchian 2017):

Rent’ is the payment for use of a resource, whether it be land, labour, equipment, ideas, or even money. The term is often restricted to payment for use of land or equipment. ‘Economic rent’ is payment for use of any resource whose supply is fixed. Rent serves a social purpose because market levels of rent indicate which uses of fixed resources are the highest valued, and direct such resources to those uses. ‘Monopoly rent’ is paid to producers in markets that are artificially restricted; it may be dissipated by ‘rent seekers’ who compete for monopoly status.

Hence rent can have various meanings depending on the context. Only the last definition of rent that is:

‘Monopoly rent’ is paid to producers in markets that are artificially restricted; it may be dissipated by ‘rent seekers’ who compete for monopoly status.

Has anything to do with competition. Even here there must be some artificial restriction on the market so there is some monopoly (i.e. one seller). All other definitions of rent have nothing to do with competition and some of the above definitions are fully compatible with perfect competition (e.g. even if there would be perfectly competitive market for land and there would be some marginal costs of making it productive - which there actually are although usually they are small (you have to maintain land for it to be usable for housing etc) - the perfectly competitive price for land would still be called rent).
For example, it can trivially be proven that in oligopolistic competition firms can make positive profit, and prices will be higher than marginal costs (see examples Belleflamme & Peitz Industrial organization: markets and strategies). However, oligopolistic profit would not be considered monopoly rent - even if firms have market power.
In order to have monopoly rent in this case you need to make argument that the plot of land is sufficiently distinct from other plots of land so it can be considered to be unique and its owner would thus become a monopolist because there would be only one seller of this one unique piece of land. You can probably make this assumption for any special location (some place with unique excellent view) or locations with some historical value making them special (e.g. land under the White House), but such assumption would be inadequate for any random slot of land in some city. In many cases all plots of land in a given block or even in a whole section of city can be treated as completely homogenous without loss of generality.


Why doesn't Dollar exchange rate go down?

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


Can you provide your research question in one concise sentence? It seems like you've proposed half a dozen topics some of which are peripherally related. You need a quantifiable dependent and independent variable as well as essential control variables.

The question needs to be quantifiable and have a wealth of data already available. I'd highly recommend for your undergraduate paper instead of asking a question and then searching for the data to back up the answer, you instead peruse some interesting data sources and ask a question based on what is available.

Check out sites like https://www.data.gov/open-gov/ which have a wealth of easily downloadable datasets that you can explore. Find datasets related to topics that you find interesting and go through the available data and begin to think of what can act as an independent or dependent variable. Base your question so that the dataset you have already found and think is interesting perfectly fits instead of the other way around.

Unless you plan to do original research it will be quite difficult to simply find data to fit your question unless you already knows it exists.


How is it possible that shipping of eBay items from China to US is 'free'?

The major reasons that I understand are that:

the Chinese government subsidizes shipping.
the US Postal Service, eBay China, and Hong Kong Post office have a trilateral agreement called the ePacket service which roughly speaking, allows shipping of small packages to the US at bulk pricing (instead of at the price for individual sales).

I don't think it's common for there to be "free" shipping though.

I'm retracting the part about China subsidizing exporters.


Do modern economists still believe balance of trade is an important concept in economics?

The economics of trade can broadly be divided into two parts.  There is a microeconomic part concerned with patterns of trade in particular kinds of goods, their causes such as factor endowments and costs, and effects on welfare, key concepts being comparative advantage and the gains from trade.  Then there is a macroeconomic part concerned with overall volumes of trade and payments for traded goods, and their relations with exchange rates and domestic macroeconomic conditions.  The two parts can be linked, as in the Dekle et al paper referred to by emeryville, but more often are considered separately.

The concept of balance of trade belongs in the macroeconomic part, although
economists often use the more precise term balance on current account, which includes trade in goods and services and certain other items. It is generally considered that a continuing deficit on current account is harmful because the net outflow of funds cannot indefinitely be met by running down the country's international currency reserves, and must eventually be balanced by an inflow of funds associated with increasing international debt and/or foreign ownership of domestic assets.  The moderate aim of a balance on current account avoids two disadvantages of mercantilism, which aimed to achieve a surplus: firstly, it led to conflict because it was impossible for every country to have a surplus, and secondly, it reduced welfare, because restrictions on imports meant that the (microeconomic) gains from trade were not fully achieved.

Thus the balance of trade or balance on current account remains an important concept in the macroeconomics of trade.


Preference for consumption smoothing and actual smoothing

The argument relayed in the question as regards consumption smoothing is flawed. Consumption smoothing does not mean consumption equality over periods, but rather, tendency to avoid corner solutions, or near-corner solutions. So it has nothing to do with whether, in the context of this family of models, $\beta (1+r) =1$ or not (after all, in a more comprehensive model, this condition is the long-run equilibrium one, and it does not hold for the transition towards equilibrium).

Consumption smoothing in the intertemporal setting has similarities with "variety in consumption" in a static setting with more than one goods: there, with a concave utility function, we get convex indifference curves and so interior solutions, i.e. a solution where the consumer consumes a mix of goods available, not just one, or very few of them, given the linear budget constraint

As general equilibrium theorists point out, timing of consumption can be seen as just one more feature of a good, and so, when the same good has a different "consumption time stamp", it is a different good after all.

So, in the basic two-period setting, we have a bivariate intertemporal utility function

$$U(c_1, c_2) = u(c_1) +\beta u(c_2)$$

To examine its indifference curves we fix the value of the function at $\bar U$ and we examine the second derivative of $c_2$ with respect to $c_1$:

$$c_2 = u^{-1}\left (\frac 1 {\beta} \cdot \big[\bar U - u(c_1)\big]\right)$$

$$\implies \frac {\text{d} c_2}{\text{d} c_1} = \frac 1 {\beta} \frac {-u'(c_1)}{u'\left (\frac 1 {\beta} \cdot \big[\bar U - u(c_1)\big]\right)}$$

and

$$\frac {\text{d}^2 c_2}{\text{d} c^2_1} = \frac 1 {\beta}\frac{-u''(c_1)\cdot u'\left (\frac 1 {\beta}  \big[\bar U - u(c_1)\big]\right) - (1/\beta)u''\left (\frac 1 {\beta} \big[\bar U - u(c_1)\big]\right)\cdot [u'(c_1)]^2}{\left[u'\left (\frac 1 {\beta} \cdot \big[\bar U - u(c_1)\big]\right)\right]^2}$$

For the indifference curve to be convex we need this derivative to be positive, and so we need the second derivative of the period-utility function $u$ to be negative, $u''()<0$.

Then with a linear budget constraint with negative slope (say for exogenous endowments per period),

$$c_2 = y_2 +(1+r) (y_1-c_1) = \big[y_2+(1+r)y_1\big] - (1+r)c_1$$

we can get the familiar graphical solution of interior tangency at the optimum, which excludes corner solutions we would have obtained if the indifference curve between present and future was concave (and so the period-utility function was convex).

So it is all about the utility function and has nothing to do with the Euler equation taking a specific value.


Is America getting to a point where there are many more people than jobs or money to go around? Are times better or worse than 50 years ago?

A few points to note.

1.) With more labor comes more goods that need to be produced. This can be in the form of goods, services, or capital needed to augment the production of labor. If we are talking about whether there are enough raw/natural resources needed to make these things as population increase, note that your worry is not new. As population increases, we create more efficient ways of using the resources we already have. Think of our usage of resources/labor as a transversality condition. As time approaches infinity, the population will not grow faster than the rate of our technological efficiency, simply because of the need to survive. In the meantime, we'll be utilizing additional labor.

2.) I noticed that you had said,

  In America, over 300 million people and most already in poverty.

You could make the argument that more than 150 million Americans are in poverty, but that measure of "poverty" is going to include a lot of well-off Americans. I'm not exactly sure what idea of poverty you have to reach this conclusion.

The US Census Bureau's measure of poverty has been hovering around 15% for a while. That's not great, but that's not necessarily worsening rapidly by any means.

  automation is increasing so rapidly it is expected that by 2025, even truck driver jobs will start to diminish

I'd like to see exactly who said this as well, if you have the citation. Otherwise it's just hearsay.

I think your uncles and aunts have been influencing you with a little bit of their hindsight bias.

3.) You noted that,

  Retailers are already shutting down due to online competition from Amazon and restaurants are getting there too with tablets being placed at tables to take orders.

Does this necessarily decrease labor or displace labor into other jobs that value human labor more? A quick example: Line workers in the United States have been declining steadily over the last decade, and many of them are reaching retirement age. It pays well and is manual labor, but there simply aren't enough interested young workers. If we were to see too much labor in technology-heavy industries, we could say that eventually the labor market would clear and go into well-paying jobs like this one. There are still opportunities out there for Americans.


The phase diagram for the simple RBC model

There are two tricks to safely construct a phase diagram, as regards the dynamics off it.

First, solve for the "isoclines" as weak inequalities rather than as equalities. This method makes also clear the dynamics off the isocline.

Consider a standard capital accumulation equation

$$K_{t+1} = (1-\delta)K_t + F(K_t) - C_t \tag{1}$$

We want to obtain the isocline, but also the dynamics off it. Re-write as

$$K_{t+1} - K_t  = -\delta K_t + F(K_t) - C_t$$

Now require that

$$K_{t+1} - K_t \geq 0 \implies -\delta K_t + F(K_t) - C_t \geq 0$$

$$\implies C_t \leq F(K_t) - \delta K_t \tag{2}$$

With equality, $(2)$ is the expression for the isocline. The inequality tells you that for capital to tend to increase ($K_{t+1} - K_t > 0$), consumption must be lower than the level indicated by the isocline. Etc

The second trick is already used in $(2)$: although this is the capital difference equation, I wrote it as though it is an expression determining consumption. In this way, one can look at the phase diagram and for both difference equations, treat the variable in the vertical axis as the "dependent" variable of the two isocline functions. This is the most natural to the eye, and helps avoid the up/down, right/left confusion that can result if one tries to rotate in its mind the phase diagram, for one of the two equations. It also makes easier to determine the slope/shape of the two isoclines.


A share or stock is part of an individual company. Unit (Trusts) are a collection of different (and usually related) shares.

For example, I am currently investing in a Singapore Equity Fund. And this is known as a Unit Trust. And within the Singapore Equity Fund, my investment is made up of different company shares, e.g. the local bank shares, telecommunication company and some other companies.

And these Unit Trusts are usually managed by a Fund Manager who belong to a Fund Management Company (or known as Fund House). And there are many different Fund Management Companies in Singapore with their own expertise and knowledge.

Source: here


How did the massive flight to long-term bonds create a liquidity crisis?

This is because in order for many business to stay liquid they often have to issue short term debt. Many financial firms need liquidity so much that they literally make loans that are for duration of only one day.

However, the more people invest their savings in bonds which are usually long term debt (most bonds have maturity over 5-10y), the less money is there available to borrow short term. That means that even profitable business that has healthy profit ratios could get itself into bankruptcy just because of not being able to get short term loan to cover some important immediate financial obligation.