Would someone be able to help me solve capital per capita in the steady state (check my work) Question: Suppose $C_t=(1-s)Y_t$ where $s>\sigma$ as in the basic Solow model. Solve for capital per capita in the steady state.
$Y_t=K^{\alpha}_tL^{1-\alpha}_t$
$Y_t=C_t+I_t+G_t$
$K_{t+1}=I_t+(1-\delta)K_t$
$L_{t+1}=(1+n)L_t$
$G_t=\sigma Y_t$
Attempt:
$sy=sky^{\alpha}$: savings and investment per capita
$(n+d)k$: investment needed to keep capital per capita constant
n: population growth rate
d: depreciation
$\dot{k}= sky{\alpha}-(n+d)k=0$
Comment(s): I am unsure if this is even correct. My problem is that I didn’t even utilize the information given about consumption above. Any suggestions that could lead me down the right path?

There are some mistakes in the steps you took although they went in right direction. The correct steps are below.
First we can start by expressing output in per capita terms by dividing first two equations by $L_t$:
$$ \frac{Y_t}{L_t}=\frac{K^{\alpha}_t L^{1−\alpha}_t}{L_t} \implies y_t = k_t^{\alpha}$$
and
$$\frac{Y_t}{L_t}=\frac{C_t}{L_t}+\frac{I_t}{L_t}+\frac{G_t}{L_t} = y_t  = c_t + i_t + g_t$$
where lower case letter refer to per capita variable (e.g. $\frac{Y_t}{L_t} = y_t$). Using this and the $L_{t+1}=(1+n)L_t $ the evolution of capital in per capita terms will be given by:
$$ (1 + n)k_{t+1} = (1 − \delta )k_t + i_t \implies k_{t+1} \approx (1 − n -\delta )k_t + i_t  $$
Here we can use the fact that:
$$i_t = y_t - c_t - g_t = k_t^{\alpha} - c_t - g_t$$.
Hence:
$$k_{t+1} =  (1 − n -\delta )k_t + k_t^{\alpha} - c_t - g_t $$
and as a consequence
$$k_{t+1} - k_t=  -(  n + \delta )k_t + k_t^{\alpha} - c_t - g_t $$
Now since $c_t=(1−s)(y_t-g_t)$, where ($-g_t$) is there because consumption depends only on disposable income after taxes and $g_t = \sigma y_t$ and remember $y_t= k^{\delta}_t$ we get:
$$k_{t+1} - k_t  =  -(  n + \delta )k_t + k_t^{\alpha} - ( (1−s)(k_t^{\alpha}-\sigma k_t^{\alpha})- \sigma k_t^{\alpha})  \\
 =  -(  n + \delta )k_t + k_t^{\alpha} - ( k_t^{\alpha} - s (1-\sigma) k_t^{\alpha} )  \\ =   s (1-\sigma) k_t^{\alpha}  -(  n + \delta )k_t $$
where the last equation is really just this models version of $sy-(n+\delta)k_t$.  Now finally dividing by $k_t$ to get to growth rates we get:
$$ \frac{k_{t+1} - k_t }{k_t}=  s (1-\sigma) \frac{k_t^{\alpha}}{k_t}  -(  n + \delta ) $$
Now solving the above for steady state where $\frac{k_{t+1} - k_t }{k_t}=0$ (by definition a steady state),   gives us:
$$ 0 =  s (1-\sigma) \frac{k_t^{\alpha}}{k_t}  -(  n + \delta ) $$
which finally can be solved for optimal steady state per capita capital:
$$ k^* =  \left( \frac{s(1-\sigma)}{n+\delta} \right)^{\frac{1}{1-\alpha}}$$
In addition very similar models to this one are covered by Barro & Sala-i-Martin Economic Growth 2nd ed. So you can check it out for further details.


Lotteries = probability distribution? Are "lotteries" in the model for choice under uncertainty not just probability distributions?

Yes. See for example this passage from Choice under Uncertainty by Jonathan Levin:

2.1  Prizes and Lotteries
The starting point for the model is a set $X$ of possible prizes or consequences. In many economic problems (and for much of this class), $X$ will be a set of monetary payoffs. But it need not be. If we are considering who will win Big Game this year, the set of consequences might be:
$$X=\lbrace\text{Stanford wins}, \text{Cal wins}, \text{Tie}\rbrace.$$
We represent an uncertain prospect as a lottery or probability distribution over the prize space. For instance, the prospect that Stanford and Cal are equally likely to win Big Game can be written as $p=(1/2,1/2,0)$. Perhaps these probabilities depend on who Stanford starts at quarterback. In that case, there might be two prospects: $p$ or $p'=(5/9,3/9,1/9)$, depending on who starts.

(not sure what I was thinking yesterday evening. It seems like I completely misunderstood the question)


Efficient revealed preference check of whether two preferences over lotteries are the same? I want to find conditions under which two utility functions can be known to be linear transformations of each other.

Consider a (possibly finite) arbitrary set of outcomes $X$ (Not necessarily interpreted as commodities), and a specific utility function $u^*:X\to \mathbb R$. We want to find out whether an agent's utility function is a linear transformation of $u^*$ or not. Consider a set of lotteries $\mathcal L$ on $X$. Now suppose we give an agent choices between subsets $C\subseteq \mathcal L$. What I want is: What choices do we need to give to the agent to know that his utility function is a linear transformation of some utility function $u^*$?
Note: we don't need to check whether the agent has rational preferences. We assume from the outset that he has a vnM utility funciton.

This is simply revealed preference, but I don't recall reading about anything about this specifically.

Perhaps I'm way off base on this, but given the relatively strong requirements imposed in the question, I'm tempted to say that we can never truly be able to state with certainty that some individual's utility function $u_i$ is absolutely a linear transformation of some other function $u^{*}$ considered ex ante. While depending on the specific $u_i$, $u^{*}$ and initial questions asked, it could be possible to dismiss the two as not satisfying the transformation requirement, but I don't think one could ever actually confirm it.

The underlying reason for this thinking is the inclusion of vNM utilities and lotteries over outcomes. Since the former assumption imposes cardinality on our utility framework, there is always the possibility of discrepancies between $u_i$ and $u^{*}$. Even considering just one good (money, for example) any sequence of observed choices made by some individual following a utility function $u_i$ might only differ from how an individual following $u^{*}$ behaves in the "gaps." No matter how fine the probabilities and dollar amounts get, we can always come up with some alternative $u'$ which replicates the decisions up till that point. (We can always consider, for example, some $u^{'}$ that's a piecewise on some interval where $u^{*}$ is smooth.

Of course, as our ability to observe smaller and smaller intervals increases from repeated choice observational data, the possible deviations between $u^{*}$ and some alternative $u'$ trends towards zero. But again, finding out that all observations thusfar suggest the individual's utility $u_i$ is a linear transformation of $u^{*}$ doesn't guarantee that there isn't some interval of the function where they're different.

It should also be pointed out that this really only considers extreme cases- for all experimental purposes we only need a function that approximates an individual's utility function. But I do think it's tougher to truly prove one is a linear transformation of the particular $u^{*}$ in mind.


Diminishing mariginal utility and risk preferences Diminishing marginal utility is a concept only in cardinal utility theory rather than ordinal utility theory. As diminishing marginal utility implies a concave shape of the utility function, does it necessarily mean that agents with diminishing marginal utility must be risk-averse (also has a function with a concave shape)?

Does cardinal utility theory assume the law of diminishing marginal utility in all of this theory? Could you have increasing marginal utility within cardinal utility theory?

Mas-Colell, Whinston, and Green Proposition 6.C.1 (p. 187) says that for an expected utility maximizer with a Bernoulli utility function $u(\cdot)$ on amounts of money, saying that "the decision maker is risk averse" is equivalent to "$u(\cdot)$ is concave".

However, these other assumptions matter. A concave utility function isn't enough. Diminishing marginal utility in amounts of money doesn't have to imply risk aversion. For example, with gamble $(F)$ taking two values $W_L,\: P(W_L) = \theta$  and $W_H>W_L,\:P(W_H) = 1 - \theta$, and a utility function $u{}$ with diminishing marginal utility in wealth, consider this person's welfare function over risky lotteries $(V)$:
$$V(F, u(), \theta) = u(W_H)$$
This person is not risk averse. They love risk (for example, they prefer a risky lottery to the expected value of that lottery). But, in situations without risk, they have diminishing marginal utility of wealth.


Throw-away paradox with independent goods The throw-away paradox is a situation in which a trader can gain by throwing away some of his initial endowment.

The specific example, brought by Aumann and Peleg in 1974, concerns an economy with two commodities and two traders:

In one situation, the initial endowments are (20,0) and (0,10). In competitive equilibrium, the bundle of trader A is (4,2).
In the second situation, trader A throws away 10 units of commodity x, so the initial endowment is now (10,0) and (0,10). In equilibrium, the bundle of trader A is (5,5) - more of ''every'' commodity than in the first situation!

In their example, both traders have the same utility function, which has the following characteristics:

It is homothetic;
The slope of the indifference curves at (y,y) is -1;
The slope of the indifference curves at (2y,y) is -1/8.

One such function is $$u(x,y)=\frac{1}{(x+ay)^{-3}+(ax+y)^{-3}}$$

But, in this example, the products are dependent.

MY QUESTION IS: Is there an example of such a "throw away paradox", when the products are independent?

NOTE: both products are goods (have non-negative utility).

It seems (from the first page, at least; I don't have JSTOR access right now) that the essence of Aumann and Peleg's example is that

  this rise in price of the commodity [trader A] holds is more than enough to compensate for the drop in the amount.

One similar situation from history occurred during the New Deal, when farmers were paid to plough over cotton fields and send hogs to be slaughtered for no reason, in order to take excess quantities of these goods off the market.

Obviously, the difference here is that this was a centralized intervention in a decentralized (and huge) market. The set of incentives are more complicated, and the many "trader A's" in this scenario were compensated for throwing away their goods. But the sentiment is very similar.


Why Banks give more discounts/offers on Credit Card as compared to Debit Cards? Whether a credit or debit card is used to make a payment at a merchant, there will be outflow of money from the bank. What extra benefit do the bank get from promoting credit more than debit card?
Is it just the obvious answer that by promoting credit card, there is a chance that user will default on the payment and allow bank to charge interest?
On the downside, by paying through credit card, the user still has money in her savings account and so from bank has to maintain higher reserve ratio with the central bank.
Finally, does it have something to do with the fee bank charges with merchants? Is the fee higher for use of credit cards as compared to debit cards?

Yes of course you are right about both of your points. The fee charging the credit card POS transaction is about 2% to 3% depending on the company. The fee charging to debit card transaction is about flat 25 cents or lower.
For online transaction, the credit card fee can be as high as 4%, and the debit card fee can be negligible. Banks make more money on credit card.
So, to answer your question:

Credit department usually have more money to make promotions.
Average people (in US) have almost zero savings so they cannot use their debit card very often. But everyone has a credit card.
Of course, credit card can default, and the bank can legally charge hefty interests.

And as mentioned by Brian, competition is an important reason.


A Question About The Laws Of Demand The law of demand holds that ceteris paribis, a decrease of demand can be caused by an increase in price. However, it is also true that when demand decreases, the price will decrease, it will fall. How can one explain this seeming contradiction? I know it's because of the invisible hand of the market forces, but can I don't know how to specifically explain what is that makes this make sense, and ensures that it is not contradiction with the law of demand. Can someone please explain?

We have a problem of terms here.  "Demand" is usually used to refer to the function where for a given price, a given quantity will be demanded.  That quantity is referred to as the quantity demanded.

  a decrease of demand can be caused by an increase in price.

This is a shift along the demand curve (function).  It changes the quantity demanded, but the demand curve itself stays the same.  I would say instead:

  An increase in price will cause a decrease in the quantity demanded if all else is equal.

This could happen if the supply curve shifted.

  However, it is also true that when demand decreases, the price will decrease, it will fall.

This is a shift of the curve itself.  I.e. the curve or function changes as a result of a change in demand.

Even if the supply curve is fixed, the intersection could still change because the demand curve moved.

The point is that you are using demand in one place to refer to the curve and in another place you are using it to refer to the quantity demanded.  If you use different terms for those two things, it's easier to see that your statements are not in conflict.  They are talking about different things.


Is UK house price spiral connected to debt based monetary system? (cross-posted from Personal Finance & Money)

Is the monetary system's debt basis* driving government policy on housing and property, and how could this ultimately affect personal housing affordability?

The UK has an ongoing 'situation' with property.  A recent topical example is the government's promise of a 'right to buy' for housing association properties, to acclaim and criticism.  The government seem generally keen to get citizens mortgaged up, or are they just aiming to satisfy the public's home-owning aspirations?

These are some typical headlines:-

UK housing crisis 'in breach of human rights'

UK has world's second-highest house prices beaten only by millionaire's playground Monaco

Is the monetary system's debt requirement driving this property bubble?  And if so, what are the characteristics of it.

Edit

For example, the US subprime debacle, considered by some to be caused by pressurised lending, possibly driven by a monetary system that needs to grow by increasing the debt pool.  If this is the case, it could be viewed that government would support the taking of mortgages and increasing debt, in order to keep the money pool growing and stave off recession.

*Ref: What is a debt based monetary system?

The price of housesis determined by the supply and demand for housing. The consensus view is that house prices in the UK are so high because of low supply and buoyant demand. In particular, the UK is currently building houses at a rate of less than 150,000 per year, but is creating twice that many new households. This is a situation that has persisted for some time. If there are more buyers than sellers then sellers can increase their prices with little fear that they will be left without a buyer at the end of the day.

To understand the cause for high house prices, one therefore needs to understand the reason for supply being so low, and demand being so high. In the latter case, the availability and cost of credit is certainly an important factor. If banks are willing to lend (say, because the government provides guarantees or other subsidies for doing so--as in the Funding for Lending scheme), and if interest rates are low and stable then people will be very willing to take out a mortgage. This is an important precondition for strong demand because most people cannot afford to buy a house without a mortgage.

This, though, is only part of the picture. Note that many countries currently have low and stable interest rates, but have not experience the rapid inflation of house prices seen the in the UK. Here are some other factors that are important in the UK context:

Limiting supply:

The UK has a restrictive planning regime that makes housebuilding (especially in high-demand areas) difficult. This has, for example prevented the expansion of towns into green belt land, or large increases in the density of housing in major cities.
Much of the land best suited to development is so-called ``brown field'' land that was previously put to some other use. Cleaning and preparing this land for use in the housing sector is costly and represents a risk for developers.
House builders earn essentially zero profit on affordable homes, making the development of such homes unattractive. This role was previously filled by the British government, but social house building has fallen dramatically since the 1980s.

Promoting strong demand:

The UK government has introduced a number of policies that directly stimulate demand for housing (such as the Help to Buy scheme).
The UK has a net inflow of migrants of around 200,000 per year--all of whom need to be housed.
Demand is not evently spread across the country. The UK economy is unusually concentrated around London and the South East, which puts particular pressure on the housing market in this area. House prices elsewhere have seen more modest growth.
The British are unusually attached to the concept of home ownership (unlike, for example, many continental Europeans who are perfectly happy to rent). This means that British buyers are less sensitive to prices and will continue to demand houses even as the prices increase--as we have seen.
Related to the above, tennants have relatively few rights in Britain. This makes long-term renting less attractive, and pushes people to buy houses.
Anecdotally, there appears to be strong demand for UK housing from foreign investors who treat the property as an asset, but do not occupy it.

Many of these things could be fixed with appropriate market interventions. However, there is a political economy dimension to the problem in that most of the British electorate lives in an owner-occupied house and therefore has a vested interest in maintaining the value of their house and preventing additional development in the area to the greatest extent possible. This possibly explains why candidates in the forthcoming election have focused mainly on proposals to subsidise demand (which would only exacerbate the problem!) or vague promises to build more houses, rather than on concrete plans (e.g. to reform planning) that would put-off a lot of middle-class voters.


Are there any non-paywalled reputable economics journals? I'm contributing to another open-source economics project, and was looking to compile a list of primary sources for modern developments in the field.

Basically something to help bridge the (occasionally decades long) time lag between what's taught at an undergrad/ introductory grad level and what's being researched in the field today.

Unfortunately as many in academia know, companies like Elsevier and others have most major publications locked up behind corporate paywalls, which makes them broadly incompatible with the principles of OSS/OSD.

There's Arxiv (and Vixra for the braver), but preprint servers are not really what I'm looking for. It's hard to separate the wheat from the chaff on many of them.

I'd like something with some editorial content, and especially peer-review.

I'd appreciate any suggestions.

Theoretical Economics (TE) and Quantitative Economics are two open access, peer reviewed journals. The former I know is of very good quality, arguably the top "field journal" in microeconomic theory.


CO2 footprint per bitcoin transaction Out of personal interest I wanted to find out which carbon footprint one bitcoin transaction produces. Following I will present my calculation. The result surprises me and my question is Is this realistic? Did I make mistake?

Variables

Transaction throughput: $\approx 4\frac{tx}{s}$  source
Bitcoin energy consumption $\approx 8.00GW$ source
Carbon emission per $\approx \frac{0.5kg}{kWh}$ CO2 germany (Not sure if China is lower or higher here, since mining mostly happens in China)

Calculations
Transactions per hour: $4\frac{tx}{s} = 60*4\frac{tx}{m} = 60*60*4\frac{tx}{h} = 14.400\frac{tx}{h}$
Energy Consumption per hour: $8.00GWh = 8 * 10^6kWh$
Energy Consumption per transaction $\frac{8 * 10^6kWh}{14.400tx} \approx 555\frac{kWh}{tx}$
Carbon footprint per transaction $555\frac{kWh}{tx} * \frac{0.5kg}{kWh} \approx 277\frac{kg}{tx}$

If the whole energy used for bitcoin was produced in germany one bitcoin transaction would have a carbon footprint of 277kg. If we take Finland for example with more reneweable energies ($\frac{0.113kg}{kWh}$) it would be 77kg CO2.

For reference: A single flight form Hamburg to Munich (600km, aprox. 1h) is 161kg myclimate. The compensation of 277kg CO2 is roughly $6.50 with atmosfair.

I did some napkin math based on your data. At 4 tx/s and 8GW, that is 2GWs per transaction. 0.5kg/kWh is around 139kg/GWs. Thus each transaction is around 278kg. Looks like we reached the same answer.

But is this the carbon footprint of one Bitcoin transaction? To put it differently, if there was a global carbon tax, would it makes sense to charge for 278kg per transaction? Probably not. In fact, almost certainly most of the tax would just apply to the electricity bill of Bitcoin miners, which is split between hashing for the block reward and processing transactions.

There are roughly 2000 transactions per block. Each transaction costs roughly \$1. The block reward is 12.5 Bitcoins as of now. At \$8200 per Bitcoin, roughly $\$2000/(12.5\space\text{BTC} \times \$8200/\text{BTC} + \$2000)=0.0191$ or 2% of a miner's electricity bill goes to transaction processing. So perhaps it makes more sense to say that each transaction costs around $278\space\text{kg} \times 0.02=5.56$kg of carbon.

So what about the rest of the carbon? In some sense, the main job that PoW does is preserving the integrity of existing token balances. The block reward is seniorage. This a similar principle to how central banks print more money and thus reduce the value of existing bank notes and coins. As of now there are close to 18 million Bitcoin in existence. Continuing with your carbon emission numbers, each Bitcoin holder that isn't transacting is then responsible for $((8/(18 \times 10^6)) \times 139) \times 0.98=0.000060542$kg of carbon per second per Bitcoin or 5.23kg of carbon per day per Bitcoin.


What is the difference between an Ordinary Demand equation and an Engel curve equation? I mean, an Ordinary Demand Equation measures changes in quantity of X due to changes in price Px.  Engel Curve measures changes in quantity of X due to changes in income M.  But ODE has M in it's equation, and is simply just an algebraic variant of the Engel curve!

Engel curve assumes the price is constant, and demand curve assumes income constant. There is only demand function, no engel curve equation or demand equation.


How come the average studio rent in Vietnam is bigger than the average salary? A studio in Ho Chi Minh city center : roughly 500 USD/month
Average salary in Vietnam : 300 USD/month
I have noticed the same thing in other "poor" countries : a studio rent is so expensive compared to the average salary. Is there an explanation ? And how do vietnamese people pay their rent ??

The rent figure in the question relates to the centre of Ho Chi Minh City and it is a fallacy to infer that it is typical of the whole of Vietnam.  There is a body of theory going back to von Thunen suggesting that land rents will generally fall with distance from a city centre, forming a rent gradient. Given a free market in land and property, residents and entrepreneurs will choose where to live or site their businesses with regard both to price and to costs of travel and transport, and this tends to result in such a gradient in land rents.  Property rents will depend on the size and type of property as well as land rents per unit of area, but otherwise similar properties will tend to be cheaper with greater distance from a city centre.

In the case of Ho Chi Minh City, this World Bank Report indicates (p 153 Section 3.4.1. Prices) that the market for land is subject to considerable government intervention, but that land prices are nevertheless much lower in peripheral districts than in the city centre.

While the factors listed by emeryville may also play a part, a large part of the answer to the question "How do Vietnamese people pay their rent?" is probably therefore that most poorer people do not live in the parts of large cities where the rents are highest.


Why is Engel curve a straight ray through the origin if $D_wx$ = x(p, 1)$? I see in the textbook that the Engel curve will be straight if $D_wx(p,w) = x(p,1)$ but it's not immediately clear to me why this is the case. Could someone kindly explain to me?

The function $x(p,1)$ is constant in $w$. If you integrate it wrt $w$, you end up with a straight line (wrt $w$), whose equation is ...


Daily stock data request I want to get past daily charts for stocks I'm looking at but I can't seem to find any websites that display this real-time data. The daily high, low, close, and open isn’t enough information to suit my needs.

Yahoo Finance is a site thats pretty useful for getting historical stock data.

You can get some pretty big datasets (i.e. you can get daily stock market data for Microsoft going back to 1989 till now).

Hope this helps.


What utility functions are equivalent to additive functions? Call a utility function $u(x,y)$ additive if there exist functions $v_x,v_y$ such that:
$$u(x,y)=v_x(x)+v_y(y)$$

Consider the function $u(x,y)=xy$. It is not additive, but, it can transformed using a positive-monotonic-transformation (PMT) to the function: $u'(x,y)=\log u(x,y) = \log{x}+\log{y}$, and the function $u'$ is additive.

My question is: what conditions on a function $u(x,y)$ guarantee that it can be transformed using a PMT to an additive function?

I.e, if I see a function $u(x,y)$, how can I know whether it represents a preference relation which can also be represented by an additive utility function?

Ted Bergstrom has Lecture Notes on Separable Preferences that seem to have what you are looking for. For example:

  When are preferences additively separable?

  The most useful necessary and sufficient condition for preferences to be additively
  separable is that every subset of the set of all commodities is
  separable. The proofs that I know of for this proposition are a bit
  more elaborate than seems appropriate here. A somewhat more general
  version of this theorem can be found in a paper by Gerard Debreu (Topological methods in cardinal utility).
  Debreu’s paper seems to be the first satisfactorily general solution
  to this problem. Other proofs can be found in (Foundations of Measurement) and (Utility theory for decision making).


Are there any Sovereign Debt Guarantees, apart from those issued by the US? The US has been undertaking an irregular form of foreign aid, Sovereign Bond Guarantees, which entails guaranteeing some of the public debt of their allies, source here: https://www.cgdev.org/blog/whither-us-sovereign-bond-guarantee-program
The entire idea is that some states cannot access financing because they are not perceived as trustworthy, stable, or established enough. This creates a negative spiral, as high interest rates increase the probability of default. Guaranteeing the debt is bound to decrease the interest rate, making financing much easier and cheaper.
My question is: Has any other state done anything like this before? Who, when, where? Guarantees of private debt are common, but are there any other cases of state debt being guaranteed?
Is this an efficient form of foreign aid?

Has any other state done anything like this before? Who, when, where?

Yes, one (relatively) recent example from 2010 is EU member states guaranteeing portion of Greek debt see the Guardian article about it (although technically the countries are all in loose (con)federation).
Another example could be UK guaranteeing Irish land bonds in between 1920–1938 (see Foley-Fisher & McLaughlin 2016).
It is also commonly done by supranational organizations such as World Bank (of course World Bank is not a state but it gets its funds from donor states so you can view it as donor states running the program through the World Bank).

Is this an efficient form of foreign aid?

Well this is extremely broad question because efficiency could be examined from multiple angles, and as always an important question in public economics is compared to what?
The abovementioned research by Foley-Fisher & McLaughlin (2016) shows that such guarantees can reduce but not eliminate the risk premium. So they have a positive effect on reducing country's servicing costs. However, I am not aware of literature that would compare and contrast efficacy of this foreign aid program relative to some other programs that might perhaps use the same resources more efficiently. This being said debt guarantee is likely to be much less costly for donor country, so it would not be unreasonable to conjecture that it could be part of efficient foreign aid policy mix.


Essential goods: How does one restrict the utility function? I understand that solutions on boundary of the set under consideration when doing constrained optimization are often problematical. Usually it is said that we assume that goods are essential to insure an interior solution.
But are there not a set of conditions that can be imposed on the utility function for example - rather that stipulating it as a primitive - to insure that the solution is interior?
I realize that this offcourse depends on the particular program under consideration. So to be concrete I am primarily interested in the standard program where
$$\max_x \ u(x) \\
s.t. \ \ px \leq w$$
where $p>>0$ and $w>0$.

In order to have $x^*_j>0$, it is possible to impose either
(i) a condition on the marginal utility: $\lim_{x_j\rightarrow0} \partial{U}/\partial{x_j}(x)=+\infty$
(ii) or an inequality $x_j \geq a_j>0$ where $a_j$ is interpreted as a subsistence level of $x_j$
Often the utility function is reparameterized and written $U(x-a)$ with the constraint $X:=x-a\geq 0$, which ensures that $x^*\geq a$ at the inner optimum.
Example: in the Cobb-Douglas case with subsistence levels, we have
$$ U(X_1,X_2)=U(x_1-a_1,x_2-a_2)=(x_1-a_1)^\alpha(x_2-a_2)^\beta $$
Provided that the income $m$ is high enough, the Marshallian demands are given by:
$$x^*_1 = a_1 + \frac{\alpha}{\alpha+\beta}\frac{m-p_1a_1-p_2a_2}{p_1}\\
x^*_2 = a_2 + \frac{\beta}{\alpha+\beta}\frac{m-p_1a_1-p_2a_2}{p_2}. $$


Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x_1, x_2\} + x_3$ I know how to solve the two-good case with $u(x) = \min\{x1, x2\}$, but the addition of $x3$ confuses me.

Problem

Derive the demand function $x(p,w)$ from $u(x) = \min\{x1, x2\} + x3$

What I did so far

We assume that in optimum $x1 = x2$.

Set up the budget constraint $p1x1 + p2x2 + p3x3 = w$

Rewrite budget constraint as $(p1+p2)x1 + p3x3 = w$ or $(p1+p2)x2 + p3x3 = w$

We can write $x1*$ or $x2* = \frac{w-p3x3}{p1+p2}$ and $x3* = \frac{w-(p1+p2)a}{p3}$

Confusion

How to proceed? Can I still use a Lagrangian to solve this?

Hint: Imagine that there are two coffee bars, $A$ and $B$. There is only one type of coffee in the world. My preferences are such that I always want 1 unit of sugar with 1 unit of coffee; if I consume units of coffee and sugar in the ratio $1:1$, additional units of only one of the two don't give me extra utility.

At coffee bar $A$ they sell coffee and sugar separately. That is: there is one counter for coffee, where coffee is sold for a price of $p_1$ per unit. There is another counter for sugar, where I can buy one unit of sugar for a price of $p_2$.

At coffee bar $B$ however, they only sell one unit of coffee with one unit of sugar in a bundle, the price of which is equal to $p_3$. They do not sell anything separately

At what prices do I prefer to buy my coffee with sugar at $A$, at what prices do I prefer to buy my coffee with sugar at $B$?


Easterlin hypothesis In my understanding, the seminal contribution of Easterlin (1974) showed that within a single cross section, both within and across countries, happiness correlates positively with income. However, growth in income over time  within a country is not met with similar increases in happiness. Is my understanding correct?

The basic idea of Easterlin hypothesis is that 10 units of additional income does not require 10 units of additional happiness. The idea is close to the decreasing marginal utility of consumption.

Also, commiting suicides are less in countries where there are so many conflicts. Commiting suicide is more often in countries where prosperity level is higher.


Ex-dividend (Asset Pricing) I am reading some lecture notes on asset pricing, and they use the term "ex-dividend" price of an asset.
I googled and found that ex-dividend means the time between announcement and payment of a dividend.

So, what does it mean by ex-dividend price? What does the word 'ex-" refer to?

Thank for your help in advance!

When a firm announces a dividend, it pledges to pay a given amount at a given date ($t_p$) to its stock holders. As traded shares may change hands frequently, the firm defines who has the right to claim the dividend as the shares owners at a given date ($t_e$), that usually is some date between the announcement date and the payment date. During the $t_e$ to $t_p$ period, the stock can trade, but its buyers won't have the right to receive the dividend, even though it hasn't been paid yet. This is why we say ex-dividend, because the share has no longer attached the right to claim the next dividend.


Oddness of equilibrium points I have seen that generically any finite games have odd number of equilibria. So for $2\times 2$ games can we say that generically they must have $3$ equilibria? If not can you give an example of games which have $5$ or $7$ equilibria? Many thanks!

It depends on what you mean by generically. The Prisoner's Dilemma has exactly one equilibrium. If you generate the payoffs in your $2 \times 2$ game by drawing payoffs from continuous i.i.d.'s then there is a non-zero probability (seems to me that the exact number is 25%) that you will get a game similar to the Prisoner's Dilemma, i.e. a game with strictly dominant strategies for both players.

There is also a 'smaller' class of games with even number of equilibria, you can read about them here:

http://mindyourdecisions.com/blog/2014/10/07/game-theory-tuesdays-why-most-games-have-an-odd-number-of-nash-equilibria/

  The Oddness Theorem (Wilson 1971) states that nearly all finite games have an odd number of Nash equilibria. In this post, we’ll explain what the theorem means in practical terms.

You can also have a game with an infinite number of equilibria. (E.g. a $2 \times 2$ game with all zeros.)

However if the number of equilibria is finite you cannot have more than three in a $2 \times 2$ game.


How does national debt work? I'm trying to understand national debt. I gather that the United States, and other nations with central banks, accrue debt basically by printing new money at their central bank. This, I hypothesize, is to avoid giving private banks too much power. What I'm having trouble with is understanding the interest rate on these "loans". Given the peculiar circumstance of the arrangement, the national debt provides a way to monitor the possible inflationary effects of printing new money. It is paid back only as a way to take money out of circulation, and/or to allow the government to solidify wealth created by the economic stimulus, and to invest it abroad. But there's no apparent reason for one part of the government to charge another part of the government interest, so far as I can tell -- unless it represents something else. So what is the interest rate doing? And is there something I'm missing in my explanation?

Your understanding is wrong.

Nations accrue debt by selling bonds. They pay interest on those bonds to the bond-holders.


Does constant market cap imply reversion to the mean If the market cap of a market is constant, do stock prices necessarily follow the principle of reversion to the mean? How would one prove this? (I'm pretty sure this is trivial, but I don't know how to express the necessary ideas).

Identically:
$$ Market\_Cap \equiv Number\_of\_Shares \cdot Price\_per\_Share$$
If a market cap is constant than stock prices only fluctuate because of changes in the number of shares. Therefore, this would imply mean reversion in share prices only if the fluctuations in the number of shares were also mean reverting.

As a general matter in the United States over the last hundred or so years, the average price per share has mostly been \$20-\$40 while market capitalization has increased substantially, implying a large increase in the number of shares. This has mostly been achieved by stock splits, stock based acquisitions, and secondary equity offerings.


Why is deflation a likely short-term of an increase in M2? The year-on-year growth in M2 — a broad measure of US money supply —
has rocketed this year due to the efforts of monetary and fiscal
policymakers to reduce the economic damage caused by the pandemic.
Although the severity of the shock makes deflation the most likely
short-term outcome, Mr Wilson argued that there is now a “greater
likelihood for inflationary pressures to build”.
Source: Financial Times, August 10th, 2020.

What fact in macroeconomics explain deflation being the most likely short-term outcome of an increase in M2?  A reference would be appreciated. Thank you.

None, you are misreading the passage. The paragraph does not say that increase in M2 will lead to deflation.
As the paragraph clearly states the deflation is most likely because of the severity of the 'shock'. Shock here is not the increase in the money supply it is the recession. Fall in real output is deflationary.
According to standard textbook equation of exchange  (see for example Blanchard et al Macroeconomics an European perspective)  price level $P$ is given by:
$$P=MV/Y$$
where $M$ is money supply, $V$ velocity and $Y$ output. This equation is an oversimplification as in more advanced models also expectations of these variables and other factors play a role (see Romer's Advanced Macroeconomics or Krugman (1998)), but for this question more complex model would arguably be an overkill.
As the equation shows price level (change of which gives you inflation) increases with $M$ but also decreases with $Y$. The article in the Financial Times simply states that although $M$ increased considerably deflation is still expected due to the fall in $Y$ (i.e. the shock).


Relationship between convexity and a perfect complements type utility function Consider someone who consume two goods and hates them both.
Given the utility function:
U(x,y)= -max{x,y}
1.What would be the shape of the indifference curve?
2.Why are these preferences weakly convex?
3.What does the negative sign imply mathematically?
4.Will it become an min{x,y} function?

Instead of directly giving you the answers, I'm going to give you a series of hints to help you figure out the answers on your own.

  1.What would be the shape of the indifference curve?

Consider three different consumption bundles: $(3,10)$, $(10,10)$, and $(10,3)$. Verify that these three bundles yield the same utility to the consumer. In other words, they should lie on the same indifference curve. Then draw a curve through the three points. Verify that all points described by $(x,10)$ and $(10,y)$ for $x,y\le10$ should also be on this indifference curve.

  2.Why are these preferences weakly convex?

First remind yourself what weak convexity means. Then compare the utilities that the individual gets from the following pairs of bundles:

$A_1=(10,10)$ and $A_2=\alpha(10,3)+(1-\alpha)(3,10)$ for $\alpha\in(0,1)$
$B_1=(10,10)$ and $B_2=\alpha(10,3)+(1-\alpha)(10,10)$ for $\alpha\in(0,1)$

  3.What does the negative sign imply mathematically?

You said that the consumer hates both goods. Compare the utilities from the bundles $(10,10)$ and $(5,5)$ and see which is higher (and thus more preferred).

  4.Will it become an min{x,y} function?

Try sketch an indifference curve for $u=\min\{x,y\}$ and compare to those in part 1.


Hausman Test for Simultaneous Equations Given a set of structural equations:

Demand Function: $$Q_1 = \alpha_0 + \alpha_1 P_t + \alpha_2 I_t + \alpha_3 R_t + \mu_{1, t}$$
Supply Function: $$Q = \beta_0 + \beta_1 P_t + \mu_{2, t}$$

Where

$P$ = price
$Q$ = quantity
$I$ = income
$R$ = wealth

How would you proceed with the Hausman test of simultaneity? Suppose you reject the null, which states there is no simultaneity between the error term and the endogenous variable; how can you proceed to obtain the parameters in the model?

Generally, price is endogenous in this set of simultaneous equations.  One strategy we can use to overcome the bias is to find a valid instrument for price—call it $Z$.  We’d need something that satisfies $Cov(P, Z) \neq 0$ and $Cov(Z, \mu_1) = 0$.

The trouble with simultaneous equations is that upon observing some $(P, Q)$ pair, all we know is that it lies at the intersection of supply and demand. As we get more pairs (more data), we’re not tracing out supply or demand curves—we’re just getting a bunch of equilibrium points and aren’t
certain whether it’s supply or demand (or both) that moved!

To estimate the demand curve, what we'd like to do conceptually is to hold it fixed while we shift the supply curve around.  In theory, these new equilibrium points would trace out the demand curve itself.

Returning to the instrument, the statement $Cov(P, Z) \neq 0$ means we'd like to find some variable $Z$ that shifts the supply curve.  Maybe this is something like subsidies to tech firms or weather in agricultural regions.  Then you'd hope $Cov(Z, \mu_1) = 0$ so $Z$ doesn't shift demand around, too (then we'd be back where we started).

If the instrument were to be valid, you could form a consistent estimator.


Uniqueness of equilibria in first-price auction with discrete valuations Assume we have a first-price auction with discrete and independent private values and identical distributions of all bidders. It is known that there exists a Bayes-Nash equilibrium where bidders bid on disjunct bid intervals. For example, we have valuations 0,1,2. Then a bidder with valuation 0 bids zero, a bidder with valuation 1 plays a mixed strategy on some interval $[0,\overline{b}_1]$ and a bidder with valuation 2 plays a mixed strategy on some interval $[\overline{b}_1,\overline{b}_2]$.

Is it true that this Bayes-Nash equilibrium is unique? If this is true, how one can show that overlapping bidding intervals are impossible? Or is it possible to show at least that this is the unique symmetric equilibrium, i.e. an equilibrium where all bidders employ the same strategy?

I tried to find the answer in the literature but I only found papers which derive the symmetric Bayes-Nash equilibrium with disjunct bidding intervals without discussing other possible equilibria. Thank you!

Ruling out (strictly) overlapping intervals should be possible using the fact that players must be indifferent among all actions in the support of the mixed strategy, or that these type of auctions is efficient.

Uniqueness is tricky, simply because there are many possible interval structures like that one.  But I guess you mean, equilibria are always of this form. In that case, uniqueness should be possible among symmetric equilibria, after ruling out the overlapping intervals, you need to show that the support of the mixed strategy is convex (which should be the case, otherwise money is left on the table), that the intervals are ordered (which comes from efficiency),  and put restrictions on the bidders with the lowest valuation.

Without symmetry, you can have situations where players with the same valuation use different mixed strategies  (even with different support), so the problem there seems untractable to me.


How does QE effect the collaterals? For instance, the ECB accepts green bonds as collateral. And also they are more likely to include green bonds in a QE program.
Does this face make a green bond more valuable? How would it work in a real life example?

Yes, if green bonds are accepted as collateral they become more valuable/demanded by prospective buyers. When ECB directly buys these as part of QE then again they are more in demand. When demand shifts to the right and supply stays the same price increases.
In real life, ECB could just buy these green bonds on the market as part of their QE, for example, they could directly buy Enel Green Bonds, that increase in demand will raise their prices so when Enel issues new Green Bonds they can charge more for them than they face value.


Would healthcare costs increase (in the long term) if all smokers quit? According to research by Jan J. Barendregt, M.A., Luc Bonneux, M.D., and Paul J. van der Maas, Ph.D.:

  RESULTS

  Health care costs for smokers at a given age are as much as 40 percent higher than those for nonsmokers, but in a population in which no one smoked the costs would be 7 percent higher among men and 4 percent higher among women than the costs in the current mixed population of smokers and nonsmokers. If all smokers quit, health care costs would be lower at first, but after 15 years they would become higher than at present. In the long term, complete smoking cessation would produce a net increase in health care costs, but it could still be seen as economically favorable under reasonable assumptions of discount rate and evaluation period.

When it comes to short-term effects, Cancer.org claims that:

  From 2000 to 2012, tobacco-related health costs and productivity loss in the United States totaled $289 Billion
  The average price of a pack of cigarettes in the United States is \$6.36. But each pack of cigarettes creates $35 dollars of health-related costs for the smoker.

However no information is given on long-term effects.

The question is therefore: if everyone stopped smoking, would healthcare systems around the world see a net increase or decrease in expenses in the long term?

It is a reputable journal and the results are surely correct on a "total dollars" sense. I guess the point they are making is that because health care expenditure of old age individuals is very likely to be high, there is some 'social benefit' of dying before old age.

However, it seems somewhat meaningless:

A) First, by this logic, murders also decrease health care costs. We're not trying to keep smokers form smoking solely because they will be a health care burden. We also want these people to live long, rewarding lives.

B) People contribute to society, their families, their friends and so on. They also save and, specifically, they pay health insurance premiums while they are alive. So, while they might require more care in the long run, non-smokers might well be able to pay or it with the taxes on their income and the productivity they bring to society. Similarly, we all invest through our taxes, on public education, and it goes to waste when somebody that has received public education dies.

C) There are enormous variations in the amount of healthcare spending that old people receive across countries, so the estimates of how much health are old people will receive has got to be very imprecise.

D) Investments pay a positive rate of return, so if we saved the money now we could pay for a lot more care later. Put differently, all the resources that would not be devoted to the care of smokers now would be used to improve our lives meaningfully, potentially even helping us do research into how to take care of old people effectively, which would again reduce the future expected cost of caring for the smokers.


Would it be accurate to say that the economies of most of the countries are capitalistic? What is the proportion of countries that are capitalistic? What is the proportion of the planet's population who live in such countries? How is this, (somewhat subjective?)

A nice way to check this is by looking at the economic freedom index
As we can see, this is a scale, there is no perfect capitalistic country and most of the countries are not very free economically


How to derive cubic cost function from a problem of constrained optimization? The cubic total cost function usually take the form

$TC(q)=a+bq+cq^{2}+dq^{3} \qquad a,b,d>0, c<0$ and $c^{2}<4bd$

I know that from a constraint maximization problem

$min\quad wL+vK$

subject to

$q_{0}=f(k,l)$

i can express it with the lagrangean function

$\mathcal{L}=wl+vk+\lambda(q_{0}-f(k,l))$

with some algebra for the case of a Cobb-Douglas production function $q_{0}=k^{\alpha}l^{\beta}$ i can reach

$TC=q^{\frac{1}{\alpha+\beta}}w^{\frac{\beta}{\alpha+\beta}}v^{\frac{\alpha}{\alpha+\beta}}\left(\frac{\alpha+\beta}{\alpha^{\frac{\alpha}{\alpha+\beta}}\beta^{\frac{\beta}{\alpha+\beta}}}\right)$

I could give values to $\alpha$ and $\beta$ to obtain a cubic function, but not the one I described in the preamble. It could also fix some other factor such as the size of the factory, but would not work.

Any idea?

Thanks in advance

Given a Cobb-Douglas production function your cost function will be cubic exactly if $\alpha + \beta = \frac{1}{3}$, and in this case you will have $a = b = c = 0$. There is no going around this. If you want to have the kind of cost function you describe you will have to slightly alter your Cobb-Douglas function, e.g.
$$
f(k,l) = (k-1)^{\alpha} \cdot (l-2)^{\frac{1}{3} - \alpha}.
$$


Industrial Revolution: Induced technical change and factor shares I have been reading about various explanations for the British industrial revolution. A strand of research lead by Allen (2009) tries to provide an incentives based explanation whereby high wage and cheap energy (coal-based) economy of Britain induced labour-saving and capital-deepening technical change. That's, low cost of capital relative to high wages encouraged innovative activities which lead to the substitution of expensive labour with machines i.e. mechanisation of manufacture, textiles, agriculture etc. and this transformation sustained the productivity growth.

If the businesses tried (perhaps, managed) to reduce their labour costs, the labour's share in national income should decline over time. However, looking at the time series of labour's share in national income estimed by Clark(2009), I see the opposite.

The data does not show any support to Allen's hypothesis, which, if true, I would expect the aggregate wage bill to go down in the 19th century due to labour saving and the share of capital to go up due to capital deepening.

Any thoughts or suggestions as to why the wage bill increased despite the efforts to save labour?

According to Allen (2001), real wages expanded throughout the 19th century in the UK. You seem to imply that they did not. The graph below shows that the UK (London) had higher wages+cost of living than the rest of Europe (except the Netherlands) for several centuries, whereas the rising productivity in the 19th century (because of industrialisation) enabled the possibility of rising wages (see more graphs and tables in the paper).

The author states:

  The high real wages in the northern Europe were the result of high nominal wages. These, in turn, reflected a growing productivity advantage that these economies enjoyed during the early modern period. [...] The advantage of northern Europe, therefore, did not lie in cheap labor but rather in high productivity: Exporters in northern Europe could successfully compete against those in the south and pay a higher wage only because their productivity was higher. By the same argument, the eighteenth century rise in English wages above those prevailing in the Low Countries or, indeed, anywhere else on the continent, attests to rising productivity in British manufacturing (cf. Temin, 1997; Berg and Hudson, 1992). The English labor market was so inflated in the late eighteenth century that even the winter wage of men in agriculture exceeded the wage of craftsmen in many parts of Europe. This premium became even greater during the industrial revolution. English construction wages leaped up again in the first half of the nineteenth century, and for this period we know that the wage advance was general. The only way that Britain could pay the highest wages in Europe and dominate export markets as it did was to have the most productive manufacturing sector. Wage history indicates the mid-nineteenth century preeminence was built up over several centuries.

A recent piece by the Bank of England presents a long series of data on different variables, including labour productivity and wage growth. The graph (below) gives further support to Allen's analysis.

Thus, even in a period of high capital deepening, if real wages (and employment) are rising because of Hicks-Neutral technical change (on top of labour-saving technical change) a rise in the labour share over that period is possible. This can also be seen mathematically.

Consider a constant returns to scale CES production function:

$$ Y = A\left[\alpha K^{\rho} + (1-\alpha)L^{\rho} \right]^{\frac{1}{\rho}} $$

In a competitive market, the real wage is:

$$ w = (1-\alpha)\left(\frac{Y}{L}\right)^{1-\rho} $$

The wage share is:

$$ \frac{wL}{Y} = (1-\alpha)\left(\frac{L}{Y}\right)^{\rho} $$

Adding capital to the right-hand side produces:

$$ \frac{wL}{Y} = (1-\alpha)\left(\frac{L}{K}\frac{K}{Y}\right)^{\rho} $$

Capital deepening means $\frac{L}{K}$ falls. In a world with a mild degree of Hicks-neutral technical change (growth in $A$, as you would expect in the industrial revolution and Allen argues), it is reasonable to expect $\frac{K}{Y}$ is falling. Therefore, the term inside the parenthesis is falling. In the case of $\rho<0$, i.e. relatively low substitution between capital and labour (as is the empirical regularity, at least in recent decades; maybe different around the industrial revolution?), such biased plus unbiased technical change leads to an increase in the labour share.

Notice that in the case of $\rho=0$, the CES degenerates to the Cobb-Douglas function, in which case the labour share depends only on $(1-\alpha)$ and not on the capital-labour ratio.

Finally, the above is a highly ad-hoc, not general equilibrium analysis.
I just wanted to make the point that the equations allow for labour-saving technical change to expand the labour share.


Why would increased inflation increase the value of the dollar and bond yields? I was reading this Fortune article (http://fortune.com/2016/11/14/donald-trump-victory-dollar-inflation/) and came across this confusing quote:

"'Clearly the market has settled on a 'buy dollar' theme on the basis there will be a debt-fueled U.S. fiscal binge that will push up inflation,' TD Securities European Head of Currency Strategy Ned Rumpeltin said.

and the start of the article says that "the risk of faster inflation and wider budget deficits...sent Treasury and other benchmark global yields shooting higher."

Why would this be the case? Shouldn't it be the opposite (higher inflation-->less valuable dollar)? Or are markets anticipating the Fed to more aggressively raise the interest rate?

My interpretation of the argument is that real GDP is also supposed to rise, not just inflation. Increased growth makes US dollar assets more attractive, hence drawing portfolio inflows. The rise in inflation is a side-effect of the scenario, and not the cause.


Am I using quantity and price correctly in trying to calculate price elasticity of supply? The problem I am considering involves a firm that is a price-taker and sells its good at price $p$. From the production function, I calculated the cost function and the profit-maximizing level of output. This allowed me to define my quantity supplied in terms of price. I got

\begin{equation}
q(p) = \frac{p}{2c}
\end{equation}

where $c$ is a constant.

I want to calculate price elasticity of supply.

\begin{equation}
E_s = \frac{dq}{dp}\frac{p}{q}
\end{equation}

Thus, I got
\begin{equation}
\frac{dq(p)}{dp} = \frac{1}{2c}
\end{equation}
Here's where I am confused:

Can I now just multiply that derivative by $\frac{p}{q}$ to get the price elasticity of supply? My confusion is that $q(p)$ is a function of $p$. So am I supposed to merely multiply by  $\frac{p}{q}$ or $\frac{p}{q(p)}$?

It does not really mater, as you will get the same numerical values eventually. You may choose whatever is more convenient in each particular situation. Convention is, however, to replase $q$ with $q(p)$ to derive a formula for elasticity as a function of the price only.


Calculating mixed strategy equilibrium in battle of sexes 0
down vote
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In the following game, the mixed strategy equilibrium is found as player 2 playing B 3 out of 5 times and A 2 out of 5 times but I am not able to get it. Please find the mistake in the following calculation:
                         Player 2
                    A                      B

         A     3,2                    1,1

Player 1

         B     0,0                    2,3

Payoff for player 1 if he plays A: 3q+1(1-q)  assuming player 2 plays A with probability q. And if he plays B payoff is 0q + 2(1-q)
For an equilibrium both payoffs should equal so 3q+1(1-q)=2(1-q) which gives q=1/4 i.e. probability of player 2 playing A which is not correct.

Thanks in advance.

Your calculations are correct. If we take this game:

\begin{array}{| r | r |}
  \hline
\hline
  & A& B\\
  \hline
A&3,2&1,1\\
B&0,0&2,3\\
  \hline
\end{array}

then the mixed strategy probability used by the column player must make the row player indifferent: $3q+1(1-q)=0q+2(q-1)$, implying $q=1/4$.

From your question, I infer that you have a solution claiming that the answer should be $q=2/5$. In that case, it looks to me like there has been a typo somewhere. Indeed, if we take the following game:

\begin{array}{| r | r |}
  \hline
\hline
  & A& B\\
  \hline
A&3,2&0,0\\
B&0,0&2,3\\
  \hline
\end{array}

We find the mixed strategy equilibrium implies the column player using probability $q$, with $3q=2(1-q)$ so $q=2/5$.

Note that this second, modified game is symmetric (as textbook battle of the sexes games usually are), further strengthening my suspicion that the confusion has been caused by a typo in the description of the game.


Determinants of economic growth in ARDL model - nominal or real variables? I'm investigating the determinants of economic growth of my country. Some of them are of long term other are of short term. For that I'm trying to construct an ARDL model, but I'm confused about the right variables to choose and whether I implement them in difference in level or difference in logarithm.

I found out that we use the logarithm of real GDP in differences which tend to represent the growth rate. The explicative variables are foreign direct investment credits to private sector education spending health spending.

My question is: if I'm using real GDP as a response variable, do I have to use deflated explicative variables? Or it's better to  use nominal GDP and nominal explicative variables?

My experience is that most of the papers estimating these sort of regressions use real variables, all of them deflected with the same index. As Roy says, you not want to confound an effect by inflation.

For example, assume the "true" model is that with variables in real terms:

$$ Y_t = \beta_0 + \beta_1 X_t $$

Converting into nominal variables, you get:

$$ Y_tp_t = \beta_0 p_t + \beta_1 X_tp_t $$

Then, a correct estimation of the "true" model when using nominal variables would require you to add prices as a regressor (or inflation if using log of differences). Thus, you have a further robustness check of your model by estimating it in nominal terms and adding inflations as a regressor.

Someone could rightly ask, what if the "true" model is in nominal terms? That is slightly odd though. Such model would be something like

$$ Y_tp_t = \alpha_0 + \alpha_1 X_tp_t $$

But say that there is a change in $p_t$ and in $X_t$ such that $X_tp_t$ remains unchanged. And yet, $Y_tp_t$ would change because of the change in $p_t$, withouth any right-hand side variable changing - a clear inconsistency.


Financialization of the economy What is the financialization process of wealth in the economy? What
  are the determining factors? What are its consequences?

  What is the role of financialization in the economic crisis of 2008?

I do not know if my ideas are right, but

Financialization of the economy would not be the process of selling debt in the form of financial securities?

The relationship between financialization and the 2008 crisis would be the fact of the credit facility and the sale of debts caused an imbalance in the economy.

Financialization is just a broad term for when financial markets become bigger and have more influence on the market economy.

I'd say that it wasn't so much markets becoming bigger that directly caused the 2008 crisis, but more that the shadow banking financial market became bigger (intermediaries not subject to the same regulation as normal banks). Financialization arguably caused the need for more niche ways of getting money into the market in this way, and as financial markets got bigger, particualrly in regards to housing, more banks ended up securitizing subprime mortgages, and that was a big factor in causing the 2008 recession.


Looking for an article in Behavioral Economics about Inequality I have been searching for an article that I know exists, but somehow am unable to find.

The article is about an economic game where participants are assigned to a group, and can observe how much others have contributed to the common 'money pool.' According to the article, if people see the actual monetary amounts given by others, they will tend to like/not punish the person who has given the most. However, when they see the percentage of the incomes given to the money pool, and find out that the person who has given the most has actually given the least (percentagewise) from his income, they tend to severely punish him.

So, the authors conclude that people care about ratios given by others.

I do not know exactly which economic game this is, but I am certain of having read this.

Although your description is very detailed, there is plenty of research on this topic. I think you are looking for this current published paper:

Starmans, Christina & Sheskin, Mark & Bloom, Paul. (2017). Why people prefer unequal societies. Nature Human Behaviour. 1. Article number 0082. doi:10.1038/s41562-017-0082.

This paper covers the latest research about inequality. If its not the specific one you are searching for, please look at its 102 references and let us know.


DSGE model with agents that develop their skills Are there DSGE models with agents with different skill levels (and according wage differences) who can develop or lose their skills and with employees with dynamic/changing skill levels and skill domains? Can such models be used for developing and validation policies that are designed according to Amartya Sen Capability Approach theory? Capability Approach is the leading approach for government programmes that invest in human capital development and poverty eradication, e.g. Germany's policies are based on it. In such a way we could use DSGE for validating and forecasting and design of wider policies, no just monetary or fiscal policies. If there are no such DSGE models, are there any other tools for modelling human capital development. Why not to use DSGE as the common framework for all the major policies?

Most DSGE models don’t model heterogeneity in individual labor market. Although I suppose you could do that if you would really want to but, it would be incredibly data intensive to actually estimate.

You can have some DSGE models with endogenous growth where human capital accumulation plays a role but most of them are based on just exogenous technological growth.

Well you can in principle use DSGE to evaluate policy I would not use it for evaluating some microeconomic policies. There are several reason for this:

Even simple DSGE models are incredibly data intensive. Introducing heterogeneity in individual labor markets by let’s say assuming there is some probability distribution over human capital and further possibility for heterogenous human capital accumulation would push this even further. I am not sure you would find dataset to do this even if you would have full access to all available data.
DSGE models are built for describing and forecasting macroeconomy or macroeconomic policy analysis. While in principle I can imagine you could try to use them for evaluating some microeconomic policy by just changing parameters of one market and then examining the impulse response functions I don’t think you should and I never seen it done before. DSGE is not build for that kind of task. Form what I understand about Sen’s capability approach most of the things that he suggests require microeconomic policies not macro ones as he focuses on things like ignorance, oppressive state policies, lack of financial resources, ill health, lack of proper education etc. These are not really macroeconomic domains.
There are definitely more better and appropriate ways how to evaluate policies on microeconomic level, so what would be a point of using DSGE if it’s inferior tool for given task?

To answer the question if there are better ways how to evaluate policies the answer is yes.

For, example randomized control trails or if that is not possible there are methods such as regression discontinuity, differences in differences, synthetic control, instrumental variables. These are actually used all the time to evaluate policies that improve education, healthcare, lack of access to financial resources of poor. For example, I used to work in the Netherlands at CPB which was analytical unit that evaluates economic policies. I was in macro department but we had department for healthcare economics, labor economics and economics of education where my past colleagues worked on evaluating various programs aimed at improving education sector and hence also human capital accumulation and they mostly used the kind of models I mentioned.

Once you would determine the optimum policies on micro level you could use DSGE for evaluating what would be the impact of increasing taxes to pay for all those policies or spending on those policies since that’s one of the downsides of micro approach that you don’t see the general equilibrium effects of all that spending and taxing.


Why CPI differs so much from consumption deflator? Why are the two series so different for the US? Data is here: https://fred.stlouisfed.org/graph/?g=lqVJ and photo added below:

Private consumption in GDP should include all items consumer by households, whereas the CPI is a basket of "representative" goods. Is this part of the difference? For example, that goods not in the basket have become cheaper than those in the basket?

The discrepancy between these two standard measures of inflation stems mostly from the differences between the basket of goods used by each index.

The CPI is based on survey data taken from some representative sample of consumers. This data represents a basket of "typical" household consumption. The PCE index is also based on survey data, but taken from firms instead. PCE index data represents a basket of sales derived from firm production. It is not difficult to imagine that this discrepancy in baskets can be magnified by certain prices, corresponding to goods in the difference set, receiving a much higher weight than others, thus driving a wedge between the indices. You allude to this in your question.

Additionally, and by construction, the CPI covers a smaller set of expenditures than those covered by the PCE index. The PCE index includes expenditures which are not paid for directly by the agent, such as medical care expenses from employer-provided health insurance, employee retirement payments, etc. The CPI does not take these sorts of transactions into account and instead covers strictly out-of-pocket expenses.

Lastly, the evolution of baskets characterized by the two indices over time is quite different. The CPI has a "stickier" basket that is much more resistant to quality-change and price substitution over time than the PCE index, which directly incorporates price substitution between goods in forming its representative basket.


Demand for minimum of $4$ different goods The consumer has the utility function with $4$ goods $$U=\min\left \{ \sqrt{x+y},z+w \right \}$$ The prices are $p=(3,2,2,1)$ with wage $m=1$.

Find the demand.

So far I have observed that it is perfect complements BUT it must be between the 4 goods. So some combination of $x,y$ to $z,w$. Usually we know that the optimal choice is when $x_2=x_1$ with demand $x_{1,2}=m/(p_1+p_2)$(but with 4 goods, I lose my grib. How do I approach this? Do I just square the right side and let both equal eachother?

You can solve it sequentially by noting the nesting structure of the utility function $U$.
So first note that the utility function combines utility functions you are probably already familiar with $U=\min\{u_1,u_2\}$ of complements and $u_1=\sqrt{x+y}$ and $u_2 = z+w$ both of which are perfect substitutes. Where $u_1$ and $u_2$ are nested within $U$.
The solution procedure is based on the following argument: However much money $m_{u_1}$ the agent decides to spend on $u_1 =\sqrt{x+y}$ she must be minimizing the cost of getting $u_1$ utility points. Similarly, however much money $m_{u_2}$ the agent spends on $u_2= z + w$ it must be the case that the agent minimize cost. So first find the expenditure functions for these inner problem.
Secondly the agent must the maximize the outer utility $\min\{u_1,u_2\}$ subject to the expenditures of the inner problems adding up to total income.
Solve the second inner problem:
The second inner problem is
$$max_{z,w} \{z+w \lvert p_zz+p_ww\leq m_{u_2}\},$$
where $m_{u_2}$ is money spend on $u_2$.
How do you get the most utility for the buck when utility is $u_2 = z + w$? You simply buy the cheapest good so the price of one point of $u_2$ utility is $p_{u_2} := \min\{p_z,p_w\}$. The demand for $z$ and $w$ depends on the amount of money you decide to spend on $u_2$ assumed for now to be $m_{u_2}$. Given this amount demand for $z$ is
$$z = \frac{m_{u_2}}{p_z} 1[p_z <p_w]$$
and
$$w = \frac{m_{u_2}}{p_w} 1[p_w <p_z].$$
I leave it to you to handle the threshold case where $p_z=p_w$. How much utility $u_2$ do you get? Well this must be $u_2 = m_{u_2}/\min\{p_z,p_w\}$ - this is the value function for this inner utility maximization problem - hence it must be the case that
$$m_{u_2} = \min\{p_z,p_w\} u_2,$$
which is the expenditure function for this inner problem.
Solve the first inner problem:
The first inner problem is
$$max_{x,y} \{\sqrt{x+y} \lvert p_xx+p_yy\leq m_{u_1}\},$$
where $m_{u_1}$ is money spend on $u_1$.
How do you get the most utility for the buck when utility is $u_1 = \sqrt{x+y}$? It is perfect substitutes so you buy the cheapest good so demand is
$$x = \frac{m_{u_1}}{p_x} 1[p_x <p_y]$$
and
$$y = \frac{m_{u_1}}{p_y} 1[p_y <p_x],$$
where $m_{u_1}$ is amount of money spend on $u_1$ assumed known. How much utility $u_1$ do you get? That must be $u_1 = \sqrt{m_{u_1}/\min\{p_x,p_y\}}$ such that
$$m_{u_1} = \min\{p_x,p_y\} u_1^2$$
Solve outer problem:
The outer problem is
$$\max_{u_1,u_2}: \ \ \  \min\{u_1,u_2\}  \\[8pt]
s.t. \ \ \ \ m_{u_1} + m_{u_2} = m $$
for which we rewrite the budget constraint to
$$\min\{p_x,p_y\} u_1^2 + \min\{p_z,p_w\} u_2 = m$$
and then use that $u_1=u_2$ because the problem is perfect complements. You then have two equations in two unknowns $u_1$ and $u_2$. Solve for $u_1$ and $u_2$ and plug solutions back into expenditure functions for inner problems to get $m_{u_1}$ and $m_{u_2}$ which you then plug into the equations for the demand.


Military expenditure over time The following graph from the world bank website shows the world wide military expenditure in percentage of the world GDP over time from 1988 to 2015

I am trying to find similar data over a much longer period of time. Over the last 3000 years would be ideal! Of course, I realize that such data might result from very rough estimations and might eventually be specific to a certain area of the world and arguably not representative.

Where could I find similar data over a much longer period of time?

This question has first been asked here on History.SE almost two years ago. It got a good reception but no answer. Following advice of the community, I asked the question to be migrated. The question has been judged on-topic for economics.SE by moderators. As the question is too old to be migrated, it has been closed on history.SE and I am reposting it here.

This is a "there can be no adequate answer" answer, for periods prior to "imperialism as a world system."  (Personally, I'd pick 1880s here, ymmv.)

Gross domestic product as a conceptual tool contains a number of assumptions about how economies function which are unsustainable prior to the generalisation of capitalism in the Marxian sense.  While it might be possible to produce homologues for GDP in societies prior to "production" in the capitalist sense, these link poorly with the assumptions you wish to use GDP for.  In societies without a generalised measure of value, production occurs in traditional manners.  The state, particularly prior to Louis XIV era innovations, lacks the capacity to mobilise the economy to particular ends.  This is to say, there is no "gross" productivity, and there is no capacity of a state to mobilise a percentage of productivity.  The state acts as an agent amongst others in traditional relations of production to move portions of portions of social product to its ends.

Earlier the ability to talk about the state comes into question.

Apart from these issues of concepts of measure, there are issues with measurements themselves.  Data series are incredibly fragmentary and difficult to interpret.  Consider, for example, Measuringworth.com's data series on English wage/price series.  The wages and prices originate in monastic records which were not typical of the relations between agricultural labourers and land controllers.  Even the data points from "private" markets in labour here are suspect, 'with' or 'without' beer?  'With' or 'without' crofts being destroyed regularly?  The customary nature of pre-capitalist economies makes data sets less and less meaningful numerically because of the number of externalities.  Even if data points rigorously record the externalities ('with' beer, but 'with' destruction of waste communities of free peasants, and 'with' regular rapine due to civil war), other data points won't have adequate records.

The alternate way forward would be situational and context interpretive single case studies.  To look at institutional stressor indicators due to war.  Did dynastic families fail to reproduce, or were they subject to heightened baronial outrage; were peasant revolts common, what grains were eaten, etc.

We can't apply a stable category, due to categorical assumptions about capacity to mobilise economies and what is worthful being changeable.  We can't gain equivalent data points, due to the complex structures of worth in the premodern.


Why would a common currency such as the Euro that can't be devalued be incentive for banks to lend money to a country? I'm reading an article that is claiming that when the Euro was created, banks began lending more money to countries than before because as the Euro is a common currency across many countries one country can't devalue it. According to this article,

  If you take 10 million Deutsche Marks from Frankfurt and you give it to a Spanish, Greek or Italian firm or bank - and that is prior to monetary union - and then suddenly there is a substantial devaluation of the currency of Spain, of Italy or Greece - something that was happening at regular intervals prior to monetary union - then you know that the capacity of the creditors to repay the loan shrinks. Because their income comes int he local currency, they will not be able to repay when the local currency is devalued.

Why does this matter? If a country was using the Euro, wouldn't they be getting(ignoring increase/decrease in exports and imports due to the devaluation) roughly the same amount of money but in Euros instead of the local currency? I would appreciate clarification on how and why this devaluation is different in terms of repayment.

EDIT: For context, the source I'm reading is as follows: Varoufakis, Yanis. "CREDITORS UNINTERESTED IN GETTING THEIR MONEY BACK: DISSOLVING THE EUROZONE PARADOX." The Journal of Australian Political Economy, no. 77 (2016): 23-36.

When you lend Spain 10 million Deutsche marks, the loan is denominated in a foreign currency: they have to return you 10 million Deutsche Marks (ignoring interest for the moment). But the Spanish earn their income in local currency. If in the meantime their local currency depreciates relative to the Deutsche Mark, the value of the repayment becomes greater in terms of the proportion of their income (which is in local currency) and their ability to repay becomes smaller.

If you lend them Euros and they receive their income in Euros, a devaluation doesn't affect the (local) value of the debt.


What would you call a real market that is close to perfect competition? I want to explain perfect competition to students using a few practical examples without going into much of the theory. But I want it to be theoretically accurate and I don't want to claim that those are examples of 'perfect competition'. I am thinking about calling it 'near perfect competition', but I wonder if there is a conventional term for a market that is close to perfect competition. This wikipedia article mentions 'close-to-perfect competition' but I'm not sure if that's a conventional term.

I do not have a special term, but I give this analogy:

We know what a triangle is. But in the real world, it is impossible to draw a perfect triangle and there do not exist examples of perfect triangles.
Similarly, we have just learnt what perfect competition is. But in the real world, there do not exist examples of perfect competition. Nonetheless, here are some examples of real-world markets that come "close to" perfect competition ...
We stress that these markets are not actual examples of perfect competition. (To repeat, such examples do not exist.) Instead, these are merely examples that come "close to" perfect competition.


Why do some phones depreciate faster than other? Based on evidence from reselling sites (eBay, Amazon etc.) we can observe a trend that iPhones on average depreciate far less and slower than for example Samsungs (or other phones that lose their value even faster). Now why is that?

Note that I am not talking about nominal prices (iPhones are on average more expensive than Samsungs) but the percentage change. I am also not asking as a "fanboy" - it is just an observation I made.

I think it might have something to do with how much a phone model is valued in certain markets. For example, the amount of utility you get from a certain phone model is higher than another phone - they are not perfect substitutes for each other. Hence, the discounted utility of the phone will still be higher, because the user still values it higher.

There is no strict formula that I know of for this comparison, but by simple logic, if you feel proud of having an iphone, it's demand will be high, will be more plastic, and hence, whether the phone is used or unused, it will sell at a higher price, so will depreciate lesser.

Must note, though, that the depreciation is not constant over time. It reduces much more in the beginning, and then sort of flattens out towards the tail end.


Is price in this situation exogenous or endogenous? My supply function is $Q = a + bP + u$. My demand function is $Q = c + u$. The error terms $u$ in both equations are mutually i.i.d random variables with a mean of zero and a constant variance. My question is: since the demand curve is a constant, is price an endogenous or exogenous variable?

It is endogenous, because a demand shock will affect prices.

To see this more clearly, add another regressor to the demand, for instance, income. It is clear that income is exogenous, as it is not affected by prices or quantities, or shocks. This cannot be said of prices.

This is also evident if you write the system as it should have been written in the first place:

$$ P = \alpha + \beta Q + \epsilon $$
$$ Q = c \quad \quad \ + \mu$$

This is a simultaneous equation system, where both $Q$ and $P$ are endogenous. Here you can see more clearly that a demand shock $\mu$ affects prices via $\beta$ (if $\beta=0$, the two equations are independent).

This means that the OLS estimation of $b$ is inconsistent. A consistent estimation can be obtained with 2SLS, using a proper instrument.


Can a closed economy flourish? I was wondering if it is possible to run a country based only on domestic economy and not to enter the world economy. Basically, if certain economy of a certain country fails and poses threat to world economy, can other countries seal off their economies and still function with sustained growth and flourishing markets based on domestic economy itself?

I know this a naive question, but I tried to find an answer on on the internet and didn't get a satisfactory answer.

It depends on what you mean by "sustained growth" and "flourishing markets".

Clearly the Earth as a whole is a big market. If you do not look at human made borders: the global economy is currently growing and some would say it is flourishing. There is no physical reason why this could not be done without the borders.

There are areas where the current technology cannot support the current population without outside help. An example is the heavily industrialized North Korea (which seems to motivate your question) which gets large amount of aid in food from the UN.


Is the trade deficit driven by lack of domestic savings? NYU Prof Joseph Foudy said the US trade deficit was caused by a lack of domestic savings and that tariffs on China would just shift the deficit to other countries. Zacks says

  A country’s trade balance (current account balance) is the difference between the value of exports of goods and services and the value of imports of goods and services. Through national accounting identities, the trade balance can also be expressed as the difference between national (both public and private) savings and investment.

So isn't Foudy really saying we have a deficit because we import more than we export? In other words isn't the lack of domestic savings identical to the deficit rather than its cause?

And we are back to Triffins' Paradox, apparently one of the most under studied and relevant concepts of our time which would answer many of these questions.

when one nation's fiat currency is used as the world's reserve currency, the needs of the global trading community are different from the needs of domestic policy makers. That is the reason we have a trade deficit.

Understood in this light, rising U.S. trade deficits in the 1990s and 2000s were required to provide enough dollars to lubricate rising global trade:

So, what does it mean if our trade deficit begins to decline? From the point of view of this professor, it would mean that we Americans are now saving money, but once again, we live in the age of globalization and we have the worlds reserve currency, so our economy is the whole planet not just within our borders.

Meaning, a declining trade deficit sounds good because we individualize our thinking about economics, oh boy, we are becoming savers, instead of spenders. We do not seem to care that it means fewer dollars are being exported. Who cares, right?

Well, consider that the global economy is about 60 trillion, of which about 25% is the U.S. economy. Into this vast sea of trade, the U.S. "exports" about 400-500 billion in U.S. dollars via the trade deficit. Put in perspective, it isn't that big compared to the machine it is lubricating.

So what happens when there are fewer dollars being exported? Demand for existing dollars goes up, pushing the "price" of dollars up--basic supply and demand, again, it sounds good, until you consider how it affects U.S. corporate profits.

No, their profits don't go up. Most large U.S. global corporations already earn 60+% of their revenues overseas, in other currencies. As the dollar weakened during massive QE, global corporate profits skyrocketed as earnings in euros, yen, etc. rose when stated in dollars.

As the U.S. dollar strengthens, overseas profits will decline when stated in dollars. Shrinking trade deficits means fewer dollars exported into the global economy, which means demand for dollars for trade, reserves and to pay debts denominated in dollars will face shrinking supply. That will drive the "price" of dollars higher.

As the price of dollars rise, U.S. corporate profits will decline as all the goods and services sold overseas in other currencies are converted (at least for accounting purposes) into U.S. dollars.

So let your professor know to be careful what he wishes for as shrinking trade deficits may appear to be positive for the domestic economy, but they won't be positive for a stock market dependent on profits generated by global corporations who earn 50%-60% of their revenues overseas.


Finding individual utility There are N agents living in an economy with two goods, $X$ and $Y$. Their preferences are described by the following utility function $u(X,Y) = 2 \sqrt{XY}$. Each agent is endowed with 1 unit of $X$ and $y_{i}$ units of $Y$. Each unit of $Y$ is sells for $p$ units of $X$.

The question is to show that each agent gets a utility of $\frac{1 + py_{i}}{\sqrt p}$.

Here is what I have tried:

The agent chooses $X,Y$ in order to maximise $2\sqrt{XY}$ subject to $X + pY = 1 + p y_{i}$ So I have expressed the resource constraint in units of good $X$. The LHS is what the agent can buy and the RHS is the endowment, also expressed in units of $X$.

I then re-arrange the constraint in terms of $Y$, i.e, $Y = \frac{1}{p} + y_{i} - \frac{X}{p}$ and substitute this in to the utility function, with the FOC with respect to $X$ and then substitute the optimal value of $X$ back in to the utility function to get an expression in terms of $y_{i}$. However, the expression is not what I am supposed to get.

If anyone wants to check my algebra, here it is:

The utility function becomes $2\sqrt {(X/p) + Xy_{i} - X^2/p}$ Differentiating this w.r.t $X$ I find that $X^* = (1/2)(1 + y_{i}p)$. I substitute this in the utility function, $2\sqrt{X^*y_{i}}$ but this does not equal $\frac{1 + py_{i}}{\sqrt p}$.

Any ideas on where I am going wrong?

Your mistake probably occurred at the final substitution stage. Optimal utility should be $2\sqrt{x^*y^*}$, which is not the same as $2\sqrt{x^*y_i}$.

In general, maximizing a two-good Cobb-Douglas utility function $u(x,y)=Ax^\alpha y^\beta$ subject to budget constraint $p_xx+p_yy=m$ has general solution
\begin{equation}
x^*=\frac{\alpha}{\alpha+\beta}\frac{m}{p_1}
\quad\text{and}\quad
y^*=\frac{\beta}{\alpha+\beta}\frac{m}{p_2}.
\end{equation}

In your case, the parameters $A,\alpha,\beta,p_x,p_y,m$ take the following values:
\begin{equation}
A=2,\quad\alpha=\beta=\frac12,\quad p_x=1,\quad p_y=p,\quad m=1+py_i.
\end{equation}
Plugging in the values, you get optimal consumption:
\begin{equation}
x^*=\frac{1+py_i}{2},\quad y^*=\frac{1+py_i}{2p}.
\end{equation}
Hence optimal utility is
\begin{equation}
u(x^*,y^*)=2\sqrt{\frac{1+py_i}{2}\cdot \frac{1+py_i}{2p}}=\frac{1+py_i}{\sqrt p}
\end{equation}


How can I estimate the disconnect between book value and market capitalisation? There are several questions on Stack Exchange as to what difference the stock price makes to a company after its IPO. Surely, management cares, it is important to be credible to trading partners, etc.

However, with passive investment being about 50%(?) of the stock market and at the same time the stock price not having a direct influence on the balance sheet, external shocks like the coronavirus won't be blamed on management. To some extent the stock price is just determined by people talking up (sellers) or down (buyers) the stock price. Perhaps short sellers talking it down and long holders talking it up.

How do I make a quantitative indicator that describes the disconnect between the market capitalisation and the book value? What options are there?

Sub 1: When it is said there is an asset price bubble, it usually means stock prices (or RE). Are the assets that actually are on companies' balance sheets also inflated?

I thought it interesting to be an investor: to invest in companies that have worthwhile plans. In reality however, I seem to be buying stock (secondary market) from previous stockholders (primary market). The problem is that the primary market largely ceases to exist after the IPO. You might say that stock buybacks and re-emissions are primary market operations, so I guess my question is focused on the difference between those two.

Sub 2: Why are secondary market participants called investors?

Sub 3: Would it be possible to keep the primary market alive by changing the law?

The context of the question is analysis of the plans of the company, the market price, and the book value.
Primary investors provide cash or other resources to the company in exchange for original debt or equity claims against the assets of the company. The company is expected to purchase assets with the cash as it executes the business plan. Secondary investors purchase the debt or equity claims from a primary investor so the company does not get any cash from these secondary transactions. The question is how to estimate the disconnect between market capitalization and book value.
Understanding Price-to-Book Ratio:
https://www.thebalance.com/fundamental-analysis-understanding-price-to-book-ratio-3140794
The calculation of book value:

(Assets - Liabilities)

Ongoing, financially-sound companies will always trade for more than their book value because investors price the stock based, in part, on their anticipation of the firm's future growth.

The Affordable Growth Rate (AGR) is a formula appearing in the book 101 Business Ratios by Sheldon Gates. According to Gates the formula was used by Hewlett Packard. This article describes AGR

https://www.inc.com/magazine/19861201/9293.html

The AGR is a growth strategy based on two assumptions. The first is that your sales can grow only as fast as your assets. If yours is like most firms, for example, you can't increase your sales by 30% unless you increase your receivables, your inventories, and your fixed assets by about 30% as well. The second assumption is that your firm has a target debt-to-equity ratio and that your lenders are willing to continue to extend credit at that ratio. This assumption implies that as your equity grows, debt can grow at the same rate, allowing you to maintain a constant debt-to-equity ratio.

The sources of cash to grow assets, and therefore sustain sales growth, is debt, equity, and retained earnings. When a firm is taking venture risk the future cash flows in the form of retained earnings are not expected to be sufficient to cover the growth of assets in support of sales growth. When a firm is throwing off cash it has high retained earnings or profit that can also be used to pay dividends. There is another book called The Cash Flow Problem Solver, by Bryan E. Milling, which describes in detail how a company can grow too fast and cause a cash flow crisis that results in bankruptcy.
There is no direct link between market capitalization and book value because market capitalization is the last sale of one or more shares of stock in a secondary market transaction based on the desire of the buyer to own shares at that price and the seller to own cash rather than shares at that price. The market capitalization contains a liquidity premium if the shares are relatively easy to buy and sell on the secondary market and a growth or discount factor, based on expected future events, so there is a disconnect between market capitalization and book value.
If the firm is expected to remain a going concern and grow assets, sales, and profits in the future, especially after reaching cash flow break-even following new injections of debt or equity, and if it can grow from internal finance of retained earnings from operations after getting past cash flow break-even, then there is a premium in the share price above book value. There is no particular formula for evaluating the plans, asset position, debt and equity claims of a company, and there is no particular formula to forecast future sales, profits, and retained earnings, and there is no particular way to put a premium or discount factor on the share position, so there is no particular way to link market capitalization to book value.


Macroeconomics: effect of technology/workforce in the short run My friends and I have homework and we can't come to a consensus on these questions on how they affect aggregate demand, aggregate supply, and equilibrium:

Foreign investors building machineries with advanced technology for the country’s electronic
industry

For this we thought Supply up; AS to right; C up; AD to right; no change in equilibrium

Thousands of workers leaving the country in search of higher salary

and for this we thought: Supply down; AS left; C down; AD left;
no change in equilibrium

For question 1, I think that investment has a demand-side effect on the economy. I think it isn't a supply-side effect because it isn't stated that the investors are responding to a supply-side shock. So I'm saying that AD shifts right. With shifts in the curves, there will be a change in equilibrium. For example, the process you described of both curves shifting right will lead to higher output (even though the price level might not change).

That being said, the "foreign" part of the question does make things a little less obvious. Why would the question want to emphasise the foreign part of this investment? An improvement in technology in one firm will eventually trickle to other firms (vertically or horizontally). Technological improvement shifts the supply curve rightwards, but because this is a long-term effect, I did not say in the first paragraph that there is a shift of the supply curve. Also, if a foreign country sends its profit to its home country, there is effectively a small decrease in the demand curve, but on the whole that would be small enough that it would not offset the increase in demand that the investment brings.

The second question is obviously trying to highlight a decrease in supply, as you have said. The quantity of labour decreases; production decreases.

But... to throw a spanner in the works... this does sort of imply that the workers are consumers. If consumers leave the country, consumption decreases, which decreases aggregate demand (as you have said). One needs to know why the people needed to leave. That being said, with the word "workers" I think the question wanted to highlight the supply side effect.


Solution to maximization not Pareto efficient In my economics class, we saw a proof that if an allocation $ ((\hat x_h), (\hat y_f)), h\in H$ (the set of households), $f\in F$ (the set of firms) is Pareto optimal/efficient, it must necessarily be a solution to the maximization problem:

$$ max \quad U_1(x_1) $$

Subject to:

$$ U_h(x_h) \ge U_h(\hat x_h), h=2,...,m $$
$$ x_h, y_f \quad feasible \quad \forall h \in H, \ f \in F $$
$$ \sum_{h=1}^m x_h \le \omega + \sum_{f=1}^r y_f $$

Where $\omega$ is the total endowment in the economy, m is the total number of households, r is the total number of firms, and $U_h:\mathbb{R}^n_+ \to \mathbb{R}$ is the utility function of household h.

I am curious if anyone can give me a simple example in a pure exchange economy (so obviously removing the firms from what is given above) where the utilities are such that $\hat x_h$ solves the maximization problem, but is NOT Pareto optimal (i.e. something showing that the converse of the statement above does not always hold). Preferably, I'd like to be able to draw it in an Edgeworth box, to convince myself of the need for additional assumptions on the utility function(s) to make the fact that $\hat x_h$ is a solution a sufficient condition for $\hat x_h$ being Pareto optimal.

An example with two agents and two goods: let
$$
U_1(x) = 0, \hskip 20pt U_2(x) = x_1+x_2, \hskip 20pt w = (1,1).
$$

In this case allocating all the goods, so (1,1) to the first consumer solves the above problem. Even though any other feasible allocation fulfills the conditions, none of them gives a higher utility to the first consumer.

Yet this allocation is clearly not Pareto-optimal, allocating (1,1) to the second consumer would be a Pareto-improvement.


Alternating offer bargaining game In an infinite-period alternating offer bargaining game if we suppose the discount factor is $\delta=1/2$, and the increment is $0.01$, what will be the subgame perfect Nash Equilibria?

It seems that the "proposer proposes $0.66$ and responder accepts" will be a subgame perfect Nash Equilibrium, but are there any other equilibria? How about the case when the proposer offers $0.67$?

Consider the following strategies. In any period a player makes an offer, they offer a share of $0.33$ to the other player, keeping $0.67$ for themselves. In any period a player accepts or rejects an offer, they accept any offer that gives them at least a share of $0.33$ and rejects anything worse.

Clearly, the outcome of these strategies will lead to the immediate acceptance of the offer. All that remains is to check that these strategies form an equilibrium. We do so by appealing to the one-shot deviation principle.

Consider the perspective of a player deciding to accept or reject. They will not want to deviate from the prescribed strategies only if

$$ 0.33 \ge 0.67 \delta \iff \delta \le \frac{33}{67} $$

However, this violates the assumption that $\delta = \frac{1}{2}$. Thus, the given strategies cannot form an equilibrium.

For characterising other equilibria, see van Damme, Selten and Winter (1990).