Estimating the cost of an assett that needs to be replenished I am working with hard drives.  For simplicity,  let's say all drives have the same capacity, 1TB and all cost $100.

They typically last about 4 years,  when they need to be replaced.    They drop in price about 50% over that period of time.  They cost 100 dollars for the first for years,  $50 for the next 4 years, etc.

What's the usual way of estimating the cost of something like this?

The retail price should include the total net present value of use of the item. At any given point in time, the value of the item is the purchase cost minus accumulated depreciation. Depreciation should include both physical wear and any non-physical types of depreciation such as obsolescence.


demand impact on shares price Knowing that share prices are determined by the forces of supply and demand, other factors can also play a role in this but lets consider the fact that prices are only based on supply and demand.In this case is it possible for someone to buy a big amount of shares thus making the price rise and then sell them to make a profit ? If so how can the impact on the price be calculated depending on the amount of shares bought ?

What you're failing to consider here is that in buying a large amount of shares, the buyer also makes the price high for himself. And if he sells a large amount of shares at the same time, he's likely to lower the price of the actions while selling them. Poor boy has no chance.


why in some countries trade deficits for a few years generates economical crisis and in United States 40 years of deficit hasnt? why in some countries (e.g. Argentina) trade deficits for a few years generates economical crisis and collapse and in United States 40 years of deficit havent? Which are the economical effects in both countries and why they are different?

Persistent trade or balance of payments deficits generate debt and other liabilities, either in the currency of the importer or in some foreign currency.  This may be sustainable so long as lenders expect to be repaid in something of value.

The United States borrows in dollars, and the general expectation among its creditors is that its debts will be honoured (there was some doubt in 2011 and 2013) and that others will accept dollars in the future.

For Argentina, this expectation is much weaker.  In the past there have been defaults on borrowing in dollars (eight times since 1824, most recently in 2001 and 2014).  Alternatively, Argentina could borrow in pesos, but there have been frequent bouts of hyperinflation, which makes foreign lenders reluctant to lend.

So for the United States, its historical behaviour has created a degree of trust among its creditors which allows a sustained deficit.  Argentina's history makes it harder to borrow, so any new suggestion of a persistent deficit means it soon finds financing imports more difficult, thus creating a crisis.


Why some countries are wealthier than others? Twin-peak of economic growth is one of the concepts discussed in economics. Most of explanations for poverty traps are baseed on the lack of infrastructures and public goods.
How could be another main reasons to explain this important issue ?

Any academic reference is appreciated.

One argument brought forward (it is a generalization/argument for lack of infrastructures) is the Acemoglu-Robinson hypothesis of extractive versus inclusive institutions.

Long-story short: some institutions are good for (long term) growth ("inclusive"), and some are good for short-term extraction of resources ("extractive"). Depending on whether the elites / rulers of a country (colony) had long-term plans of "staying in a country" or whether they wanted to just "quickly get everything they can" out of the country, they installed these different type of institutions.

See also their slides and book.


Are there economic journals which are keen to publish puzzling empirical observations? In his book "Patterns of Speculation: A Study in Observational Econophysics"(2002) Bertrand Roehner makes a bold assertion:

Physical journals welcome all kinds of experimental observations, especially if they are puzzling and cannot be explained by existing theories. Recent illustrations are the numerous papers about avalanches in sandpiles. Economic journals, on the contrary, are very reluctant to publish empirical observations, especially when they have no clear interpretation within the existing theoretical framework.
Another feature of great importance is the small volume of economic journals:
the total number of pages published annually in physical journals is probably of the order of 10–20 times larger than for economic journals. As a result the acceptance ratios for papers in economic journals are between 5 percent and 25 percent, which in turn induces authors to write on the most fashionable topics in the hope of raising the interest of referees, rather than to pursue an original and consistent research project.

Was he right? Has the situation changed since 2002?  Are there economic journals which are publishing puzzling empirical observations, i.e. those observations which have no clear interpretation within the existing theoretical framework?

Was he right? No.

Has the situation changed since 2002? Yes, there are lots more journals, and much higher diversity of publishing. Sadly, that also means there are also a lot more venues that publish at the bottom of the quality scale: one even shares a name with you.

Are there decent economic journals which are keen to publish puzzling empirical observations? No, generally they'll look for something well-written, novel, intelligent, and within the journal's scope. Just being a puzzling empirical observation simply isn't enough for any decent venue. You'll want a blog for that.

As for a slice of historical publishing of puzzling empirical observations, why not try a Google Scholar search for "productivity puzzle"?


What does the Fed do with their profits? As far as I understand the system the Fed prints money which it then uses to buy bonds. Bonds are basically statements of debt meaning that the Fed receives interest from the parties it has bought the Bonds from, because of the nature of debt overall if the debt is repaid the Fed has not only recouped the money they have printed that also have made a profit. What do they do with that profit? To they buy more bonds? Give it to the treasury? Where does the printed money end up?

Fed sends its net profits to the US treasury. Fed keeps portion of the money it earns to cover its operating expenses but everything above that is necessary for it's functioning and dividends to member banks is remitted back to the treasury see the explainer by Fed St Louis here.

For example, according to ABA Banking journal the Fed net revenue in 2018 was $\$55.5$ billion, from which $\$54.9$ billion was payed directly to the US treasury.  The dividend payments according the source totaled $\$714$ million, rest was all used to cover various operating costs.


Saturation of durable goods It seems one factor ignored (or is it?) in economic theory is saturation of durable goods. By this I mean the fulfillment of fixed need for durable goods.

We can imagine income to be divided between consumables, durable goods, capital investments (like real property) and savings. Spending on durable goods is often equated to that on consumables, but this does not seem right to me.

For me personally, for example, I notice that I am spending less money overall and saving more money, not because I want to save more, but because I have simply bought all the stuff I need. After 30 years of buying tools, appliances, books, furniture I literally have every single tool and appliance I need. Ten years ago I was still buying all kinds of stuff, drill presses, rotary saws, juicers, you name it. But now that I have all that stuff I don't need to buy anymore. I mean I don't need two lathes, I just need one lathe.

So, especially if we consider a static or aging population there would seem to be an effect whereby the population is "all tooled up" and no longer needs to spend on durable goods (except for maintenance purposes). Is this phenomenon recognized by any economic theory?

"Durable goods" are a form of utility-generating capital. But they are capital, and what is actually generating utility is the flow of services from them, not them directly. So when we buy a durable good, this is not consumption, it is investment. The phenomenon of uneven intertemporal allocation of purchasing expenses in durable goods is not related to "saturation", in the sense the word is used in microeconomic theory: saturation and non-saturation is a static concept. Intertemporally, the capital stock may very well decline, as an optimal choice : we pile up capital early on, and then, the rate of usage is greater than the rate of further accumulation: we use what we have bought in the past, wearing down the stock.

The right way to model durable goods (and it has been done of course), is to specify a utility function like

$$U = U(C, h(D))$$

where $C$ are non-durable goods and $h(D)$ is the service-flow function related to durables $D$. Sometimes we simply write $C_D$ (consumption of the service flow). The difference is that the stock of durable goods is a state variable, alongside any other state variables the model has.

As a recent example of a theoretical model (not a canonical one), see the paper
Mansoorian, A., & Michelis, L. (2010). Monetary policy in a small open economy with durable goods and differing cash-in-advance constraints. Economics Letters, 107(2), 246-248.

Public Capital also enters sometimes the utility function, to represent the services flow that come from public infrastructure (contrasted to current public expenses). See for example

Chatterjee, S., & Ghosh, S. (2009). Public goods, congestion, and fiscal policy: Do consumption-based instruments matter?


Show that there is no continuous utility function which represents the lexicographic preferences Show that there is no continuous utility function which represents the
lexicographic preferences $\mathscr{L}$ given by $(x_1, x_2) \succeq  (y_1, y_2)$ if and only if $x_1 > y_1$ or $x_1 = y_1$ and $x_2 > y_2$.

Hint:

To ensure the existence of utility function representation, we must have continuous preferences (and this is a sufficient condition). From the Mas-Colell book:

The preference relation $\succeq$ on $X$ is continuous if it is preserved under limits. That is, for any sequence of pairs ${(x^n, y^n)}^\infty_{n=1}$ with $x^n \succeq y^n$ for all $n$, $x = \lim_{n \to \infty} x^n$ and $y = \lim_{n \to \infty} y^n$, we have $x \succeq y$.

We then look at the definition of utility function representation.

The function $U$ represents $\succeq$ on $X$ if $\forall \ x,y \in X, x \succeq y \iff u(x) \geq u(y)$, where $u: X \to \mathbb{R}$.

Though it may be easier just to show that the preferences themselves are not continuous, and thus there is no utility function representation, continuous or not.


Finding Pareto Optimality Consider an exchange economy with two individuals and 2 commodities. The endowments of the commodities are 1 each. Which one of the following are Pareto Optimum.

a. {$\frac{1}{2},\frac{1}{2},(\frac{1}{2}\frac{1}{2})$} b. {$(\frac{1}{4},\frac{1}{4}),(\frac{1}{2}\frac{1}{2})$} c. {$(\frac{3}{4},\frac{3}{4}),(\frac{1}{2},\frac{1}{2})$} d. None of the above.

I have a hunch that it is d. I am assuming that preferences are perfect complements and hence all the options from a to c will give the two individuals lesser utility. Hence d. Is this the right way to go about it. If not, please help?

To be a Pareto optimum, there must not exist another feasible allocation that makes every agent at least as well off and one or more agents strictly better off.

So, let us consider the options here.

Answer B - look at the individual allocations here and consider them relative to the economy's total endowment. Since the allocations given here do not exhaust the economy's total endowment, we could make one of the agents better off by simply giving him some of what has not been allocated. Doing this would not make the other agent worse off. So B cannot be P.O.

Answer C - Consider the allocations here relative to the total endowment. Is such an allocation feasible?

Answer A - Has the total endowment been allocated? If so, is there any way to increase what one agent has without decreasing what the other has?


Okun's law nominal GDP growth Does Okun's law also work for nominal (not real) GDP growth?

Does Okun's law work at all?

It was an empirical observation of the relationship between unemployment and an estimate of the "output gap" (the relative difference between actual GDP and potential GDP)

To the extent that the relative difference between actual GDP and potential GDP may be the same whether calculated using nominal GDP or real GDP, then the relationship should hold either in both cases or in neither. Otherwise the argument becomes one of saying that the output gap is affected by inflation


Why is the cash in circulation on the rise in rich countries? The amount of cash in circulation is on the rise in rich countries (US, EU, etc; except the cashless economy, Sweden). In the digital era, isn't this phenomenon contradictional?

For example, here's the ratio of the value of cash to GDP in the Euro Area:

Cash: Notes and coins in circulation (Currency)

Possible reasons:

Shadow economy is growing.
More cash = more corruption.
Lack of financial literacy.
Feeling of safety. Lack of trust towards technology and banking
system.

What is the main reason why the cash in circulation is on the rise in rich countries?

For starters, I've confirmed your results for the United States using data from federalreserve.gov and alfred.stlouisfed.org:

If we take a look at the breakdown of bills in circulation, we can see that the value of $100 bill has drastically increased relative to the total value of bills in circulation but the others bills have not.

So people are indeed using cash less often for everyday purchases that most likely involve lower denomination bills. In short, people are most likely hoarding more cash in the form of higher denomination bills as a result of recent interest rate trends. According to a blog post by the St.Louis Fed, "the nominal interest rate on short-term bonds has declined essentially to zero, and, in this case, the best form of risk-free liquid asset is no longer the short-term government bonds, but money."

You might ask why people wouldn't just hold more money in electronic currency versus paper cash? If we compare paper cash to MZM (which includes various forms of electronic currency storage), we see that the % of the value in paper cash have actually gone down.

That said, if there was more confidence in technology and banking system, the % in paper cash could decline further. There also seems to be some arguments for a larger underground economy in the US since 2008. I couldn't find any long-term trends on financial literacy, but I also don't see how it would affect people to use paper cash over other forms of credit.


Clustered standard errors (My research question is economics based, but for simplicity, I'm using a non-economics example)

Suppose I'm trying to find out whether average body temperature of a population is equal to 37 degrees Celsius. I take a random sample of people and take their body temperature.

The problem is, some people have taken their body temperature once, but others have taken their temperature multiple times (twice, thrice, or even ten times).

Ordinarily I would regress body temperature on a constant, and do hypothesis testing with $H_0: \beta_0 = 37$. However, I am worried about serial correlation.

Would clustering the standard errors by person be sufficient to correct for this serial correlation? (e.g. using reg bodytemperature, cluster(person) in Stata)

I am not sure this will answer your question, but let's me try with a concrete example using Stata and its 1978 Automobile Data in order to regress car's price on mileage (mpg).

sysuse auto, clear
reg price mpg, robust

This gives a price estimate of -238.9, with a standard error (s.e) of 57.5. Then, if I run the same regression after duplicating the observations three times.

expand 3
reg price mpg, robust

I get as expected a much lower s.e. of 32.9. Finally, clustering the s.e. by make (a Car Id)

reg price mpg, cluster(make)

gives a s.e. of 57.2 and makes the trick.

However, if you expand twice some observations and thrice others (as in your example). Then, you will get a larger s.e but also a different estimate. But, again, clustering by make reduces the s.e. Here is the code:

sysuse auto, clear
expand 3 if price>4000 & price<=6000
expand 2 if price>6000
reg price mpg, robust
reg price mpg, cluster(make)

Note that the price and mpg variables have been expanded without any change for each car. In your example, if the ones who have taken their temperature multiple times have each time a different temperature, then you may consider introduction an individual fixed effect.


Is there any academic paper documenting the importance of the Operating Cycle? Content from a website that :

The Operating Cycle offers an insight into a company’s operating
efficiency. A shorter cycle is preferred and indicates a more
efficient and successful business. A shorter cycle indicates that a
company is able to recover its inventory investment quickly and
possesses enough cash to meet obligations.

I am wondering if there is any academic paper that documented the same thing for citation purposes and I am also looking for academic papers talking about the operating cycle in a quite comprehensive context.

I typed "Operating Cycle" into Google Scholar, and got some hits like
The Operating Cycle: Risk, Return and Opportunities by John C. Groth
Abstract:

Highlights the operating cycle, its importance, and reviews basic relationships related to the cycle. In particular, it focuses on capital “flow through”, invested capital, capital at risk, and economic returns generated relative to capital employed. Reveals an amplification effect that results from improvements in the management of the cycle, that benefit traceable to a reduction in operating risk allowing incremental benefits from financial leverage. Suggests specific actions to take with respect to the cycle that will improve the value of your firm. Shows that small improvements in operating factors within the cycle yield amplified benefits to the firm. The discussion ignores taxes except in instances when tax effects are important. This does not detract from the discourse or conclusions. Reveals that increases in firm value that result from improved management of the operating cycle stem from several sources: greater levels of economic returns from operations; a reduction in operating risk; less capital invested and at lower risk; lower cost of capital; and increased tax benefit.


Equilibrium with substitute goods I am attempting to solve the following problem
The demand functions for two substitute goods, the production cost of which equals $c_1$ and $c_2$,
are $q_1 = a_1 + b_{11}p_1 + b_{12}p_2$ and $q_2 = a_2 + b_{21}p_1 + b_{22}p_2$.
How can I find equilibrium under simultaneous and sequential interaction in a price oligopoly
(the values of the coefficients $a_1,a_2,b_{11} ...$ can be selected by yourself.
Although, if I'm not mistaken, the sign matter)
I need help in understanding the difference between simultanious and sequential interaction solution

Let's start by writing down the profit functions:
$$
\pi_1 = p_1 q_1 - c_1 q_1 = (p_1 - c_1) q_1 = (p_1 - c_1)(a_1 + b_{11} p_1+b_{12} p_2)
$$
and similarlily:
$$
\pi_2 = (p_2 - c_2)(a_2 + b_{21} p_1 +b_{22} p_2)
$$
In a simultaneous equilibrium, both firms simultaneously maximize their profits taking the strategies of the players as given.
Doing this will give you a best response of player 1 that will be a function of $p_2$: $p_1 = p_1^\ast(p_2)$. Similarly, the best response of player 2 will be a function of $p_1$: $p_2 = p_2^\ast(p_1)$.
In a Nash equilibrium, you are looking for a solution for both equations simultaneously:
$$
p_1 = p_1^\ast(p_2),\\
p_2 = p_2^\ast(p_1).
$$
In a sequential equilibrium on the other hand, you assume that one firm, say 1, chooses $p_1$ first and next firm 2 decides in $q_2$, after being informed about the value of $q_1$ chosen by firm 1.  Firm 1, however, is smart enough, such that it can predict the optimal action that firm 2 is going to take in stage 2.
As such, we solve the game by backward induction, first solving for firm 2, giving $p_2 = p_2^\ast(p_1)$ and then we substitute this into the profit function of firm 1.
$$
\pi_1 = (p_1 - c_1)(a_1 + b_{11} p_1+b_{12} p_2^\ast(p_1))
$$
This substitution conforms to the fact that player 1 knows that by choosing $p_1$ it will influence the price of firm 2. So firm 1 takes the future behaviour of firm 2 into account when choosing its optimal level of $q_1$.
Maximizing $\pi_1$ with respect to $p_1$ will give an optimal value $p_1^\ast$ (which will no longer be a function of $p_2$).
Then, to compute the equilibrium, you substitute this value into the best response for firm 2:
$$
p_2 = p_2^\ast(p_1^\ast).
$$


Why hasn't massive derivatives exposures at banks already led to disaster? I recently heard that Deutsche Bank had
$72trillion of "derivatives exposure", which
is many times greater then the entire German GDP.

Now as I understand it, derivatives are essentially
just bets on the movement of assorted prices...
so I am assuming that "derivatives exposure" means
the total amount you would have to pay out if
you lost every single one of your bets. The
likelyhood of this scenario may of course be
vanishingly small, but presumably with
$72trillion of exposure, you wouldn't need
much of a losing streak in order to leave
you bankrupt.

So some people are saying - "ooh this looks
scary, it could lead to disaster"... but my
reaction is "ooh this is scary... but why on
earth hasn't it led to disaster already?".

Now I know there were multiple
disasters around 2007/8 already and derivatives
may have played a significant role in that... but
I'm referring to, lets say, the past five years.
How could Deutsche Bank have gotten to
$72trillion of exposure without blowing up
again? What kind of bets have they been doing
such that they haven't had enormous losses?

EDIT: FYI this question has a followup here.

While gross notional exposures are huge, net exposures at the banks are much smaller, on the order of 0.1 percent of gross exposures. Since most financial risk (but perhaps not operational risk) is proportional to net exposures this is a more sensible measure of total derivative risk at the banks. Since net exposures at the 6 banks with the largest derivative exposures circa 2014 were on the order of \$300 billion while their total assets were more than \$10 trillion, we may not have seen a disaster because the actual risk is appropriate to the scale of their broader operations.

Here is an example of how this works. At time 0 a bank does derivative trade with notional of 100 with A and collects the offer (or ask) price. That is, the bank sells the derivative to someone who wants to buy it. At time 1 a bank does derivative trade with B with notional of 100 and collects the bid price. That is, they buy the derivative from someone who wants to sell it. Total (gross) derivative exposure is 200, two derivative contracts each with an exposure of 100. However, net exposure is zero, and the bank keeps the spread as profit for its trouble. There is likely some remaining risk in the form of operations and credit risk, but this is what the spread and initial and variation margin are for.


How to approach such question of two periods and asymmetric information game? There are two players 1 and 2, playing a two-period public good contribution
game. The benefits from the public good per-period to each player is $b_1$ and $b_2$
respectively, which are common knowledge. For the provision of the public good
only one player needs to contribute. Once a player contributes and the good is
provided then both can derive the benefits. The public good lasts for only one
period and contributions are required in each period to renew it.
The per-period cost of contribution for player 1 is private information which can
take two values, $\underline c$ (low type with probability $p$) and $\overline c$ (high type with probability
$1 − p$) for which following condition holds $\underline c < b_1 < \overline c$. However, the cost of
contribution for player 2 takes the value $c_2$ which is common knowledge and is
lower than its benefit i.e. $c_2 < b_2$.
The game is played as per the following sequence:
First period: Only player 1 moves. He can choose to ‘contribute’($C$) or ‘Not to
Contribute’($N$) towards the first period contribution of public good. If player 1
chooses $N$ then both gets 0 otherwise if player 1 chooses $C$ then both players get
their benefits but only player 1 pays the cost. Note that the player 2 observes the
player 1’s action of either $C$ or $N$ but not its type (i.e. the private information
regarding costs).

Second period: The game is played sequentially where player 2 moves first and
chooses $C$ or $N$. Player 1 observes it and decides on $C$ or $N$.
If at least one of them contributes then both players get their benefits bi and those who contribute
pay their respective costs. If no one contributes each gets 0.
Players discount their payoffs by $\delta$, which is common to both. In answering the
questions below, you need to write strategies and beliefs precisely.

(a) Find an equilibrium where different types of player 1 choose different actions
in first period (separating equilibrium).

(b) Find an equilibrium where different types player 1 choose the same action in
first period (pooling equilibrium).

(c) Find a hybrid equilibrium where low type of player 1 in first period chooses
$C$ with probability $\alpha$ and $N$ with probability $(1 − \alpha)$, and player 2 in second
period randomizes between $C$ with probability $\beta$ and $N$ with probability $(1 − \beta)$.

I have attached my workings.

You want to solve these types of games using the logic of backward induction and when beliefs become necessary, assume a pooling or separating equilibrium.

For example, start with the final nodes. It is clear that player 1 will choose C if no one has contributed before, and he is of the low type. He will choose N if someone has contributed before or if he is of the high type.

Knowing this, when player 2 makes her decision it is also easy to see that she will never contribute if player one contributed in the first period. If player 1 did not contribute in the first period, payer 2's decision depends on whether she thinks that player 1 is of the high type or of the low type. She would want to contribute if the belief that player 1 is of the high type is high enough otherwise she would prefer to choose N.

This is were assuming a separating or pooling equilibrium comes in handy. For a separating equilibrium, player 2 will learn player 1's type by the moment she has to make a decision, so she would choose C if player 1 is of the high type and choose N if it is of the low type (this is because she anticipates perfectly what player 1 will do in the second period since she knows his type).

Giving player 2's strategy, player one in the first period will choose to not contribute if he is of the high type (it is not profitable for him and he anticipates that 2 will realize he is of the high type and pay the public good), and player 1 will choose to contribute if he is of the low type (since he anticipates that player 2 will know he is of the low type and not contribute, so he would end up paying for the public good in the second period, but for him, it is better to get $b_1-\underline{c}$ rather than $\delta(b_1-\underline{c})$).

We conclude that this is indeed an equilibrium because each type of player one ends up choosing a different action in the first period (separating) and every player is best responding to the other player's strategy, there is no profitable deviation. In this case, player 2 assigns a probability of 1 to player one being
of the high type if he does not contribute in the first period and 0 if he does.

Let's now assume a pooling equilibrium. In this case when player 2 makes a decision she doesn't know what's player 1 type. She only knows that with probability $p$ he is of the low type and $1-p$ he is of the high type. Regardless of this uncertainty, if player one already paid for the public good, player 2's best response is N, if player one did not pay for the public good, player 2 can pay for it and get $b_2-c_2$ or not pay for it and get $b_2$ with probability $p$ or zero with probability $1-p$. Therefore, she chooses C if and only if $b_2-c_2\geq pb_2$. That is if $b_2\geq \frac{c_2}{1-p}$ (i.e. if she values the public good enough).

Suppose the last inequality does not hold, in that case, player 2 does not pay for the public good. Given this strategy player one of the low types would prefer to choose C while player 1 of thee high type would prefer to choose N. This contradicts the assumption of a pooling equilibrium. In contrast, if the inequality above holds, a pooling equilibrium exists only if $b_1-\underline{c}\leq \delta b_1$. That is if $b_1\leq\frac{\underline{c}}{1-\delta}$ (if he doesn't value the public good to much so as to not be willing to wait).

I gave less detail for the pooling equilibrium, but hopefully, you can follow were the inequality comes from.

Lastly, for the last type of equilibrium you just have to realize that for player 2 if player 1 has not contributed to the public good yet if could be because he is of the high type (mass $=(1-p)$) or because he is of the low type and did not contribute (mass $=p(1-\alpha)$). Therefore, it is of the high type with probability $\frac{1-p}{1-\alpha p}$ and of the low type with complementary probability. So for player two to want to randomize she should bee indifferent between contributing or not. Therefore $b_2-c_2=\frac{p(1-\alpha)}{1-\alpha p}$. This equation gives you the equilibrium value of alpha. Similarly, player 1 of the low type should be indifferent between paying in the first period or with probability $\beta$ get the good for free, and probability $1-\beta$ pay for the good in the second period. Therefore $b_1-\underline{c}=\beta c_1+(1-\beta)\delta(b_1-\underline{c})$. Which will give you the equilibrium value of $\beta$.


How can we get negative **real** interest rate? According to Fisher's equation,

Real interest rate=Nominal interest rate - expected inflation rate

So, how can we get negative real interest rate? I'm in doubts. On one hand, purely from algebraic point of view it seems that expected inflation rate must be higher than nominal interest rate. BUT, I know that expectations of such high inflation would cause the nominal interest rate to adjust accordingly, to be higher than expected inflation rate. So such situation would appear to be impossible when inflation rate is expected.

On the other hand, replacing "expected" with "actual" turns the tables. If high inflation rate caught us by suprise it's totally possible for nominal interest rate to be lower than inflation. BUT Fisher's equation uses only expected inflation as its argument, not actual inflation. We don't have any right to supply Fisher's equation with unexpected actual inflation.

There is a market for inflation-linked bonds. The quoted yield on the bonds is the equivalent of a real yield, with the inflation rate corresponding to expected inflation.

The real yields On US inflation-linked bonds are currently negative. Link to FRED data.

There is no mystery to this.

Nominal yields are effectively pinned to the expected path of the nominal policy rate.
Inflation rates follow developments in the economy.
There is no law of nature that says that the nominal yield has to be above the rate of inflation.


Are there Utility Monsters in Economics? Economics, especially in the modern school is broadly influenced by the utilitarian concept of utility. More so since the labor theory of value has been broadly replaced by the theory of marginal utility.
Additionally, perverse incentives are commonly understood and well documented, and seem to be small scale imitations of Nozick's classical "utility monster".
Are there any observations of larger "utility monsters" (wherein consumption by an individual increases aggregate utility for a group while individual utility is reduced for all but the "monster" of the group)?
Does a theory of declining marginal utility necessarily prevent such a thing if utility is said to remain non-negative? (i.e. simply having the ability to ignore excess goods). Obviously it prevents it if utility can become negative, unless the number of units of the good in question are fixed at less than the number required to reach negative total utility.
For a simplistic toy example, imagine a closed system consisting of myself, my five-year-old daughter, and two cars (full-sized). Allocating a car to her produces little marginal utility since she can't drive (or even reach the pedals), though presumably it's a non-zero amount. Consequently taking a car from her and giving it to me produces a net gain for the "economy", despite producing a presumable reduction in utility for her (assuming I'm not going to drive her around because I'm a terrible father in this example). Further, even assuming if she owned both cars, taking them both from her and giving them to me would produce an aggregate gain, as I could exploit the one car better than she could the two, and the second (or even third, etc), would not be an inconvenience, and in fact still offer me greater marginal utility as backup vehicles.
The question is, do such scenarios arise in practical economic settings where one group or individual is simply so much better able to make use of a good than another as to justify (in the sense of aggregate utility) taking it from the less able?
I understand this could be a contentious question, but I'm asking not from a moral standpoint but strict aggregate utility.
Updates
The constraints regarding the system I'm modeling are (and looking for a general solution to):

Marginal Utility for every unit of a good must be positive (or zero), finite, and declining (though never to below zero).
Finite Goods:

The available quantities of all goods must be finite, though they can be arbitrarily large.
There can be an arbitrarily large, though finite number of other goods in the system.

Aggregate Utility must increase for all, while individual utility must decrease for all except one (the "monster") when a good of a certain class (let's say "cars") is transferred from any member of the group to the "monster".
Condition 3 should be met for all transfers of "cars" from "innocents" (people not the monster) to the "monster", to the exhaustion of "cars" from the system.

Again, this is not a question about "Can mutually beneficial trade exist under any circumstances?" We've known that since before Ricardo. This is a question about the requirements for Aggregate Utility increase at the expense of most individuals when talking abut individual preference.
Inspiration for the question:

There is a type of protection called a liability rule, where I, $A$, can take something from $B$, if I pay the damages $c$ which are court-ordered preemptively. Copyright law is all about liability rules. If the damages are correlated with $B$'s valuation appropriately, then efficiency holds. You are interested in the opposite case. If IP law doesn't get it right, this would be an example matching your hypothetical as I understand it. And some might say this is justified. A company might want to keep some research under wraps to prevent competitors from also using it and making it even more valuable to society through investment. So the expiration of a patent might fit this scenario in a roundabout way too if we start the model where the company already owns the patent and a court is deciding when to let it expire.

Reference: Exchange Efficiency With Weak Property Rights.


What happen to Euro if Greece defaults I have some money in Euros but living in USA. Today they are going to decide if the Greece will stay in Euro-zone.

I was wondering what will happen to Euro if Greece leave the EU. Or what is expected to happen?

I'm planning to exchange the Euros in August. Is it a good idea or should I do it right now or just keep the Euros?

Depends on WHY you have the Euros.

If you are saving up with a BMW or a holiday in France, it is very different to you holding them just hoping the Euros will go up.

I expect that if Greece leaves OR if Greece remains after a REAL agreement is made and KEPT TO, then the Euro will not be effected much.   But if Greece remains, but nothing changes in Greece, then the Euro will be dragged down by the next set of counties that think they can getaway with it.


Determine the homogeneity of a demand function If a demand function $X(P_X, P_y, I)$ depends only on prices and income. Is this function a homogeneous function?

All (marshallian) demand functions are homogenous of degree zero in prices and income. This is a well known result.

That means that $x(\lambda p, \lambda I) = x(p,I)$, where $p$ is a vector of prices (i.e. x could be a function of any number of prices, including $P_x$ and $P_y$, which were given in your example).

So if we multiply all prices and income by the same amount, demand doesn't change. This is very intuitive. Imagine the government would just add a zero to all prices and to your paycheck. There is no reason for you to change your demand as nothing really got cheaper nor did your income increase in real terms.

To see this formally:

Proof:

$x(p,I) = argmax \; U(x)$ s.t. $px \leq I$.

$x( \lambda p, \lambda I) = argmax \; U(x)$ s.t. $ \lambda px \leq \lambda I \Leftrightarrow $

$x( \lambda p, \lambda I) =  argmax \; U(x)$ s.t. $px \leq I = x(p,I)$
$Which \; is \; the \; definition \; of \; homogeneity \; of \; degree \; zero. QED. $

The last step follows because we cancel $\lambda$ in the budget constraint on both sides.


Does the government have a role to play in certifying people's abilities for the labor market? The nature of information often makes it look like a public good. Is this the case for certification of peoples abilities? Is there a role the government could play in certifying people's abilities? Maybe do people thing that that's one of the roles that public universities play? Spence I guess is the typical reference that suggests that people go to school for certification/signaling of abilities rather than to acquire skills. Maybe that's a reason that there are many public universities?

Information is certainly not a public good. Job applicants know their skills with certainty, while employers do not know the skills of applicants. The application process is designed to increase the employers information set so that they can select the best candidate. However, applicants have an incentive to lie, so this process may not always be effective.

Certification, on the other hand, is a credible quality signal that cannot be (easily) faked. This massively reduces the employer's search and opportunity costs. This is not just theory: many job applications simply require a university degree, and virtually all require at least some type of certification.

Whether the government has to play a role in the certification process is another question. An ideological rather than an economical one, if you ask me. Regardless of the answer, it should be noted that many advanced certification standards are upheld by non-governmental bodies. Even if public universities are considered part of government, they are usually accredited by non-governmental organisations. And so are most driving schools, cooking schools, professional degrees, etc.

The question seems to have changed a lot since this answer.


Existence of competitive equilibrium between max utility function and min utility function u1(x1,y1)=max(x1,y1)
ω1=(0.2,0.2);
u2(x2,y2)=min(x2,y2)
ω2=(0.8,0.8)
The utility functions for two individuals and their endowments are given above for a two person two good economy. My question is that is there any competitive vector of prices that gives rise to competitive equilibrium in the economy?
I used the Edgeworth box analysis and determined that the indifference curves for both the individuals will coincide completely and will be L shaped for individual 2 and an inverted L shape for individual 1. However, individual 1 will always look for a boundary optimum while the optimum for individual 2 will be at the kink of the L shaped indifference curve.
I assumed good 2 to be the numeraire good with price = 1, and assumed the price of good 1 is simply p. So income of individual 1 = 0.2p+0.2 and income of individual 2 = 0.8p+0.8.
I also inspected three cases
CASE 1
When p>1.
Demand for good 1 by individual 1 will be zero, because good 2 is cheaper. Demand for good 1 by individual 2 = (0.8p+0.8)/(1+p).
I equated demand and supply, and found that the price was coming out to be negative, which is an impossibility so I ruled out this case.
CASE 2
When p<1. Demand for good 1 by individual 1 = (0.2p+0.2)/p and by individual 2 = (0.8p+0.8)/(1+p).
I equated demand and supply, and found that the price was coming out to be negative, which is an impossibility so I ruled out this case too.
CASE 3
When p=1. Individual 1 will either demand zero units or all 0.4 units that he can afford at that price. Individual 2's demand, meanwhile, will be 0.8 units of good 1. I got stuck here. It seems apparently that a competitive equilibrium does not exist. Am I wrong somewhere?

Indeed, there is no competitive eq. To see this case-by-case analysis is the best way forward.

If either price is 0, consumer 1 will demand an infinite amount, markets will not clear. If prices are both positive, consumer 1 will only ever demand 1 of the 2 goods. But, consumer 2 demands an equal amount of each good is such any such case. No allocation is compatible with both these demands.

The failure lies in the fact that the demand functions (in particular of consumer 1) are not continuous. This happens because 1 has a convex utility function.


Is it sufficient to conclude by looking the following weekly demand schedule that the good is Perfectly Elastic? The following is the demand schedule for cement over a period of one week:-

NOTE: I have written the Price and Quantity demanded in tuples of the following form (Price, Quantity). So in the first case, the price is Rs 275 and the quantity demanded is 80 bags of cement.

Monday-(275,80)

Tuesday-(275,30)

Wednesday-(275,60)

Thursday-(275,70)

Friday-(275,50)

Saturday-(275,80)

Sunday-(275,100)

From the above data, you can see that the price is invariant over one week and that all consumers pay this price. However, after further investigation, I found that the price changes after a period of 15 days. Using this limited sample can one conclude that the demand for cement is perfectly elastic in the short run?

EDIT1: After @Ubiquitos' advice I came up with the following idea, which is partly described in a comment. Nevertheless here is the full argument:

Suppose that the equation of the Demand curve is given by the following equation$$q=\beta_0+\beta_1P+\epsilon_1$$ and the equation for the supply curve is given by$$q=\gamma_0+\gamma_1P+\epsilon_2$$. Notice that there is no other exogenous variable in any of the equations except $P$. I know that this quite a crude assumption as we know that there are non-price determinants such as taste and preferences that affect the quantity demeanded.Thus, it is possible that the error term,  $\epsilon_1$ and $\epsilon_2$ are related to $P$ and thereby create a Selection Bias. Therefore, the parameters in both the equations cannot be determined. But I am still not sure how does this reasoning directly answer my initial question.

PS: If there are loops in my arguments, then please do suggest some rectifications as I am a beginner in econometrics...

No, you do not have sufficient information to conclude that the demand is perfectly elastic.

The following figures show two ways that demand curves that are not perfectly elastics could have generated the first two data points in your series:

It should be easy to see how to add other demand curves to generate the rest of the data points.

This is actually a common and more general problem: price and quantity are jointly determined by the interaction of supply and demand. Given two data points, it is impossible to determine whether they were caused by a shift in supply or demand or both. There are two solutions to this dilemma:

estimate a simulatenous equation model that accounts for both supply and demand. You can read about simultaneous equation models in a good econometrics textbook or, for example, in Dan McFadden's lecture notes.
work in a context where you know either the supply or the demand curve are fixed. If you know the supply curve didn't move then any change in price or quantity must have come from a shift in demand and you know that all of your data points lie on (and characterise) the supply curve. The converse is true if you that the demand curve did not move.


Advice on method for analyzing the effects of increase in minimum wage As a hobbyist and generally curious person with a lot of free time at home, I was curious what would be a good method to analyze the effect of an increase in the minimum wage of a country if you only have access to public data?
What initially came to my mind would be to create a simple regression with three variables time, labor cost per employee and total employment numbers where

time would consists of maybe 3 years data prior and after the increase of the minimum wage
the labor cost per employee would be our predictable variable, which we will use to understand better the changes in employment numbers

However, I am having seconds thought about how accurate the output of the regression would be as there are many other factors that can influence the employment numbers. This, I decided to ask if any of you might have any idea of what other variables can be included or simply suggesting a different mathematical approach for this? Thank you in advance.

The output from the model you mention would be not accurate at all for several reasons, including amongst other reasosns:

Your post you mention you want to use labor costs as predictable variable - there is no such thing as predictable variable in econometrics. If you by that mean predicted variable (i.e. dependent variable) it would be wrong to have labor costs as dependent variable. Even if you would want to include it as a predictor looking only at labor costs is not that useful in this case since firms can shift increases in labor costs on their customers instead of reducing employment, and indeed research shows that most of the labor cost increases by minimum wages are just shifted onto consumers (e.g. see Harasztosi & Lindner, 2019). Furthermore, labor costs can increase for plethora of other reasons completely unrelated to minimum wage.

Unless you live in a country with public access to firm level data on employment having 1 country and 6 years is not enough. As a rule of thumb you need 30 observations per independent regressor. Given that data for most controls you need will be avaiable at best at monthly frequency, but most likely at quarterly/yearly frequency you will simply not have enough data points for running parametric model (such as regression). You can expand your dataset by including multiple other countries, in such case having 3 years before and 3 years after might be enough.

Controlling only for 2 other variables beside for dependent variable is not enough and you will likely have model suffering from omitted variable bias.

If you want to analyze a particular increase in minimum wage quite common method in the literature is differences in differences (DiD). There are also more complex techniques, but simple regression would not cut it here (even if it is just for fun, if you care at all about quality of results) and  DiD is not that much more complex.
Your regression specification would look like:
$$y_{it}= \delta_i + \lambda_t + \rho D_{it} + X_{it}'\beta+ \epsilon_{it}$$
where $y_{it}$ will be your dependent variable, $\delta_i$ country fixed effects, $\lambda_t$ time fixed effects, $D_{it}$ is a dummy that tells you whether country $i$ did implement increase in minimum wage at time $t$ or not, and $\rho$ will tell you the effect of this policy. Finally,  $X_{it}'$ is a vector of control variables. You want to control for anything else that you think  might affect the employment in the country.
This is slightly more complex because you will need at least one extra control country that did not increased its minimum wage at the same time (although this should not be that hard to find). In addition, you might want to add more countries into the data set if for no other reason then just to have more data.
Now what you actually want as your dependent (i.e. predicted) variable is not labor costs but unemployment if that is what you are interested in. The reason for this is that research regularly shows that minimum wage increases lead to increases in consumer prices which means that most of the increase in labor costs is shifted on the shoulder of consumers  (see Harasztosi & Lindner, 2019). Hence, even if your model would find large effect on labor cost it might have zero to none effect on employment in the industry. So if employment is what you are after you need employment as dependent variable.
The above would still not be likely good enough, on its own, to be publishable (there are more issues that would need to be addressed) but it would at least count as some first preliminary model from which you can draw some tentative conclusions. You might also want to have a look at some econometrics handbook before doing this to learn more about how to estimate these sort of models. For the model above I think Mostly Harmless Econometrics  by Angrist and Pischke, chapter 5 on DiD would be sufficient reading (or have a look at some online tutorials).


Can indifference curves slope up and to the right when both goods are inferior goods? Just a general question related to Micro. I always thought they sloped down to the right. Thanks!

The negativity of slope of the indifference curve depends on the monotonicity of utility function and non-satiation, not on whether the goods are inferior or normal goods. Inferior goods are goods which are consumed less when income increases but that is not the same as saying that the utility is not monotonically increasing in both goods or that non-satiation is violated.
However, the above being said there are cases where indifference curve can be upward sloping. Those are cases when some good creates disutility (so the utility function is no longer monotonically increasing in all arguments). For example, in case where we have utility of the form:
$$U(x,y) = \sqrt{x}  - y $$
Where $x$ can be considered some standard consumption good and $y$ is treated as a 'bad good' (e.g. pollution - but note this is not the same as being an inferior good). In this case we would get an indifference curve that would have positive slope and it would be 'slope up and to the right'. This is because in such case person would be only willing to increase the consumption of dirty good if at the same time the person is compensated by higher consumption of the good $x$.
Also more generally, indifference curves can have various shapes. For example, if we assume that satiation is possible indifference curves become circles. However, if there is tradeoff between consuming $x$ and $y$ (when they both monotonically increase utility) and when people are non-satiated (more is always better) the indifference curves will be downward sloping, since indifference curve represents a collection of all points where the utility from consuming different bundles of $x,y$ is constant. If person likes to consume both goods then a persons utility when you reduce $x$ will remain same only when you give person more $y$. Only when utility stays constant when you increase consumption of both goods will indifference curve have positive slope, and that will generally happen when consuming more of one good creates disutility.


Prove that in presence of many goods, the law of DMRS implies that at least one good must be a net substitute for any other good I've been reading a book where the author claims that "if there are two goods they are always net substitutes. Along an indifference curve an increase in price of good 2 leads to less of good 2 and more of good 1 being consumed when utility is maximized. When there are more than two goods, the law of diminishing marginal rate of substitution implies that at least one good must be a net substitute for any other good."

The first part can be proved easily using graphs, it's the second that I couldn't prove mathematically.

Source of the quotation has been attached here, Pg-104.

I don't know what is the definition of the "law of DMRS", but I think what the author meant is summarized in these lines of MWG:

Proposition 3.G.2: suppose that $u(\cdot)$ is a continuous utility function representing a locally nonsatiated and strictly convex preference relation $\succsim$ defined on $\mathbb{R}^L_+$. Suppose also that $h(\cdot, u)$ [the hicksian demand function] is continuously differentiable at $(p, u)$, and denote its $L\times L$ derivative matrix [with respect to each $p$] by $D_p h(p, u)$. Then

$D_p h(p, u)$ is a negative semidefinite matrix.

$D_p h(p, u) p = 0$

Well, 1 implies that the elements of the main diagonal of the matrix are all non positive, i.e. $\frac{\partial h_l (p, u)}{\partial p_l} \leq 0$ for each $l$.
We say that two goods are substitutes if $\frac{\partial h_l (p, u)}{\partial p_k} \geq 0$ (a positive variation in the price of $k$ implies an increase in the compensated demand of $l$).
Part 2 of the proposition says that $D_p h(p, u) p = 0$. But as $\frac{\partial h_l (p, u)}{\partial p_l} \leq 0$, for every $l$ we must have a good $m$ such that $\frac{\partial h_l (p, u)}{\partial p_m} \geq 0$, which means exactly that every good has a substitute.


What is the difference between the cash rate and interest rate? What is the difference between the cash rate and interest rate? I (in Australia) googled cash rate and according to wikipedia it is the "central bank charges on overnight loans between commercial banks."
If anyone can explain what  "overnight loans" are and provide a simplification of this process would be really appreciated. Based on some superficial readings, the cash rate influence markets' interest rate? It would also be nice if someone can provide a definition for the respective terms. Many thanks.

In Australia, the cash rate is a volume-weighted average interest rate of unsecured overnight loans among banks which are members of the Reserve Bank Information and Transfer System (RITS). The cash rate is also known as AONIA (the Australia Overnight Index Average).
Overnight loans are just like they sound: Perhaps Bank A needs to make payments the next day but has cash coming in to cover those payments in two days. So Bank A borrows money overnight to make the payments and bridge the gap to when money covering the payments arrives. Banks do this all the time for one another since perfectly matching up the timing of cash inflows and outflows is difficult.
The Reserve Bank announces target rates for the overnight rate and then conducts "open market operations" (offering overnight loans, for example) to hold the market level of interest on overnight loans to be close to their announced target.


Why does the profit reaches its maximum value at the equilibrium point? When we talk about marginal cost and marginal benefit/cost, why does the equilibrium point is the most convenient for the production of a product. If the marginal cost and the marginal benefit/revenue are the same Wouldn't the cost of producing a product would be the same as the revenue you obtain from selling it? Wouldn't you be earring nothing when you reach the equilibrium point?

Extra question; Are marginal benefit and marginal revenue the same concept?

The point where MB = MC is the largest Net Benefit available for a given product.  Therefore, any additional benefit has a lower level of benefit than at equilibrium, and the costs increase at a higher rate than at equilibrium.  In the context of supply and demand, this is where the two lines cross.  But if you think about it in terms of diminishing marginal benefit, and increasing marginal costs then you can see why it is beneficial to product where the largest net benefit occurs.

The following graph is from Markets and the Environment by Keohane and Olmstead and deals with abatement costs, but it is the one graph I think about when someone asks this sort of question because it provides a good example.

As you can see from the graph, the largest net benefit is the furthest distance between the benefit and cost curves.  If you were to take the derivative of each of these functions, you would get linear supply and demand lines, where the largest net benefit is the cross section of the lines (as you can see in the graph below).


Optimality of Zero Capital Taxation The Chamley-Judd result of zero optimal capital taxation says that 0 capital taxation are required in order to maximize welfare at the steady state.

The result is 30 years old. Still assuming that we only care about the steady state, what's the literature's take on that? How esoteric is it? Or in other words, are there simple extensions of the model that completely overcome the result?

There is quite a bit of work being done in that area. One very recent example is Straub and Werning's working paper "Positive Long Run Capital Taxation: Chamley-Juff Revisited."
The point seems to be that we need to consider the rate of convergence to the steady state.

Also, there is other literature that gives some competing results (e.g., "the new dynamic public finance" literature). For a more complete summary of mainstream objections, see Diamond and Saez, "The Case for a Progressive Tax: From Basic Research to Policy Recommendations," (JEP, 2011). They devote a whole section to why they think the Chamley-Judd result is not policy relevant.


Where do the rich and poor live in a city? (Calculus) I am reading 'Cities, Agglomeration and Spatial Equilibrium' by Ed Glaeser.

People live in a monocentric city, where consumers of heterogeneous income $y$ work at the centre of the city. They buy $H(y)$ housing for a price $p(d)$ at distance $d$ from the centre, incurring transport costs $t(y)d$ as they commute to work.

Consumers have a utility function:

$U(C,H)=v(y - t(y)d - p(d)H(y),H(y))$

The budget constraint is:

$C = y - t(y)d - p(d)H(y)$ where C is consumption net of transport and housing.

The tangency condition implies:

$\frac{U_1}{U_2} = p(d)$

where the subscript 1 denotes partial differentiation w.r.t. the first argument etc.

By the spatial equilibrium assumption, $\frac{dU}{dd}=0$: there are no rents to be gained by changing location.

$\frac{dU}{dd} = U_1(-t(y)-p'(d)H(y))=0$

$\therefore p'(d)=\frac{-t(y)}{H(y)}$: the price of housing declines with distance $d$.

If the income elasticity of housing is greater than that of transport (i.e. $H(y)$ increases in $y$ more than $t(y)$ does), the rich (higher $y$) will live in the suburbs. Mathematically, the denominator gets larger than the numerator and the price gradient is less steep. The willingness to pay declines less with distance for the rich.

The book then defines the income associated with each distance $y(d)$ and differentiates again to find the 2nd order condition, $p''(d)>0$.

The book states that this is:

$p''(d)=\frac{t(y)H'(y)-H(y)t'(y)}{y'(d)}>0$

But I believe this is incorrect an should be:

$p''(d)=\frac{(t(y)H'(y)-H(y)t'(y))y'(d)}{H^2(y)}>0$

Am I correct?

Also, how can you ignore the fact that $y=y(d)$ when calculating the 1st order condition then introduce it when you differentiate to find the 2nd order condition?

Should you not state $U(y(d)-t(y(d))d-p(d)H(y(d)),H(y(d)))$ and differentiate twice?

1. The first question is based on a misreading of the text.
First of all it is quite correct that under the model assumptions stated:
$$(A) \ \ p''(d) = \frac{t(y)H'(y) - t'(y)H(y)}{H(y)^2} y'(d),$$
however there is no problem because the book does not state that
$$(B)\ \ p''(d) = \frac{t(y)H'(y) - t'(y)H(y)}{y'(d)}$$
the book instead states that the second order condition
$$ p''(d) > 0 $$ implies $$(C)\ \ \  \frac{t(y)H'(y) - t'(y)H(y)}{y'(d)} > 0$$
which follows from (A) - the true experssion you have derived for $p''(d)$ - by multiplication of $(H(y))^2$ and division of $(y'(d))^2$.
Nevertheless, I suspect it is a typo even though it is inconsequential.
Obviously, given (C) or [(A) and the second order condition $p''(d)>0$] it follows that $y'(d)>0$ iff
$$t(y)H'(y) - t'(y)H(y) > 0,$$
which again is equivalent to $$\frac{y}{H(y)} H'(y) > \frac{y}{t(y)} t'(y)$$
hence the high income people live in the suburbs ( $y'(d)>0$ income increases in distance from city center) iff and only if the income elasticity of housing is larger than the income elasticity of transport costs $t(y)$.

The second question: How can income be a function of distance $y=y(d)$ when we differentiate the second order condition but not when we consider the first order condition?

The idea is as usual that residents have some income $y$ exogenously given. They cannot decide themselves what income the want nor is their income a product of their location choice. When they choose an optimal location $d^\star$ they choose in such a manner that the first order condition $p'(d) = - t(y)/H(y)$ must hold. However, individuals of different income levels will choose different locations and therefore in equilibrium income will be a function of location $y = y(d)$. Therefore when you want to consider what things are like in equilibrium you can use that income $y$ is a function of $d$.
Glaeser does not proove the existence of such an equilibrium but this type of equilibria with perfect income sorting is known in the literature and the book is a textbook.
The derivation of the first order condition in this simplified model where housing demand is assumed exogenously given as a function of income goes along these lines:
The residents have utility function $U(c,H)$ and income $y - t(y)d$ net transport. They maximize with respect to $c$ so conditonal on $d$ the value function is $U(y - t(y)d - p(d)H(y),H(y))$. In spatial eq. if people with the income $y$ is in the city then they choose some $d^\star$ maximizing the conditional indirect utility function $U(y - t(y)d - p(d)H(y),H(y))$ with respect to $d$ giving the utility $U(y - t(y)d^\star - p(d^\star)H(y),H(y)) = u^\star(y)$. These individuals would only ever consider other locations if they gave the same level of utility (or higher but in that case $u^\star(w)$ would not be maximum). This allows the us to undertake the thought experiment: How would prices have to change as a function of location if other locations gives rise to the same level of utility? This thought experiment is carried out by imposing the condition that $U(y - t(y)d - pH(y),H(y)) = u^\star(y)$ at all locations and solving for the price (giving what is called the bid-function). The derivative of the implied bid-function can be found by differentiating $U(y - t(y)d - pH(y),H(y)) = u^\star(y)$ with respect to $d$ giving the condition $p'(d)H(y) = - t(y)$ which is the wellknown Muth condition.


How would a firm increase price in such a scenario? I have the following question: If a firm with a lower marginal cost wants to increase prices in a homogenous goods industry in which demand is perfectly inelastic and supply is in excess, what should it do ?.
I'm thinking along the following lines: In a homogenous goods industry, the only differentiating element is the price of the product. By setting a lower price near to its marginal cost, the firm can grab the entire demand for the product ( the demand wont increase but the demand that otherwise went to other firms could be supplied by this firm, assuming no capacity constraints). After the excess supply from inefficient firms are removed from the market, the firm can then reduce its quantity and therefore reach a higher equilibrium price. Is this reasoning conceptually correct ?.
I also have this follow-up question, if the overall industry demand is inelastic what can I infer about the firm level demand ?. Can any inference be made from the question on the degree of competition in the industry ?. Thank you!.

It could work (it would depend on model parameters) if you would assume that it is impossible for firm to enter the market once firm exists. This is actually quite complex and long problem so I will provide only partial solution.
This would be a sequential Bertrand competition problem (since you assume that firms only can compete on prices). Here in first round company A (the one with lower marginal costs $c_A<c_B$) would have a choice - either set its price $p_A=p_B$, split the market between itself and second firm B and just get the extra profit thanks to its marginal costs being lower and do this in both period 1 and period 2.
So you would have strategy of 'tolerating B' (T) giving profits:
$$T: \pi_{A,t=1}+\delta \pi_{A,t=2}= (p_A -c_A) \frac{q(p)}{2} +  \delta (p_A -c_A )\frac{q(p)}{2}$$
where $p_A =p_B =c_B > c_A$ and $\delta$ is a discount factor for future profits.
Then you could have second strategy of 'contesting B' (C). In this strategy firm A would  undercut firm B in the first stage allowing it to get monopoly profits in the second stage so the strategy profit would look like:
$$C: \pi_{A,t=1}+\delta \pi_{A,t=2} = (p_{A,t=1} -c_A) q(p_{A,t=1}) +  \delta (p_{A,t=2} -c_A)q(p_{A,t=2})$$
Where now parameters would have to be such that $p_{A,t=1}<p_A$ (i.e. the first period price has to be lower in strategy C compared to strategy T) and then the second period price $p_{A,t=2}$ would be monopoly price in that period. Whether, strategy C or T makes sense will depend exactly on parameters of this model, depending on your assumptions on discount rates, marginal costs differential between the firms and consumer demand you could end up with either T or C being dominant strategy. Also, this requires assumption that if firm B gets loss in the first round it will immediately exist and won't be able to ever enter again.
Regarding your second question inelastic demand is in principle consistent with even perfect competition. You can only make some inferences about market power once you assume what the competition is (for example monopoly market power is inversely proportional to the elasticity of demand). However, it would be beyond scope of SE answer to list effect of inelastic demand on competition across all market structures. You can have look at  Paul Belleflamme &  Peitz Industrial Organization: Markets and Strategies for overview of this.


Attributing Labor Productivity Gains to Capital Deepening vs. Total Factor Productivity Growth In a traditional Solow-Swan growth model, you can decompose growth in labor productivity (output/hour) into a component stemming from total factor productivity growth and another stemming from capital deepening (increases in the capital/worker ratio).

Let's assume that I create a new machine which doubles the output of soybean production and try to sell it to soybean farmers. Prior to adopting my machine, farmers used horses and primitive plows to grow their soybeans. From the perspective of the farmer, after buying my machine and using it, they work the same amount, but they produce 2x as much, so their labor productivity has doubled. However, to what would you attribute the growth in output? Would you attribute it to capital deepening (because the farmer is now using more capital than before), or total factor productivity?

The reason I ask is because total factor productivity growth is generally considered by economists to be a measure of "the pace of technological progress" (See: The Rise and Fall of American Growth and other books of the same nature). But the act of creating my fancy soybean picking machine was in of itself a technological act. I had to combine some other capital inputs (steel, etc.) and some labor (my own and perhaps my employees) with insight to create the machine in the first place. I'm a bit confused about the growth accounting here.

A follow up question makes the situation a bit harder. Let's say that again I have invented a new machine tool. This machine tool let's car makers make smooth surfaces that are more aerodynamic and look cooler. This improves the look and miles/gallon figure of cars made using my machine tool. Car companies realize that consumers' are going to love the new look and higher MPG of cars made with the machine, so they purchase it in droves. In this situation, would labor productivity (output/hour) or even raw output of cars increase? After all, nothing has changed about the fundamental efficiency of producing the car - if anything the cost of producing the car has gone up because the fixed costs the car manufacturer pays to buy my machine must now be amortized over every car they sell. If the former did rise, would you attribute it to capital deepening - the car OEM is using more capital than before - or total factor productivity?

The increase in output in Solow-Swan model can come both from total factor productivity and capital deepening. Let’s step back from the real life example you have given because there many factors come to place and it’s hard to satisfy the ceteris paribus.

Consider simple Cobb-Douglas production function - that is actually almost always used in standard Solow-Swan model:

$$f=AK^{\alpha}L^{1-\alpha}$$

Now here the total factor productivity is represented by the $A$ parameter.

If you look at this this way you should quickly see that growth can come both from capital deepening (if K increases and L stays constant) or from increase in total factor or even both at the same time.

In your farmer example, the new technology increases $A$ so output should increase even if the investment in the new capital would be exactly equal to depreciation of old capital (and hence no net increase in K).

However, this of course abstracts from markets for factors of production where now demand for new technology increases because the new capital is perceived as more valuable as old one.

So both things can happen at the same time in Solow-Swan model, you can have both change in output due to change in A or K. Unfortunately due to this just from the raw change in output $\Delta f$ you can’t directly deduce which part of change is due to capital deepening and which part due to increase in $A$. You either have to keep one of them constant or you need to get data on the changes in either total factor productivity or capital accumulation to be able to deduce the other (assuming labor is always fixed constant).

In the second example if there is no change in total factor productivity (not every new technology has to change it) then you could attribute changes in output solely to capital deepening.

However, the problem there is that here you have another confounding variable and that is that the quality of car probably changed in the eyes of consumer so the output will have higher value. Here you would have to modify the Solow-Swan model to account for that the new output is not same as old and you basically switch from production $f$ to some $f^*$ - the problem is here that you are also trying to fit the macro model that can easily abstract from quality differentials to microeconomic problem where those things matter, but if you would hold the quality constant you could still use it. Or you could include the quality change explicitly with some pice wise production function or assuming multiple plants with different production functions etc.


Printing money to redistribute wealth A fictional country has 100 people. The total printed money is $2000. Ten rich people own half of it ($100 each), the remaining 90 are comparatively poor : ($\$2000 = 10  \times \$100 + 90 \times \$11.11 $)

To make things more even, the government decides to print another $2000 (no independent Central Bank here) and give them to all inhabitants, $20 each. Surely, this triggers inflation, prices double. But the net result is a redistribution of wealth, the poor are now less poor than before.

This looks as a simple progressive tax scheme which is beneficial to the poorest people. It could even be applied in some periodical and predictable way.

Of course, this is utterly stupid and cannot work - I guess. Why?

The main problem is that wealth does not equal cash. Those ten rich people probably have most of their wealth in real estate and stocks. Imagine all you own is a Lamborghini, then the government prints a lot of money, does that impact you?

Depending on the situation the money printing may be progressive or regressive. And the cost are high: There will not just be one inflationary moment, there will be inflation because the initial inflation breeds an expectation of even more inflation leading to hyperinflation.

Finally when you've done this once, nobody will ever want to hold your currency again because they distrust you. Leading to a number of other problems.


Why does a company want the value of its stocks to be as high as possible? My professor claims that a company want the value of its stocks will be as high as possible. Why should the company care? The company "minds its own business" and make its money. Why should it cares if the value of its stocks is \$25 or \$300?

The board of directors is supposed to represent (or work for the interests of) share owners. Share owners prefer higher prices if and when they want to sell their shares. The board chooses the CEO and will retain the CEO if he helps share owners realize their preferences.


Doesnt the fact that cash reserves go down in recessions contradict Keynesianism? It seems cash reserve is procyclical. Also anyone have the financial cash reserve data?

You very often see Krugman an other economists imply that corporations holding cash is a bad thing or affects demand.

http://krugman.blogs.nytimes.com/2011/07/02/cash-is-not-the-problem/?_r=0

However, you have to remember that Krugman is just stating his personal opinion. He does sometimes say things that contradict academic Keynesianism.

The fact that corporations hoard less cash during recessions doesn't necessarily contradict Keynesianism or New Keynesianism, but it does require these theories to explain why corporations behave this way (which the theorists have not attempted).


Differences between Hicksian and Slutskian approaches When deriving the substitution effect for both Slutskian and Hicksian definitions, a 'phantom' budget line is drawn.However, for a Slutskian definition, the 'phantom' budget line is drawn parallel to the new budget line(change in price) and through the point of tangency for the original budget line and indifference curve.

On the other hand, for a Hicksian definition, the phantom budget line is drawn parallel to the new budget line(change in price) and lies on the original indifference curve on a different point of tangency.

Is there any significance to this inherent difference between the Slutskian and Hicksian approaches when deriving the substitution effect?I'm familiar with the definition of the Slutskian and Hicksian approaches but am unable to reconcile the definitions of the approaches with the differences in drawing the phantom budget line, and subsequently deriving the substitution effect.

Any clarifications or attempts to enlighten me would be much appreciated.

Thanks!

The income effect (IE) is about assessing purchasing-power impacts of a price change, while the substitution effect (SE) is about the impact of that price change on the relative attractiveness of the different goods. In reality these effects are not observable - when a price changes, your consumption choices will change for both reasons. But we can conceptually decompose the overall effect into IE/SE. In the SE we will be looking to isolate the impact of relative prices changing, without the purchasing-power effect.

Now, there are two ways of thinking about this:

-Slutsky: what if price changes but my purchasing power were (literally) to remain constant (i.e. I could still buy the exact same bundle as before)? How would the relative price change by itself affect my decision?

-Hicks: what if the price changes but my purchasing power were adjusted so I am still able to achieve my initial level of utility (i.e. I would be as well-off as before)? How would the relative price change by itself affect my decision?

Either way, the SE is always negative, that is, a higher price for one good will tend to make consumption of that good lower.

After you understand the SE, the IE is just the income adjustment needed in either case to get us to the actual final decision. It can reinforce the SE or contradict it, depending on whether the good is normal or inferior.

Hope this helps.


How do we estimate utility functions? Throughout the course load of an economics student's undergrad we are exposed to the concept of cardinal utility via utility functions which give us a specific quantifiable number of "utilis" as a result of our inputs which represent consumer goods.

Practically speaking though, what type of data is used here and what methods are employed to accurately measure utility in a cardinal sense?

One proxy for cardinal utility would be people's willingness to pay (WTP) for a particular product. One can estimate WTP using consumption data (e.g. from Amazon/eBay purchases), or elicit WTP using economic experiments.

Another (better?) way to estimate cardinal utility is through methods used in neuroeconomics. For example, one can monitor an individual's dopamine level/active brain regions while she makes decisions. To the extent that the neuro-transmitter/brain activities are associated with bodily (physiological) pleasure, which by the way is what Jeremy Bentham had in mind when he coined the term "util", we may assert that particular activities/decisions generate a measurable level of utility that is cardinal in the sense that it not only orders choice alternatives from least to most preferred, but also signifies the intensity of preference over each alternative.


How does Marx economics get evaluated in modern economics? As I know, Marx economics did not solve the problem of transformation as Samuelson argued.

And at least, it has been known as a dead end.

How does Marx economics get evaluated in modern economics? Is it considered as a kind of pseudoscience or something similar?

Here are some comments on Marx from people who can certainly not be called marxists.

  If Karl Marx and V. I. Lenin were alive today, they would be leading
  contenders for the Nobel Prize in economics. Marx predicted the
  growing misery of working people, and Lenin foresaw the subordination
  of the production of goods to financial capital’s accumulation of
  profits based on the purchase and sale of paper instruments. Their
  predictions are far superior to the “risk models” for which the Nobel
  Prize has been given and are closer to the money than the predictions
  of Federal Reserve chairmen, US Treasury secretaries, and Nobel
  economists, such as Paul Krugman, who believe that more credit and
  more debt are the solution to the economic crisis.

Paul Craig Roberts,  United States Assistant Secretary of the Treasury for Economic Policy under President Reagan in 1981, Source

  The American economy is still, by most measures, deeply depressed. But
  corporate profits are at a record high. How is that possible? It’s
  simple: profits have surged as a share of national income, while wages
  and other labor compensation are down. The pie isn’t growing the way
  it should — but capital is doing fine by grabbing an ever-larger
  slice, at labor’s expense.

  Wait — are we really back to talking about capital versus labor? Isn’t
  that an old-fashioned, almost Marxist sort of discussion, out of date
  in our modern information economy? Well, that’s what many people
  thought;

Paul Krugman, Nobel Prize in Economic Sciences 2008, Source

  extraordinary that 100 years after Das Kapital ... so little else
  should have emerged

Sir John Hicks, Nobel Prize-winning British economist, Source


Help trying to find Economic Profit for a Monopoly I'm given a demand function ( $p = 60-.002q$), Marginal Cost (\$10) and Fixed Costs (\$300,000) for a monopoly.

I've figured the profit maximizing output and price:

Marginal revenue function $MR = 60 -.004q$.

$10 = 60-.004q$  # To find monopoly output.

$q = 12500 \implies$ Price of monopolist is $35$  #  $p = 60-.002(12500)$.

Now, I usually figure out the economic profit by taking the area of the rectangle formed by the bounds of the demand function (at monopolist output) down and stopping where it meets the AC function, and then across to the y-intercept of the graph; but they didn't give me an average cost function.

How can I figure out the economic profit? Please help and thanks for your time.

P.S. Is there a way of finding what Average Cost is at output(12500) with the given information?

Profit is revenue minus costs. So we have $q = 12500$ and $p = 35$. (Note that I'm assuming you've correctly figured this out.) Then we have revenue:

$$R = \int_{0}^{12500} MR dq = \int_{0}^{12500} (60 - 0.004q)dq$$

And costs:

$$C = 300000 + \int_{0}^{12500} 10dq = 300000 + 125000 = 425000$$

The profit is $\Pi = R - C$.

The average cost is $C/12500$.

I leave you to crunch the integrals.

Edit: In looking at your problem, $p(q) = 60 - 0.002q$ is definitely an inverse demand function. The revenue $R = qp(q) = (60q - 0.002q^{2})$ (quantity times prices). This yields the profit maximization problem (maximizing with respect to quantity produced):

$$\max_{q} qp(q) - c(q) = (60q - 0.004q^{2}) - 10q - 300000$$

The First Order Conditions are:

$$60 - 0.004q - 10 = 0 \implies 60 -0.004q = 10$$

You did the work from there to solve for $q$.


Can I recreate an experiment on Allais paradox using student grades as payoffs? For a project in experimental economics, I thought of doing something related to expected utility theory/prospect theory, but using grades instead of money.

Is this reformulation of the Allais paradox conceptually right or not?

Problem 1.1:
Consider the following scenario:
A.1 – you can get an B+ with probability 100%
B.1 – you can get A with probability 10% or get B+ with probability 89% or not passing the exam with probability 1%.
+
A.2 – you can get B+ with probability 11% or not passing the exam with probability 89%,
B.2 – you can get A with probability 10% or not pass the exam with probability 90%.*

Then I will modify the problem to see if for higher stakes student's preferences change.

Edit:
If we consider that not passing the exam gives utility = 0, (as in the Allais paradox we have the same case because it corresponds to receiving 0$) the graph of the utility function, assuming constant marginal utility of grades would look like this:

I am not sure I understand the problems outlined in the other answers. Seems to me that if we assume students maximize their expected utility and lotteries A1 and B2 (or B1 and A2) are chosen by someone, we would have

\begin{align*}
100\% \ U(B) & > 10\% \ U(A) + 89\% \ U(B) + 1\% \ U(F) \\
\\
11\% \ U(B) + 89\% \ U(F) & < 10\% \ U(A) + 90\% \ U(F)
\end{align*}
which are contradictory. There is no need to assume anything about the function $U$ for these to be contradictory.

One runs into the usual problem of trying to elicit true preferences in a poll, but so does the original paradox.


General Results on First or Second Mover Advantage? I am just wondering whether the following question has already been answered in game theory: Fix an arbitrary (say, finite) two-player strategic form game. Under what condition, does one player (say, Player 1) want to be the first-mover than the second mover?

For example, we know that moving first is better in Cournot competition and moving second is better in Rock-paper-scissors. Is there a general condition on the payoffs of two-player games under which we can tell whether Player 1 should go first or second, if he could choose?

One nice reference that seeks to answer your question is the following paper,

https://link.springer.com/content/pdf/10.1007/BF01076104.pdf

The paper's main results are contained in the following theorem (Theorem I):

a. If both players have a dominant strategy in the basic game, the game is the same. (where the basic game is just the 2x2 bimatrix game)

b. If only one player has a dominant strategy in the basic game, then
the extended game has a unique equilibrium in un-dominated strategies.
It's different from the  basic game outcome iff that outcome is Pareto dominated by another pure strategy outcome. The extended game equilibrium achieves
these Pareto dominating payoffs by having the player with the dominant
strategy play first and the other second.

Think of this as a way to achieve a Pareto superior vector of payoffs.

(C) If the unique simultaneous play equilibrium of the basic game is
in mixed strategies, then like in part (B) there won't be a change unless there's a Pareto superior P.S. vector. If Pareto dominance does
not exist, both players will wait until the second period and play
simultaneously. If Pareto dominance does exist, the unique extended
game equilibrium attains the Pareto dominating payoffs by selecting one
of the sequential move games.


How to graph a monopoly that does not exhibit the properties of a contestable market? This question is not a homework question. I am taking a course in industrial organization, and the textbook/professor have given an illustration of a monopoly that is a contestable market. However, I am having trouble seeing, graphically, how an illustration of a non-contestable monopolistic market would look.

The properties of contestable markets are:

(i) Free entry, (ii) Absolute entry, (iii) No sunk costs with entry.

I have included the image used in both the textbook, and by the professor for contrasting purposes. One other question, if LRAC is decreasing as output increases, would that mean that the monopolist is facing economies of scale, which would cause there to be a barrier for the entrant?

Thank you in advance!

The diagram above describes a Natural Monopoly. These economies have the characteristic that the long run average costs are decreasing (and hence the LRMC is below the LRAC curve). That is, costs reduce as the firm keeps producing more. *Firms with network effects (e.g. telecom industry) is an example of such an industry.

Lets look at 2 cases: Competitive market and a single firm.

If the market is competitive, the firms will produce at a price-quantity pair such that $LRMC =P$. But at this price, the total revenue is negative (since the firm earns 0 profit at $(Q_C,P_C)$).
Thus the firms will be better off shutting down and earning 0 profits. Clearly, a competitive market won't work in such cases.

For a monopoly, the firm will charge price $P_M$ and produce $Q_M$ (the point where $LRMC=MR$). This firm earns a positive profit ($Q_MP_M>LRAC*Q_M$).


Is Iphone included in tariffs? As the tariffs war getting escalating, I am curious about how the tariffs works on Iphone. Apple is an American company, and Iphone is its product. But manufactured by factory in China. Is there a tariff imposed on Iphone when it imported back?
Are all goods that belongs to American company but manufactured in China being included? If not, what is the driver? If it is, what percent of the tariffs are actually product from American company, isn't increasing tariffs just hurting these companies?

As of April 2018, the tariffs are targetted at products in which Chinese companies dominate.  They would apply to products made by American companies in China and imported to the US, but the exact products covered have been chosen to minimise this effect.  Nevertheless,

  it will most likely increase costs for American manufacturers that depend on imported parts because it concentrates heavily on machinery and high-tech components.

In other words, US firms that use components made in China by Chinese companies as inputs in creating more complex products will be harmed.  For instance, Harley Davidson have said that

  Import tariffs on steel and aluminum will drive up costs for all products made with these raw materials, regardless of their origin.


How to calculate the degree of risk aversion of a consumer in a lottery? To give an example, say we start with 100 dollars and we enter a lottery. With probability $\pi$, this 100 dollars is reduced by 2 dollars. Otherwise our endowed 100 dollars does not change. Let's say our consumer's utility function is described by $u(c_h)=ln(c_h)$.

It's clear that the consumer is risk-averse, but how would I calculate the degree of risk aversion? How do you find the risk premium here?

Thanks.

The gamble:

$$g = \left(\pi \circ 98, (1-\pi)\circ100\right)$$

The expected value of the gamble:

$$\mathbb{E}[g]= \pi\cdot 98 + (1-\pi)\cdot 100$$

Expected utility:

$$u(g) = \pi \cdot \ln (98) + (1-\pi)\cdot \ln (100)$$

Risk premium is such that:

$$\ln \left(\mathbb{E}[g]-P\right) = \pi \cdot \ln (98) + (1-\pi)\cdot \ln (100)$$

Where $P$ is the risk premium. Solve the above equation for $P$. You can measure the degree of absolute risk aversion as follows:

$$ARA = -\frac{u''(c_h)}{u'(c_h)}$$

And the degree of relative risk aversion as:

$$RRA = - \frac{c_hu''(c_h)}{u'(c_h)}$$


Pareto efficient adverse selection Please look at the following. Question which I posted.

I did not understand the answer for the part b - Pareto efficient.

I am happy if you explain it in more details. Thank you.

Also please explain which equilibrium Pareto efficient / dominant or optimal? How can I decide whether a equilibrium is Pareto efficient/optimal/dominate ?  Thank you

First: Pareto efficiency, optimality and dominance don't all describe equilibria.  Loosely, they mean the following:

A Pareto-efficient outcome is an outcome that satisfies the condition that no agent is worse off, and at least one agent is better off, as a result of the change.

A Pareto-dominant outcome is an outcome that is both Pareto-efficient and increases overall welfare with respect to an alternative.

Finally, an outcome is Pareto-optimal if it is Pareto-efficient and is not Pareto-dominated by some other outcome.

Only the last definition has something to do with equilibria.  By the First Fundamental Welfare Theorem, perfectly competitive market equilibria are Pareto-optimal.

As others have said, we might need to know more about the model 13.B to help you, but roughly speaking, if the wage incentives in your model are such that by part a) nobody is willing to work, then nobody acts.  Likely, within your model, if nobody acts, nobody incurs a cost, and so nobody is worse off.

So, to understand b), we need to be able to see whether at least one agent is better off if nobody works.


Methodology of Economics: interpretation and explanation I am interested in understanding the interaction between interpretation and explanation in social sciences in general and in economics particularly.

It is argued that interpretation is pervasive in all methodologies, even in physical sciences. However, as I understand, interpretation cannot escape subjectivity: the interpretation must reflect knowledge and understanding of the interpreter. For example, some interpret recessions as crucial parts of the business cycle, but other interpret it in other ways.

Yet, we tend to be interested more in what causes the phenomenon, or finding the explanation of it.

My question is:

How can we think of interpretation and explanation in economics?
What is the relation between the two?  (I have senses that they can't go without the other, but are there any sources of reading in this topic?)

The standard reading on the methodology and the role of explanation in economics is Daniel Hausman's work.

Hausman, Daniel M. The inexact and separate science of economics. Cambridge University Press, 1992.

Nancy Cartwright has some work on the interpretation of causation in the social sciences.

Cartwright, Nancy. Hunting causes and using them: approaches in philosophy and economics. Cambridge University Press, 2007.

Another entry to this literature may be the Stanford Encyclopedia of Philosophy:

http://plato.stanford.edu/entries/economics/

However, I am not sure what you mean with a literature on interpretation in economics.


Calculate optimal discount for product bundling So recently I made some rules with my transaction data. Based on it I can determine which products are profitable to bundle it together.

But even though I know e.g. product A→ product B, are there any ways to determine how many bundles will be sold based on the discount value?

E.g. out of the 100 transactions with product A for price X and there are 40 transactions with product B for price Y(I know lift value might be better but let's keep it easy for now), if product A and B are bundled together, what is the discount rate to increase the optimal short term sales?

I do have products sold for product A and B for different kind of discount, so I was thinking using price elasticity to determine the discount for the bundle because if you know the price you know the quantity, but I dont think it is the right way of thinking and there is no price elasticity for both products.

The data I have:

Price of the product

Lift, support, confidence values and other values related to rules.

sold product per month

Discount value per product

I think these variables are more crucial.

Any suggestions would be appreciated.

Thanks in advance!

Do you have price elasticity figures at your disposal from other sources or were you planning on trying to estimate elasticities yourself using the data? If you are planning on estimating elasticities using the data, you need to be very careful. Running a simple log-log OLS regression will give you poor estimates because your data points are all market equilibrium points and are not a representative sample of points along a static demand curve. You have serious endogeneity issues there.

I have tried undertaking similar projects so I know the pitfalls well. If you still want to back out sales using elasticities, you could try an instrumental variables approach using some of your other variables as instruments to try and circumvent the endogeneity problem via supply-side identification. Another option is to use a simultaneous equations model where you posit functional forms for supply and demand separately and then estimate the reduced form using, say, two-stage least squares (2SLS).

If you are strictly interested in forecasting sales well and not really concerned with understanding causal channels, you can look into machine learning algorithms. Depending on how many data points and how many variables you have at your disposal, there are various models that may suit your needs. You should understand these models well before running them, however, because most of them are not like the models in your standard econometrics toolkit. For instance, the more "flexible" models (such as unpruned decision trees, multilayer perceptrons, etc.) are very susceptible to overfitting the data by essentially modeling noise, leading to higher mean squared errors than anticipated due to high variance.

If you're interested in learning more, I found this to be an outstanding, easy-to-understand introduction into statistical learning.


Experiments contradicting the expected utility model This is a question I asked on the cognitive science beta which never got any answer there. I do not know what the policy should be for question migration/reposting (maybe worth discussing in the meta?), but I hoped it might get more answers (i.e. at least one ;)) here.

I am looking for a list of experiments which cannot be accounted for by the expected utility model. By the expected utility model, I mean the model of individual preferences over vectors of uncertain events (e.g. $\Big(P(rain) = 0.4, P(sunshine) = 0.6\Big)$ and $\Big(P(rain) = 0.6, P(sunshine) = 0.4\Big)$)  which satisfies a list of axioms proposed by Von Neuman and Morgernstern, namely

Completeness
Transitivity
Continuity
Independence

A rigorous formulation of these axioms can be found on page 8 of Axiomatic Foundations of Expected Utility and Subjective Probability, by Edi Karni, from the Handbook of Economics of risk and uncertainty..

Alternatively, by Von-Neuman and Morgenstern's representation theorem (page 9 of the same reference), these axioms are know to be equivalent to the fact that the preferences of the agent can be represented by a utility function of the form (in the discrete case):

$U(L) = \sum_{all~possible~events "e"} P(e)u(e)$

where $P(e)$ is again the probability that $e$ occurs and $u(e)$ is the utility of getting event $e$ for sure.

The violations of these axioms I am most interested in are the ones related to the Independence axiom (violations of completeness, transitivity and continuity would probably deserve a separate question. See this question for an example of intransitivity.).

I am looking for situations which cannot be accounted for by the expected utility model. Some well-known examples are the the Allais and Ellsberg paradoxes (although there is still a debate regarding Ellsberg paradox). On the other hand, I do not see the Saint-Peterborough paradox as contradicting expected utility theory, because it can be accounted for by the theory if one assumes an appropriate degree of risk aversion. But you are much welcome to argue against that.

I hope this question can serve as a repository of famous experiments contradicting expected utility theory, so feel free to add many.

this paper http://else.econ.ucl.ac.uk/papers/uploaded/243.pdf (Choi 2007) has a nice state of the art experiment that deals with rationality and expected utility is a special case of it. In general only 17% of consumers are compatible with rationality ergo the remaining part cannot be expected utility maximizers.  Quah has a nice paper on the revealed preference theory of expected utility (among other models), he uses Choi dataset to test expected utility hypothesis that is going to be rejected more times than rationality https://ideas.repec.org/p/lec/leecon/13-24.html