Is there a go-to resources on the use of the scientific method in economics? I once had a physics teacher who said (paraphrased):

for any formula or principle you use on an exam, you have to be able to provide a real world test that would demonstrate the theory's validity. In other words, the test must show the theory accurately describes some real world phenomena.

I would like to better understand how economist think about "testing" their theories. For instance, psychology undergrads at my local university take a psych research methods course. I would like something along these lines for economics. But more than this, I want something that goes beyond just discussing research methods and actually assesses what makes high quality economic science. In contrast to psychology, many claims in economics are hard to test because doing so is either impossible, intractable, or impractical. Therefore, I think a good understanding of how to do economic science is crucial to learning it to figure out whether a given author is adhering to the scientific method.

Remark:

By science, I mean

CLAIM: the earth's acceleration is $g$

TEST:

We will drop a ball and measure how long it takes to hit the ground.

(1) measure a height $d$ off the surface of the earth

(2) time the ball as it drops from $d$ to the surface

(3) compute the acceleration from $d = v_0t + \frac{1}{2} a t^2$

and I will find the acceleration of the earth is $g$.

Economists often do something similar to what your physics teacher taught. One of my graduate econometrics teachers taught us to begin our empirical investigations by asking what the ideal experiment to test them would be. And a quick web search confirmed this is a widespread sentiment:

  Esther Duflo, PhD ’99, a prominent antipoverty researcher at MIT whom
  Angrist advised when she was a graduate student, says his relentless
  concentration on the problem of selection bias—for instance, the
  possibility that the better-rated high school is populated with better
  students—spurred her to go beyond his techniques and conduct actual
  field experiments. “Once you ask the question right, you can ask what
  the ideal experiment to answer it is,” she explains

The Natural Experimenter By Peter Dizikes on January 2, 2013

  For a long time I have maintained that economics is unfairly
  criticised for the use of unrealistic assumptions. (See Cartwright
  1989, 1998). I can summarise my view by comparing an economic model to
  a certain kind of ideal experiment in physics: criticising economic
  models for using unrealistic assumptions is like criticising Galileo’s
  rolling ball experiments for using a plane honed to be as frictionless
  as possible. This defence of economic modelling has a bite, however.
  On the one hand, it makes clear why some kinds of unrealistic
  assumptions will do; but on the other, it highlights how totally
  misleading other kinds can be – and these other kinds of assumptions
  are ones that may be hard to avoid given the nature of contemporary
  economic theory.

The Vanity of Rigour in Economics: Theoretical Models and Galilean Experiments by
NANCY CARTWRIGHT

  So what is, intuitively, an experiment? The key idea is control:
  experimenting involves observing an event or set of events in
  controlled circumstances. It is useful to distinguish at least two
  important dimensions of control: (1) control over a variable that is
  changed or manipulated by the experimenter, and (2) control over other
  (background) conditions or variables that are set by the experimenter.
  Both dimensions involve the idea of design or manipulation of the
  experimental conditions: the experimental laboratory is in some
  intuitive way an “artificial” situation compared to what is likely to
  happen in the “natural” or “real” world. 3 An experiment is usually
  designed with the aim of getting a clear-cut answer to a fairly
  specific scientific question. As we shall see, many different kinds of
  questions can be answered in the laboratory. But typically, such
  questions regard the mutual dependence of some variables or
  quantities, and in particular the causal relations holding between
  them.

Experimentation in Economics by Francesco Guala


Free Cash Flow to the Firm I've got this question:

  Explain why the FCFF does not incorporate interest expenses and what is the potential bias in the valuation if corporate taxes exist.

Now, we know that in the Free Cash Flow to the Firm we do not include interests because we account for the cost of debt capital in the discount rate. But what is the bias when corporate taxes exist? The flows are computed after-taxes, and then discounted. Maybe can emerge a problem when computing the tax shield, but this is easily tackled by using either Weighted Average Cost of Capital (if the project's flows have the same risk of the firm, and the firm keeps constantly the Debt/Value rate constant) or by using Adjusted Present Value when the debt ratio changes during the lifetime of the project.

Any suggestions?

Debt service cost is felt by equity owners and debt holders but neutral to the firm. Taxation does not care for cash flow, it is levied on tax law specific accounting profit, not even reporting profit, which tends to treat most interest charges (not all and not uniformly either) as a deductible cost. Thus you make an adjustment to your WACC as you said. However, interest charge does not need to be uniform during the life of the debt. Unless you do your WACC adjustment for every period and apply a different WACC for each (you should always at least justify not doing so anyway), you will end up with a inflated cash flow and higher discount rates.


Can an Out the Money put option's price $>$ its Strike Price? I'd guess yes, if the put option's IV spikes. An OTM put has merely Time Value and no Intrinsic Value.

As happened to crude oil futures in 2020, prices of certain traded instruments can go negative. In such a case, the strike can be at zero, and the put has positive value, even if the spot price is still positive.
Otherwise, it is only possible if:

interest rates are negative, and so one is willing to pay money now for less money in the future, or
somebody hit the wrong keys when trading, and it was not overridden by automatic controls.

In a positive interest rate environment, fair value is always less than the strike price if the price is floored at zero, since the maximal payout is the strike. Increasing volatility cannot affect that.


CES production function profit and supply function I need to derive the profit function for the following CES function: $$ f(z) = (\sqrt{z_{1}^{\rho} + z_{2}^{\rho}})^{1/ \rho}$$ where $\rho \leq 1$. This is the answer that I am supposed to be getting:

If $ \rho <1$ then
$$ \pi(w) = \begin{cases}
      \infty \;\;\;\;\; \text{if} & w_{1}^{\rho/(\rho -1)} + w_{2}^{\rho/(\rho -1)} <1 \\
      0 \;\;\;\;\; \text{if} & w_{1}^{\rho/(\rho -1)} + w_{2}^{\rho/(\rho -1)}
 \geq 1\
   \end{cases}
$$

If $\rho = 1$, then:

$$ \pi(w) = \begin{cases}
      0 & \text{if} \;\ Min\{w_{1},w_{2}\} \geq 1 \\
      \infty & \text{if} \;\; Min\{w_{1},w_{2}\} < 1 \\
   \end{cases}
$$

Normally I simply use profit maximization or cost minimization FOCs to obtain the profit function, as well as the supply one. But I have been trying to get around this problem and I really cannot get around these results or (of particular importance) how to derive them. That being said any tips, intuition, or just help with the derivation if you're feeling particularly selfless would be greatly appreciated.

Thanks in advance!

Hint: Solving for the FOC's assumes that the solution is interior, in this case, that profits are positive and smaller than $\infty$. I would recommend you to derive the cost function $c(y)$ and then study its derivative. If the marginal cost is always smaller than the price of the good (probably it is assumed to be 1) then producing more is always better and profits are unbounded. However, if the marginal cost is always larger than the price, then the optimal is to produce nothing and get zero profits.

Hope this helps.


What is the latest thinking on the economic calculation problem? Eric Posner and Glen Weyl write in the epilogue of Radical Markets (2018) that they “remain confident that for at least a few generations markets – Radical Markets, that is – will remain the best method of large-scale social organization”.

Are there indications that alternative calculation methods may challenge this thesis?

--
CLARIFICATION:

Typically an alternative calculation method, more efficient than markets, is considered to be possible through technology: parallel processing and more recently artificial intelligence:

  The market process … may be considered as a computing device of the pre-electronic age.

Oskar Lange (1967): The Computer and the Market

I wondered what the current discourse was on the topic beyond what is available on Wikipedia.

Depends what exactly is the authors definition of “radical markets”. A predominant consensus in the economic field is that a mixed economy which relies predominantly on market form of organization but also has government stepping in correcting major market failures and some macroeconomic management is economic system that delivers the greatest amount of material welfare to greatest number of people.

I can’t see much challenge to this consensus within the profession but I would hesitate to make predictions about future - just few years before Einstein developed theory of relativity Lord Kelvin stated that: “There is nothing new to be discovered in physics now, All that remains is more and more precise measurement." Although, the consensus is quite strong and entrenched so I would also not say that the estimate of authors of at least few generations is wrong.

Wether that’s the best is matter of personal morals. Some radical ascetic may prefer a system where everyone lives on some agrarian subsistence level. If our objective would be to just bring  everyone down to the subsistence level then markets would of course not be the best form of organization. This last paragraph might look silly to you but I am just highlighting that there is no moral consensus on what the objective of society should be, and this objective is also what determines what’s the best system, and that this is ultimately question that transcends economics.

Edit: In response to your new question in your clarification about using computer technology, the following statement:

  Typically an alternative calculation method, more efficient than markets, is considered to be possible through technology: parallel processing and more recently artificial intelligence

is not considered correct in economics, in fact this whole statement puzzles me because it presents itself as a fact while it is not true that in the wider economic literature technology, as you defined it here as parallel processing or artificial intelligence, is considered an efficient alternative or even more efficient method of economic calculation.

The fundamental problems that markets help to solve are aggregating information and providing incentives. However, when we talk about information we often talk about information which is not easy or even possible to objectively verify. For example, important information that markets aggregate is the information on consumer preferences. No matter of computing power will help you with that if people dont reveal their real preferences through lets say questionnaires because they either might suffer from social desirability bias, people might have incentives to mislead or not even themselves fully understand the preferences they have.

Moreover, market mechanism through prices actually provides incentives for people to act in accordance with the information the markets aggregate. If the prices for apples increases due changes in consumer preferences then producers do not get just the information about that in an aggregate and simply understandable way in the form of price but they are also provided with an incentive to act accordingly and expand their output.

Parallel processing and machine learning does not help with solving the underlying  problem of economic calculation in any way. Parallel processing and machine learning algorithms can certainly help governments to conduct more efficient policy by helping to model and estimate its effect and getting more efficient feedback on the response of economy to government action. But they do not help with the fundamental problem of economic calculation at all, and frankly no amount of computing power probably will as the problem of economic calculation is not a problem of lack of computing power but a problem of eliminating information asymmetry between people and 'central planners'  and giving people incentives to provide accurate information and act on it.


Market Cap ranges for Tech Companies I'm trying to get an idea of how big tech companies are based off market cap.  This is not my typical field of expertise, so please pardon me if I say something naive.

I've found this site (https://www.tradingview.com/screener/) in which I'm able to filter tickers by market cap and industry.  I tried looking through the list but didn't recognize anything in the lower areas.

I've also attempted to simply search for the market cap of tech companies I know of.  Heres' what I've got so far:

Cap   Company
----+------------
1T    Apple
950B  Alphabet
150B  Netflix
29B   Ebay
16B   Expedia
4B    TripAdvisor
2.5B  StitchFix

I couldn't find a single company under $1 Billion, thought I'm pretty certain it's possible.  Is there a minimum to this?  How can I find examples of tech companies at all ranges?  In general, how can I go about getting a grasp of size vs market cap in the tech field?

The reason why you find it mainly for large companies is that the market capitalization is by definition the market value of company’s equity.

If the company is not public it might not be possible to get the market value as for that you need to observe the price at which the company trades its equity (like shares on stock market for example). Most of the time only big companies go public because it involves a ton of extra regulatory requirements that small firm might not be able to even cope with.

Hence, small - medium size partnership or private limited companies do not generally sell equity publicly. The best you could do there would be some estimate based on some expert’s judgement of market valuation but I imagine that will be very hard to find and inherently very inaccurate. Sometimes even big company might decide to stay private to avoid greater regulatory burden but for bigger companies it’s usually easier to find some expert valuations or estimates of the firm value based on some other observable characteristics.


Does the Fed/SEC have tools to address shock-propagation from correlation of fund flows? Premise
In 2017, passively invested assets totaled 37% of mutual funds and ETFs;  by 2021 this number is closer to 50% if not more. After the market downturn in (March) 2020, the Fed updated their research paper which evaluated potential risks to financial stability stemming from passive investing:
https://www.federalreserve.gov/econres/feds/the-shift-from-active-to-passive-investing-potential-risks-to-financial-stability.htm
The piece does not have a strong position on the question, citing mixed empirical findings for the affirmative and negative as well as unclear causality. However, let's briefly play devil's advocate and imagine a worst case scenario:

Passive assets under management (AUM) increases above some tipping
point, decreasing the heterogeneity of investors and inducing a
systemically huge non-diversifyable risk (Ben-David, Franzoni,
Moussawi (2017))
Upon a risk event, the large degree of comovement of fund flows and
stocks would propagate shocks
As price insensitive players, passive investors simply redeem at
market price, yet as active managers have incentive structures not
to sell at distressed levels, the dilemma in so many words becomes:
what happens when passive wants to sell and there is not active to
buy?

Under more benign assumptions, active may simply benefit from distortions caused by passive, but in the extreme scenario we are assuming in this article, perhaps monetary policy may need to have a playbook to prevent a financial crisis. I'm not going to pretend to know exactly all the mechanics of what would happen if events 1, 2 and 3 unfold (market goes to zero, liquidity crises, ect), but that's besides the point. For the purposes of the question, let's just assume this scenario can unfold.
Question
Assuming the Federal Reserve / SEC wants to address the risks outlined above, what macroprudential tools would be relevant and what could be done ad hoc?

I’d start by briefly noting that “the Fed” didn’t say anything; that’s a research paper (by some smart people), but it’s disclaimed and doesn’t necessarily reflect the views of anyone other than the authors.
Having said that, I would then rephrase your question as follows: “what happens if everyone decides to cash in their retirement funds at once?” The answer to that would be: they would all get a very poor return, but thankfully that’s unlikely.
Very little of the question as posed has anything to do with active vs. passive strategies. “Passive” players aren’t different types of players, they’re the same types engaging in different strategies because they have different beliefs. If I invest my 401(k) in a Vanguard index fund vs. an actively managed fund with the same targets, I’m still the same person with the same risk tolerance, and I’m still subject to the same shocks from the real economy.
It’s always extremely important to keep in mind the underlying motivations and stylized behaviors of different types of players, and thankfully, retail investors do tend to avoid panic selling their holdings at market lows. This is simply because they tend to have long time horizons (most passive investors are simply saving for the future and not drawing on their assets for current income, in which case they’d hopefully have shifted to fixed income). This also largely takes fire sale dynamics off the table. Fire sales happen generally when leveraged players are forced to mark-to-market. Most retail index investors are completely unlevered, so draw-downs mostly represent buying opportunities. So because the underlying type hasn’t changed, the fact of being invested in passive strategies doesn’t really change much.
If that were not true, you’re right, the investors would suffer huge losses, but even then, it wouldn’t really be a financial crisis, and there wouldn’t be any good logic for official sector intervention. I say that it wouldn’t constitute a financial crisis because losses on equity are just someone’s investment losses (and likely soon someone else’s gains). From a financial stability standpoint, equity does not matter, debt matters. People often conflate the two, because when debt is distressed, so is equity, but that is confusing a symptom (distressed equity) with the disease (distressed debt). Keep in mind that the post-2000 equity market losses rivaled the 2006-2009 mortgage market losses (which were debt) in magnitude, but only in the latter did we see a financial crisis. In contrast, large-scale inabilities for companies to access debt markets reflect a broad tightening of credit conditions— a liquidity crisis, which is what Bagehot described and what is generally an object of concern for central banks. So while the official sector will intervene when debt markets break down, it is not within the official sector’s purview to attempt to allocate gains or losses.
Having said all that, in the spirit of trying to fully answer your questions, there are ex ante tools that exist to basically discourage opportunistic redemptions from funds. They do not really apply differently to passively vs actively managed funds, though; they instead exist to ensure that one’s redemptions don’t negatively impact other fund holders. There are a whole litany of such tools, including gates, fees, swing pricing, minimum balance at risk, and others.


Externality and Output In a positive externality, can government just set the price to the socially efficient price instead of a subsidy to correct an externality?

In principle in both positive and negative externality scenario government could just set price to the socially efficient price.
However, outside of static textbook example this is non-starter. The socially efficient price even in presence of externalities (positive or negative) is not constant and it will fluctuate across time. Hence government would have to always change the price it sets. This is problematic since estimating what the socially optimal price is in every instance and in real time is virtually impossible.
Consequently, it is considered more convenient to simply issue subsidy equal to the value of positive externality. In such way no matter how the socially optimal price fluctuates across time as long as the value of positive externality remains constant government does not need to change it across time. Value of positive externality that activity does without doubt fluctuates less frequently than prices so government wound need to reevaluate the subsidy just occasionally.


Converting price for service in the foreign market to local price I am a student researching 3D scanning service and developing it for a specific centre in my country, where the service does not exist in the way it does in USA. I know the price for the service in US. My supervisor suggests that the US prices can be converted to local prices by means of some economic indexes or tools. None of us is an economist and I don't really see how it can be done. Is there really a way to do this?

Converting the amount from USD directly to the domestic currency using market exchange rates is an easy solution, but does not take into consideration the PPP (purchasing power parity) between the countries.

One possibility is to use instead the PPP rates, which are rates of currency conversion that equalize the purchasing power of different currencies by eliminating the differences in price levels between countries.

The date can be obtained from: https://data.oecd.org/conversion/purchasing-power-parities-ppp.htm#indicator-chart, from which you can calculate the price of the service, instead of using a currency converted based on market prices. On the same link you can check for the differences between the PPP rates and the market exchange rate, which in some cases are substantial.

One limitation should be pointed. The PPP rate is not calculated for a specific kind of service, but for a basket of products and services. However, this is a limitation that also affects the market exchange rates.

Therefore, at least in my opinion, this method allows to better capture the differences in purchasing power between the countries, and allow you to apply a more reasonable and justifiable price.


Understanding Leveraged Buyout There is company A, which has Assets = \$100, Equity = \$50, Debt = \$50.

I, Ant, found a new company, company B. I personally invest 10 in this company, and I find people who lend me \$50. Assets = \$60, Equity = \$10, Debt = \$50.

With this \$60 cash I buy company A (I apply a \$10 premium because I can't expect to buy it at the current market price. Also I assume that the book value of equity is equal to the market value of equity)

The shareholder of the company A are happy as they got away with a 10 premium.

The balance sheet of B now looks like

Assets = \$100 Debt = \$150 (?) Equity = (?)

I don't know exactly how debt and equity would be in this case.
Also, I believe that the market value of the debt held by debtholder of the first company should go down, because now they have that their debt is alongside another 50 million dollars of debt against company assets that are still fixed at 100.

Can somebody help me clear up this point?

(Also, help me find the correct tags.. It seems like there are very few!)

There are two cases to consider:

1) Company B buys the shares of company A, but keeps A as a separate entity, a $100$% subsidiary. The individual Balance Sheets here will be

COMPANY B
\begin{array} {| r | r | r |}
  \hline
\hline
  \text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
  \hline
\text{Goodwill} & 10 & \text{Equity} & 10\\
\text{Participations} & 50 & \text {Debt} & 50\\
\hline
\text {TOTAL ASSETS} & 60 & \text{TOTAL LIABILITIES} & 60\\
  \hline
\end{array}

The overall value has not changed, only the composition of the Assets. Nothing changes in the Balance Sheet of Company A - it was not a party in the transaction, its shares was the object of the transaction

COMPANY A
\begin{array} {| r | r | r |}
  \hline
\hline
  \text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
  \hline
\text{Assets} & 100 & \text{Equity} & 50\\
\text{} &  & \text {Debt} & 50\\
\hline
\text {TOTAL ASSETS} & 100 & \text{TOTAL LIABILITIES} & 100\\
  \hline
\end{array}

but what is interesting here is the Consolidated Accounts, the two companies viewed as one from a financial point of view, even though for legal and other purposes they are separate entities. Here we have

GROUP BALANCE SHEET

\begin{array} {| r | r | r |}
  \hline
\hline
  \text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
  \hline
\text{Assets} & 100 & \text{Equity} & 0\\
 &  & \text {Debt} & 100\\
\hline
\text {TOTAL ASSETS} & 100 & \text{TOTAL LIABILITIES} & 100\\
  \hline
\end{array}

How come? First, Debts of both companies are owed to Third Parties, so their amount doesn't change. So Group Debts = 100. Second, The Assets held by mother company B are "internal" - the shares of company A (face value and premium), so they are ignored, "written off" in the consolidated accounts. What Assets remain are those held by company A. So Group Assets = 100. We are then led to find that Group Equity is zero... which is correct, because if we write off Assets we have to write off an equal amount from the other side, of Equity.

Can we arrive at zero by some other road of reasoning?
Well, the two Equity figures add up to \$60. Hmmm, and how much did you pay Third Parties to leave company A? \$60. What Equity was injected into the Group, exited as payment to Third Parties for the buyout. This is why Group Equity ended up zero.

2) Company B bought the shares of company A, but then merged with it. In this case we don't have individual and Consolidated Statements, only one Balance Sheet, which is the same as the Consolidated BS in the previous case.

Leveraged Buyout indeed.


Is there any mechanism to prevent tariff 'exile'? I am expecting a decline in trade between the US and its key trading partners (China, Europe, Canada, Mexico).

Is there any mechanism / force that prevents US trading partners from cooperating amongst themselves to ramp-up trade amongst themselves to compensate for not trading with the US?  Does the US offer goods, which have no substitute?

No, there is no mechanism or force that prevents the USA's (current/former) trading partners from cooperating amongst themselves to ramp-up trade amongst themselves to compensate for reduced trading with the USA.

And the USA offers very few goods or services that couldn't be substituted with goods or services from elsewhere: but note that supply chains don't grow overnight - it takes time and investment to expand supply chains outside the USA.

And as Adam Bailey notes in the comments, countries generally tend to trade more with those closest to them. To replace that trade, with trade with more distant countries, means higher transport costs, longer transport times, and possibly larger cultural and/or linguistic differences to overcome.


Are BLS labor productivity measures in current dollars or constant dollars? I am using BLS labor productivity measures to estimate the impact of automation in the US. Looking through the BLS handbook and online, I haven't been able to determine if the LPC measures are in current dollars or constant dollars. Do you happen to know?

For example, the BLS reports Value of production by industry in $ millions.  Is this a current-dollar or a constant-dollar measure?

BLS page on the topic & with access to data: http://www.bls.gov/lpc/

It depends on which BLS numbers you look at

For example in Table 2 of http://www.bls.gov/opub/mlr/2013/article/industry-employment-and-output-projections-to-2022.htm it gives for manufacturing output:

Billions of chained 2005 dollars            Billions of dollars
      2002        2012                        2002        2012
    4,320.8     4,407.6                     3,848.3     5,604.8

and the first pair of numbers uses a constant dollar (more precisely a chain-weighted dollar) measure while the second pair uses a current dollar measure

For general productivity measures, the BLS says for example at http://www.bls.gov/opub/hom/pdf/homch12.pdf

  Time-series indexes of manufacturing labor productivity (output per hour) and unit labor costs are constructed from three  basic  aggregate  measures:  Total  real  output,  hours worked,  and  nominal  compensation.

So output per hour aims at a real measure of productivity, while unit labor costs divide a nominal figure by a real figure to give something which combines real productivity and nominal wages


What is an example of a utility function where one good is inferior? Say the consumer has a standard convex, monotonic preference over Apples and Bananas.

(Update: I'd like the preference to be as 'standard' as possible. So ideally we have diminishing MRS everywhere and we also have "more is better" everywhere.)

Say his preference can be represented by some utility function $u(A,B)$. He must satisfy some budget constraint $p_AA+p_BB=y$, where $y$ is his income.

Then what is an example of a utility function in which $\frac{\partial A}{\partial y}<0$, at least under some circumstances?

This seems to me a very simple question but briefly Googling I'm unable to find anything.

A good cannot be inferior over the entire income range.

The paper A Convenient Utility Function with Giffen Behaviour shows that for a person with utility of the form:

$$U(x,y) = \alpha_1 \ln(x-\gamma_x)- \alpha_2 \ln(\gamma_y - y) $$

X is inferior if $\gamma_x$ and $\gamma_y$ are positive, $0<\alpha_1<\alpha_2$, and in the domain $x>\gamma_x$ and $0\leq y<\gamma_y$.

Update:
$$U(x,v) = x + \ln(v)$$
If the budget is $w$, $v^* = \min(P_x / P_V, w)$ so for $w>P_x / P_V$ $v$ is inferior sticky good. Realized this is actually a zero income elasticity not a negative one so it is not inferior.

I found another funky functional form for a utility function where one good is inferior but it too has increasing marginal utility of the other good: An Inferior Good and a Novel Indifference Map

$$U = A_1 \ln(x) + y^2 /2 $$ That function gives a crazy indifference map.

The classic example to me of inferior goods are things like cheap food, where delicious food which is much more expensive crowds it out because there is an additional constraint (stomach capacity) which eventually binds. It should be readily possible to make an example where inferiority is a consequence of this second constraint rather than the utility function.

Update with another example:

The paper The Case of a “Giffen Good” (Spiegel (2014)) shows that for a person with utility of the form:
$$ U = \begin{Bmatrix} \alpha X - \beta X^2 / 2 + \lambda Y + \delta Y^2 / 2 & for & 0\leq X\leq \alpha/\beta \\ \alpha^2 /2 \beta + \lambda Y + \delta Y^2 /2 & for& X > \alpha/\beta\end{Bmatrix} $$
where $\alpha, \beta, \lambda,$, and $\delta$ are constant and positive values.

But as in the above functions, this utility function has increasing MU in one good (Y). This is apparently common in Giffen settings:

  In the case of an additive utility function where the marginal
  utilities of all goods are diminishing with the consumption of the
  goods, that is, the marginal utility of income is diminishing, all
  goods are normal and net-substitutes for each other. However, if for
  some good (in our case, good Y) the marginal utility is positive and
  increasing and for the other good(s) the marginal utility(ies) is
  (are) diminishing (in our case, good X), then the marginal utility of
  income is increasing. The good that exhibits increasing marginal
  utility is a luxury good, whereas the good that exhibits diminishing
  marginal utility is an inferior good. These characteristics were
  proved by Liebhafsky (1969) and Silberberg (1972) and wen: used to
  develop the utility function above that illustrates the case of a
  Giffen good.


What does binding mean? I am curious how to solve the utility maximization problem if the representative agent has borrowing constraint.

The constraint $g(x)\geq 0$ is binding if in optimum $g(x) = 0$ rather than the constraint being slack $g(x)>0$.


Who pays externalities? Suppose the state raises taxes in order to internalise externalities. Doesn't the consumer have to pay the additional external costs then, because the prices are raised due to the taxes?

If negative externalities are priced into the market via a pigouvian tax, then those responsible for the negative externalities pay.

As a whole, the public is better off. Firstly because the market will now move to a more efficient situation, and the amount of negative externality will decrease (assuming something other than perfect inelasticity). And secondly, it will also benefit in other ways, through improved public services paid for by the taxes; and/or decreased deadweight loss, achieved by lowering non-pigouvian taxes.

Some market participants will be worse off - the polluter will be paying. Exactly how the burden is spread among those responsible, will depend on the specifics of the situation. Consumers, equity-owners, managers, employees, land-owners, in short anyone involved in the relevant polluting supply chain - each of them might bear some, none or all of the burden, and between them, they'll bear it all.


Can the weierstrass and the Kuhn-Tucker theorems be used to obtain and characterize a solution? Why or why not? Question: An agent who consumes three commodities has a utility function given by:

$u(x_1,x_2,x_3)=x^{1/3}_1+\min\{ x_2,x_3\}$

Given an income $I$, and prices of $p_1,p_2,p_3$. Describe the consumer’s utility maximization problem. Can the weierstrass and the Kuhn-Tucker theorems be used to obtain and characterize a solution? Why or why not?

attempt: I assume $x_i$ represents the quantity and belongs to $\mathbb R_{+}$. You can form the constraints as follows:
$$
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I
$$
You can simplify the objective by noting that for the utility to be the maximum. Hence, the final problem becomes,

$$\
\max_{x_1, x_2, x_3}x_1^{1/3} +x_2 \quad s.t. \\
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I \\
x_2=x_3
$$
Let's eliminate $x_3$ as we know that $x_2=x_3$. The problem simplifies to
$$\
\min_{x_1,\ x_2}\ -x_1^{1/3} -x_2 \quad s.t. \\
x_1 \geq0,\ x_2 \geq 0 \\
p_1x_1 + (p_2 + p_3)x_2 \leq I
$$
$$\
\mathcal L(x_1, x_2)=-x_1^{1/3} -x_2 + \lambda_1(-x_1) + \lambda_2(-x_2) + \lambda(p_1x_1 + (p_2 + p_3)x_2 - I)
$$

Comment: I am unsure how to take this further. I keep messing up the derivatives ( I assume) and when I try to solve for lambda I manage to fail to isolate the lambda variable let alone getting the variables x1,x2,x3. My professor encouraged me to try this complex problem as an “exercise for the reader.” How do I carry this further, or can someone show me a step by step solution from this point onwards?

I assume $x_i$ represents the quantity and belongs to $\mathbb R_{+}$. You can form the constraints as follows:
$$
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I
$$
You can simplify the objective by noting that for the utility to be the maximum, $x_2 =x_3$. Try to reason why this is true. Hence, the final problem becomes,

$$\
\max_{x_1, x_2, x_3}x_1^{1/3} +x_2 \quad s.t. \\
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I \\
x_2=x_3
$$
Can you now set up the lagrange multiplier function? As far as KKT conditions are concerned, I believe they should help because you are trying to maximize a concave function(in $\mathbb R_+$) subject to convex constraints and the strict inequality constraint is linear.

Edit 1: Let's eliminate $x_3$ as we know that $x_2=x_3$. The problem simplifies to
$$\
\min_{x_1,\ x_2}\ -x_1^{1/3} -x_2 \quad s.t. \\
x_1 \geq0,\ x_2 \geq 0 \\
p_1x_1 + (p_2 + p_3)x_2 \leq I
$$
$$\
\mathcal L(x_1, x_2)=-x_1^{1/3} -x_2 + \lambda_1(-x_1) + \lambda_2(-x_2) + \lambda(p_1x_1 + (p_2 + p_3)x_2 - I)
$$
Edit 2: I see solving the Lagrangian can be tough. Let's simplify, we know that all constraints cannot be active at the same time. It will yield an utility of zero.

Case-1: $x_1=0, x_2>0$
You can check algebraically, $x_2=\frac{I}{p_2+p_3}$. Hence, utility$(U)=\frac{I}{p_2+p_3}$

Case-2: $x_1>0, x_2=0$
You can check algebraically, $x_1=\frac{I}{p_1}$. Hence, utility$(U)=\left(\frac{I}{p_1}\right)^{1/3}$

Case-3 $x_1>0, x_2>0$
You can now use the Lagrangian, its much simpler than the original Lagrangian problem because $\lambda_1=\lambda_2=0$
$$\
\mathcal L(x_1, x_2)=-x_1^{1/3} -x_2 + \lambda(p_1x_1 + (p_2 + p_3)x_2 - I)\\
\frac{\partial\mathcal L}{\partial x_1} = 0 \implies x_1 = \left(\frac{1}{3\lambda p_1}\right)^{3/2}\\
\frac{\partial\mathcal L}{\partial x_2} = 0 \implies \lambda = \frac{1}{p_2+p_3}\\
\text{Use the constraint, }p_1x_1 + (p_2 + p_3)x_2 = I \text{ to find } x_2
$$
You can simply finish saying the solution is $\max$ of all three cases. As per the KKT conditions are concerned, one of the three solutions will satisfy KKT Conditions depending on $p_1, p_2, p_3 \text{ and } I$. Note that this is no different from the original problem and hence, KKT condition should be satisfied by one of the three depending on $p_1, p_2, p_3 \text{ and } I$. We could have obtained the same solution using the original Lagrangian. Even there we would have ended up with a $\max$ because of $\lambda_1, \lambda_2$ and invoking KKT.


Equi-marginal Principle Hi the textbook i am studding from simply states that 'the rule for rational consumer behaviour is know as the equi-marginal principle. This states that a consumer will get the highest utility from a given level of in come when the ratio of the marginal utilities is equal to the ratio of prices'. I was hoping someone could maybe give me a bit more intuition behind this. Maybe it is self-explanatory... maybe not.

Suppose there are two goods $X$ and $Y$. A consumer has lots of $Y$ and very little $X$, and as a result his marginal utility of $Y$ is a lot lower than the marginal utility of $X$ (it helps here to think about a convex utility function such as $U=XY$). We could make him better off if we could convert some of those $Y$'s into $X$s (again, this follows from the convexity of utility, a standard assumption. Intuitively, people want more of everything but still prefer balanced consumption bundles to extremes). The question then becomes, "how many $X$s can we buy for each unit of $Y$ we give up?" The answer is that each $Y$ can buy $\frac{P_X}{P_Y}$ units of $X$.Thus, we convert $X$ into $Y$ until the slopes of the marginal utilities equals the price ratio, at which point additional conversion would result in a larger loss from less $Y$ than gain from more $X$.

A more general way of looking at this is through calculus. For a constrained function that is continuously differentiable, the slopes at any interior maxima and minima must be parallel to the slope of the constraint. In this case, the function is the utility function, $\frac{P_X}{P_Y}$ is the slope of the constraint.


China - US Trade War: Holes in this analogy? I have recently listened to a podcast by Peter Schiff concerning the China - US trade war. Schiff to me is an interesting chap; he always puts an interesting spin on things. However, from time to time his rhetoric is very predictable. I knew going into the podcast that he would be pessimistic about the US situation, however I think he may have gone too far with this analogy. I'm paraphrasing here, but it's almost word for word, I'm just condensing:

  To understand who would "win" the trade war between the US and China, let's imagine a simpler model. Suppose there is an imaginary island that has 4 people on it: 1 American and 3 Chinese people. Let's say they have to survive on this island somehow. One Chinese person is tasked with going out and fishing. Another Chinese person is tasked with foraging for fruits and other edible plants. The third Chinese person is tasked with preparing and cooking the food. So what does the American do? Well, he simply eats! Now he doesn't eat everything, he leaves enough for the three Chinese people to sustain themselves, but the American does get the lion's share. This illustrates the precariousness of the US economy; should the Chinese ever decide to kick the US off the island, they have the skills they need to survive. And by analogy, the Chinese can win the trade war since they are making a lot of useful things whereas America's economy is primarily consumption.

It sounds kind of absurd when simplified this way, but I think Schiff has made some excellent points (in a rather humurours way to boot). Let us concede that trying to predict who will "win" the trade war (might be more a lose/lose) is a very speculative matter, so let's cut Schiff some slack. It's not easy to take a risk and stake one's reputation. With that said...

Question: Are there any glaring errors in this analogy? Is there a way to make the analogy more realistic?

My personal critique:

The notion that the Chinese do all the work so the American can gorge himself and get hardly anything in return for themselves seems over the top. When America consumes Chinese products, China is getting USD in return, which is the world reserve currency and they can use that to buy or invest in anything in the world. Surely that's worth something. Of course, it's true that the RMB has been climbing the currency rankings in the past few years, but still, there are limitations on RMB denominated options.
There are certain sectors that America is adept at. America has a powerful agriculture sector that produces much of the worlds wheat and a handful of other crops.

That's what I have so far. I would like to find other errors in Schiff's analogy. If possible, I would like to improve on his analogy and make it more realistic.

A very interesting question

The analogy is wrong in a few aspects

1st of all, the technology. The us produces patents and knowledge in general which china doesn't posess
Furthermore the us government supports innovation and the development of new technologies
Since it intangible, its hard to dismiss, but when you think about it, the US most valuable companies main assets are tech patents

The ingredient of creating technology is highly skilled workers, which in turn, make the us low tech industry  unsustainable, which, in its turn, gives china its advantage

China doesn't have a functioning innovation model, on the contrary, stealing patents are almost a Chinese specialty...

Another thing to consider is the game that china is playing:
The stronger the demand for its goods, the stronger the demand for labor, which increases local salaries, then the product cost itself
And along with the rise of its foreign currency balance that pressures the Yuan's rate to rise,
there is a huge pressure on the Chinese products' price in dollars

China holds it currency artificially low, essentially subsidizing its products at a large cost, and in way, hurting the us economy

So the analogy is not really holding...
The us is not the free rider in this story


Test: Part-time Workers Effect on Unemployment Rate I want to test the causality of part-time workers on unemployment rate.

Should i use part-time workers as a share of total employment or total labour force?
If I run a regression of part-time workers on unemployment rate, there could be reverse causality. So I would have to use 2 stage least square. What are the possible instruments I could use?

This is mostly related to 2):

Not only is there reversed causality, but also potential for omitted variable bias. Identifying causality instead of correlation is something that no econometric method can do for you, you will have to work for that yourself.

For example, you can

Find some proxy that is going to move part-time employment, but not any other variable that could be somehow linked to the unemployment rate
Find exogenous (random?) variation in part-time employment. The most common tool here are (quasi-) natural experiments.


Solving rational expectations model - Sims form I am trying to solve my first ratex model and make some impulse response functions using Dynare. I am following Leeper (1991). This is what I have done so far:

The utility function is $\log(c_{t})+\log(m_{t})$.

I obtain two first order conditions:

(1) $\frac{1}{R_{t}} = \beta E_{t}\frac{1}{\pi_{t+1}}$  and

(2) $m_{t} = c[\frac{R_{t}}{R_{t}-1}]$

Where $R_{t}$ is the gross nominal interest rate, $\pi_{t}$ is the gross inflation rate and $c$ the deterministic steady state value of consumption.

Suppose the monetary authority follows the following rule:

$R_{t} = \alpha_{0} + \alpha \pi_{t} + \theta_{t}$ where $\theta_{t} = \rho_{1} \theta_{t-1} + \epsilon_{1t}$,   $|\rho_{1}|<1$

The fiscal authority follows:

$\tau_{t} = \gamma_{0} + \gamma b_{t-1} + \psi_{t}$
where $\psi_{t} = \rho_{2} \psi_{t-1} + \epsilon_{2t}$

I then substitute the monetary policy rule in to (1) and both policy rules in to the government's flow budget constraint and linearize around the steady state. I end up with the same results as Leeper:

(3) $E_{t}\widetilde{\pi_{t+1}} = \alpha \beta \widetilde{\pi_{t}} + \beta \theta_{t}$

(4) $\varphi_{1} \widetilde{\pi_{t}} + \widetilde{b_{t}} + \varphi_{2}\widetilde{\pi_{t-1}}  - (\beta^{-1}- \gamma)\widetilde{b_{t-1}} + \varphi_{3} \theta_{t} \ +\psi_{t} + \varphi_{4} \theta_{t-1} = 0$

where the varphi's are steady state constants. So far I have just replicated what Leeper has done. Since I would like to make IRF's I believe I have to 'solve' the model. I haven't been taught this at university yet so all I know if from reading online lecture notes. I want to use Sims form, i.e

[![enter image description here][1]][1]

And this is the system I ended up with:

[![enter image description here][2]][2]

I forwarded (4) one period in order to obtain $b_{t+1}$ and just put everything in matrix form.
$\eta$ is the forecasting error from (3).

I apologise for the matrix, I am not sure how to write matrices in TeX but hopefully you get the idea.

Now I want to stack the matrices as the following:

The capital gamma's and phi's are the coefficient matrices from above.

There should be a matrix for the forecasting errors but I am not completely sure how to obtain it. But that is a minor issue at this point. If I have understood correctly, I can solve this by inverting the block matrix and since it is diagonal, the inverse is simply the inverse of gamma and phi. However, since phi_0 is singular I cannot invert it. So I have two questions:

(1) How do I deal with singular matrices in this context? I have seen some papers by Chris Sims where he shows to how to deal with singular matrices but my knowledge of linear algebra is too basic to understand it.

(2) Once I manage to solve the model, can I use Dynare to make IRF's?

I think I have managed to solve it. However, not the way I was initially hoping. I simplified the stacked matrices using the given conditions and some assumptions. Here is my solution:

Eq. (3) I write as $\pi_{t+1} = \alpha \beta \pi_{t} + \beta \theta_{t} + \eta_{t+1}$

Forwarding equation (4) one period and arranging it in terms on $b_{t+1} = -\varphi_{1} {\pi_{t+1}} - \varphi_{2}{\pi_{t}}  + (\beta^{-1}- \gamma)\widetilde{b_{t}} - \varphi_{3} \theta_{t+1} \ - \psi_{t+1} - \varphi_{4} \theta_{t} = 0$

$\pi_{t+1}$ simplified by eq. (3)

$\theta_{t+1} = \rho_{1} \theta_{t} + \epsilon_{1,t+1}$

$\psi_{t+1}$ can be written as its AR(1) formulation as well. Putting the four equations in matrix form results in:

Which is what I was after. However, this made me wonder what was wrong with the method I was trying above. Looking at the top corner of the coefficient matrix (i.e the 4x4 matrix in the top left corner) it is clearly $\Gamma_{0}^{-1} \Gamma_{1}$. But the rest of the matrix I am unsure of.

And question (2) remains, once I have solved for the variables of interest, will I be ready to make IRF's?


Stochastic AK model derivation Consider the following version of the stochastic Ak model written as a Bellman equation:
$$v(A,k)=max\ log(c)+\beta E[v(A',k')|A]$$
$$s.t\ k'+c\leq Ak$$ and non-negatitvities.
$A$ is a stationary first order Markov process. $E[\cdot|A]$ denotes the expectations of · conditional on $A$. We assume that $\beta\in(0, 1)$.
Now we can also show that the value function $v$ can be expressed as $$v(A,k)=\frac{log(k)}{1-\beta}+v(A,1).$$
If we denote $E[v(A',1)|A]$ as $D(A)$, which is a constant (i.e., is only a function of the exogenous parameters of the model and the realization of the stochastic process A, but is not a function of the endogenous variables). Use this and the new equation to substitute into the maximization problem in the Bellman equation. We should get a simple maximization problem in $c$ and $k$.
And what the solution is given as $$v(A,k)=max\ log(c)+\frac{\beta}{1-\beta}log(k')+\beta D(A).$$
Could someone show the steps behind this derivation

I think you may substitute it directly as mentioned?
$$v(A,k) = \max log(c) + \beta E[v(A',k')|A]$$
Applying the value function expression (note period change):
$v(A',k') = \frac{log(k')}{1-\beta} + v(A',1)$
Substituting:
$$v(A,k) = \max log(c) + \beta E\left[\frac{log(k')}{1-\beta} + v(A',1)|A\right]$$
By linearity:
$$v(A,k) = \max log(c) + \beta E\left[\frac{log(k')}{1-\beta}|A\right] + E\left[v(A',1)|A\right]$$
Since $E\left[v(A',1)|A\right] = D(A)$:
$$v(A,k) = \max log(c) + \beta \frac{log(k')}{1-\beta} + \beta D(A)$$


Why does central banks lowering interest rate incentivize more borrowing? I'm a layman trying to understand how the US monetary system works. I'm particularly interested in how the Federal Reserve can create inflation without printing new dollars and putting them in M1. My problem is that I don't get how the Federal Reserve can create inflation through lowering interest rates.
It's pretty intuitive on paper: when interest rates are lower people tend to demand more credit. Borrowing increases the M1 money supply. So we get inflation. I don't have trouble understanding that.
It's the other side of the trade that I don't understand. Why would a bank lend money at very low interest rates if that would create enough inflation that they'd be losing purchasing power? Maybe they do more than lending and it fits into a bigger picture that does make sense. But I can't find a good explanation of this.
Is there anyone that could explain/clarify this to me? I'm not an economist and the answers I find online are rather vague and complex for people like me in my opinion.
Thank you very much in advance,
Joshua

Banks lend because it is profitable for them to lend out money.  Banks do become less profitable in low interest environment, but they are still empirically able to maintain profitability, although there is evidence that goes hand in hand with some increase in risk taking (e.g. see Bikker & Vervliet 2018). Consequently, the direct answer to your question is that banks expand their lending because it is still profitable for them to do so.
Additionally, if central banks would be really determined they could expand money supply by open market operations (e.g. purchase of government bonds) and various other channels, so if a determined central bank would want to expand money supply it can do that whatever the private banks are doing.
Furthermore, inflation does not necessary means that the bank will become worse off. If there is 2% inflation in an economy but bank's profits increase by 5% during the same period then a bank is still better off in real terms.
Lastly, there is not necessarily 1:1 correspondence between increase in money supply and inflation.  For example, even in a simple money market equilibrium model (which determines price level - increase of which is inflation) given by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY$$
Where $M$ is the money supply, $V$ velocity of money, $P$ price level and $Y$ output.
Solving for price level and log-linearizing we get:
$$\ln P = \ln M + \ln V - \ln Y $$
Consequently, ceteris paribus, if $M$ increases by $1\%$ and $Y$ increases also by $1\%$ then the net effect on price level will be zero (and consequently inflation will also be zero). Even in this simple model you will only get inflation if $ \ln M + \ln V - \ln Y > 0$ so when bank increase money supply it won't necessarily result in an equivalent inflation. Furthermore, in more complex models inflation depends on other factors such as people expectations meaning the relationship is not necessarily even proportional, but discussing this in depth would be beyond scope of this answer.


The economics of a "no deal" Brexit A "no deal" Brexit is presented in negative terms.

In such a scenario the UK would set tariff schedules in line with trade strategy and protect domestic industry/agriculture with tariff rate quotas.

The UK would lose tariff-free exports into the EU and the markets with which the EU currently has free trade agreements (the two main ones being Japan and Canada).

The non-weighted average MFN global tariff is 9%. The weighted average tariff for UK exports into the EU is estimated to be around 4.5% in this scenario. Natural movements in currency value are of this order of magnitude.

There would be increased trade friction for the 44% of our exports that are sent to the EU. British exporters would have to follow the customs rules used by other 3rd-country exporters to the EU like China and the USA.

This would be a major change. Most countries export to the EU under these terms. Our reliance on services mean this change would be economically bounded.

The productive base of the UK would re-orient around the new status-quo with some sectors decreasing in competitiveness and diminishing and some increasing and expanding.

The overall success/failure of the new status quo would be determined by the wider economic strategy rather than tariff changes that are mostly small.

Why is a negative long-term forecast necessitated?

Maybe someone can get into more details, but generally speaking

  The range of estimates is large, from a loss of GDP of nearly ten percentage points (in the least
  attractive trade and inward investment scenarios modelled by the Treasury, NIESR and the Centre
  for Economic Performance at LSE)
  1
  to a gain of four points (Minford, for Economists for Brexit
  – a
  clear outlier) – see figure 1.

  The main reason for the differences lies in the assumptions made about shifting from the
  current access that the UK has to the EU single market to a new regime in which the UK
  faces restrictions.

Those were from 2016 estimates/papers.

Also, economists were not terribly good at predicting Brexit-related effects insofar, at least short term; see https://economics.stackexchange.com/a/27492/6210 While the gloom and doom may have been overstated, some effects are apparent already, in some analyses:

Apparently the chilling effect of Brexit on investments may have been a real thing (but that assumes the counterfactual dotted trend was a sure thing).

As a sort of an update, some days ago (Sep 3, 2019) UNCTAD has posted an article on the narrower issue of potential UK losses in a "no deal" scenario due to continuity trade agreements with other countries not yet agreed.

  In relation to exports to countries with which the UK has not yet secured the continuation of preferential access, the UK could face substantially higher MFN tariffs, especially on agricultural products. For example, processed food products could face an average increase in tariffs of about 17 percent. Similarly, apparel, textiles and motor vehicles would also face substantially higher tariffs. In value, most of the losses would be concentrated in motor vehicles (about USD\$750 million) and in chemicals (USD\$200 million).

  [...]

  Among the countries which currently grant preferences to the EU but for which the UK has not yet reached an agreement to grant continued preferential market access, Turkey, South Africa, Canada,  Mexico, Japan, Egypt and Morocco are the markets where the UK is expected to have larger export losses. In particular, the UK is expected to lose about USD\$500 million  of exports in the Turkey market, about 5 percent of its exports to Turkey. In South Africa, the UK is expected to lose about USD\$240 million, equivalent to about 9 percent of its exports to South Africa.

There's an update to the update as well. On Sep 11, the UK has announced an "agreement in principle" with South Africa and with a few other, smaller countries from Africa.


Is there a theory of financial regulation? I wonder whether there exists (even a young) theory of financial regulation in the sense of "how to regulate a financial institution/system in an optimal manner"? I mean, there is experience about several situations which came across in the past, like bank runs, liquidity shortages, insufficient quality of regulatory capital etc. resulting in a crisis and, thus, representing a deviation from the optimal functioning of the financial system. This is then addressed by a regulatory reform which is designed to avoid exactly the experienced situation again in the future, i.e. it is specific to the current problem at hand. Is there something more general? The current approach focuses on ex-post fixing crucial issues, but does there exist a formal normative model or theory about regulating systems like the financial system?
So far, I didn't found something about that but maybe others have?
If not yet, maybe there exists some theory about other kinds of systems which one could apply in a modified version like Cybernetics for mechanical systems or the like?

Jean Tirole just won the Nobel Prize for his studies in regulation in different markets, including the banking market.

Check:

Balancing the Banks:
Global Lessons from the Financial Crisis and
The Prudential Regulation of Banks


Solving for price incease The following table lists the basket of goods in the
  Consumer Price Index for the nation of Astro (Assume 2014 is the base year.)

  Table 6.2
             2014     2014  2015     2015  2016     2016
             quantity price quantity price quantity price
  Sunglasses  8        $9      10      $11   7       $10
  Toothpaste  15        3      18       4    15       4
  Ferrets     6         12     4        15   9        18

  Using the information in Table 6.2, the percent increase in prices over the two year period from 2014 to 2016 is approximately

The correct answer is 31% but I kept on getting 35%.
My solution was (CPI of 2016 - 100)/100

The Consumer price index of a country is defined as:

$$CPI_{t}^{t_0}={{P_{1t} Q_{1t_0}+P_{2t}Q_{2t_0}+P_{3t}Q_{3t_0}}\over{P_{1t_0}}Q_{1t_0}+P_{2t_0}Q_{2t_0}+P_{3t_0}Q_{3t_0}} \times 100$$

where $P$ is price, $Q$ is quantity, $t$ is reference to current year and  $t_0$ is reference to the base year.

So using this formula we get:

$${{10\times8 +4 \times 15+18 \times 6}\over{9 \times 8+3 \times 15 +12 \times 6}} \times 100 \approx 131.2 $$

Now finding the inflation rate we can see (CPI of the base year is always going to be $100$)

$${{131.2-100}\over{100}} \times 100 \% \approx 31\%$$

Hope this is helpful!


How can I prove $∇U(x).D_m x(p,m)= \text{shadow price}$? Why inner multiplication of the gradient of utility function in derivative of demand function with respect to income is equal to shadow price?
This is the equation which is given but I don't know where it comes from, I would be grateful if sb can give me a hint

Assuming certain regularity conditions, the first order conditions for
$$
\max_{x, \lambda} U(x) - \lambda (p \cdot x - m)
$$
are
\begin{align*}
&D_{x}U(x(p, m)) - \lambda p = 0
\\
\text{and} \quad
& p \cdot x(p, m) - m = 0.
\end{align*}
Moreover $x(p, m)$ will be differentiable with respect to $m$ at $(p, m)$, and this fact together with the second equation implies
$$
p \cdot D_{m}x(p, m) - 1 = 0.
$$
So, by the first equation,
$$
D_{x}U(x(p, m)) \cdot D_{m}x(p, m)
=
\lambda p \cdot D_{m}x(p, m)
=
\lambda.
$$
The derivative $D_{x}U(x(p, m))$ of the utility function at $x(p, m)$ corresponds to $\nabla U(x)$ in your notation.


What is the interest rate that on the vertical axis of money markets? The money market diagram showing liquidity preference and money supply intersect at an equilibrium level of interest rate, but what interest rate is it? Is it the base rate (I presume this is the rate at which commercial banks lend out loans to borrowers) or FED Funds Rate/LIBOR? Or does it simply refer to interest rates in general?

The thing to keep in mind is that these diagrams refer to simple teaching economic models. These models do not necessarily reflect the complexity of the real world.

  The money market diagram showing liquidity preference and money supply
  intersect at an equilibrium level of interest rate, but what interest
  rate is it?

Within the teaching model, there is a portfolio allocation between "money" and some interest-paying instrument (labelled "bonds" or "bills"). The interest rate is the interest rate paid on that hypothetical instrument.

The usual interpretation is that this the short-term "risk-free" rate of interest. (Risk-free implies is that they are assumed to be free of default risk.) In the United States (for example), there are a number of such instruments: Treasury bills/bonds, the fed funds rate (domestic interbank rate), OIS, repo, interest-bearing reserves, etc. These instruments have interest rates that are generally close to each other.

Simplified models that consist of a pair of intersecting lines will not be able to deal with the fact that such instruments have a variety of maturity dates (from overnight to 30 years).

The general assumption when discussing these models is that private sector borrowing rates will remain close to this risk-free curve. The fact that this is not always true is another part of reality they cannot deal with. That said, credit spreads for high quality borrowers tends to be less volatile than the level of the risk-free rate, and so the risk-free rate does roughly capture the general tendency of interest rates.

  Is it the base rate (I presume this is the rate at which commercial
  banks lend out loans to borrowers)

The only "base rate" I can think of is a rate associated with central bank dealings with banks. The prime rate is a benchmark borrowing rate set by banks for dealing with customers. For example, people have loan interest rates that contractually are set at "prime + x%".

  FED Funds Rate/LIBOR?

FED Funds represents reserve trading between domestic banks; it is considered a risk-free rate (no credit premium).

LIBOR is a rate for unsecured lending between international banks (in London). It has a credit risk premium embedded in it.


Why do most function images take the form of a curve? I always see curves (such as in dark blue below) and not any other type of (function) image. May I get a reason for why it is always like that?

This figure is only for representation.

Your final line

This figure is only for representation.

pretty much answers your question.
When explaining these concepts you want to draw something that is easy to understand, i.e. does not have too many irregularities but is also not too regular.
Linearity is a special attribute of functions. General curves show that there is usually no need for this assumption.
Continuity is a frequent though not omnipresent assumption in economics.
Rather than throw in a few points of discontinuity and provide reasons for them, it is easier to explain general concepts with continuous curves. This does not mean that most functional relationships are indeed continuous; there are plenty of counterexamples, but where this is important, there are usually discontinuous graphs and explanations thereof.


How does total money in the economy changes? I don't understand why total money in economy increases. Where does this money come from?

Fiat money in modern societies is usually printed (minted is the term used for stamping coin) under the authority of a particular institution, usually called Central Bank, Federal Bank, Federal Reserve etc. In different countries there are different rules that apply concerning its function and independence from central government.
Central Banks also are able of conducting monetary policy with various means and measures. In fact, more than anything, a Central Bank is charged with the responsibility of regulating the amount of money circulating in the economy.
A central bank can augment or decrement the amount of money circulating by using (1) a particular exchange rate or by directly influencing (2) money supply.
Examples:
(1) A Central Bank can change the exchange rate with which it loans commercial banks (the ones that the public most often interacts with), thereby affecting their interest in giving loans and/or the public's interest in saving or taking loans. This effectively changes money supply / the amount of money circulating in the economy.
(2) A Central Bank can buy (or sell) government bonds from (or to) the general public. This is called Quantitative Easing. Since that means that either it injects new money into the economy or that it vacuums existing money out of it, it directly changes the amount of money in circulation.
Please note:
There are many more examples to be given and a lot more clarification. Further reading can be done with my textbooks of preference, Mankiw's Macroeconomics and McCallum's Monetary Economics.


Is trading in the commodity futures much more riskier than trading in stock market futures? My understanding is that the price of a stock at the stock exchange is determined by supply demand mechanics during trading hours, and the price of futures is determined by the price of the underlying stock. In effect its the price of the underlying stock that controls the price of the future(Black–Scholes model) The price of the stock-future is strongly coupled to the price of the underlying stock price.

Consider the commodity exchange where the  futures price of a commodity is determined by supply demand during trading hours and is not directly determined by the real price(current price of commodity available to the public).

Contrast the scenario at the stock exchange with that of the commodity exchange. As an example, if the current real price of copper is Rs 340 per kg in the shops. The price of the copper futures is in no way directly determined by real price of the commodity the way the price of a stock-future is determined by the underlying stock. Hence the futures price of commodity is weakly coupled to the real price of that particular commodity. Hence it may be said that the price of commodity futures is much more volatile/speculative in nature than price of a stock future. Correct me if my understanding is wrong.

Let's start with the statement -

'Consider the commodity exchange where the futures price of a commodity is determined by supply demand during trading hours and is not directly determined by the real price'

first, this statement is not accurate. Not everyone that buy a commodity future ever intend to take delivery.

Second, you need to look at financial future vs. Physical future. Most of the time they move in tandem (correlation nearing 1). However, near delivery, they become less correlated. In fact, physical commodity carries delivery risk. If you have not disposed of the future in time, you'll have to take the delivery. In that case, you have to deal with storage cost.

This leads to the third point - convenience yield. Hard to quantify, hard to hedge (unlike stocks or other financial instruments) - where would you store 1MM barrels of oil today? At what cost?

Last point is - what is 'real price'? The cost of producing a barrel of oil? 1 ounce of gold? If so, how would companies (and in turn their stock) profit?

Now, to the question itself - to truly assess whether commodities are more volatile then other financial instruments you have to define several parameters including observation period, asset classes etc. If you don't you cannot make a proper comparison.

Finally, Commodities post 2009 - part of the drop in commodity prices could be attributed to the fact that due to costs and regulation banks are not such big participants in the assets as they used to be. Here, you could say that 'lack' of interference is simply bringing prices to where supply and demand dictates.

Now, compare all of the above to recent price drops in Twitter and Linked in stocks. With that in mind, Commodities look 'stable'...


Do credit cards create more printed money As far as I know, when people take a loan from a bank, most of the loan value is electronically printed money, i.e. money that did not exist before.
Is it also what happens with consumer credit cards?

If so, are we not shooting ourselves collectively in the foot by using those cards?

All this fabricated money, eventually depreciates the value of our hard-earned money.

One initial point: you refer to "printed money", which would normally be restricted to currency in circulation (notes and coins); the parts of the money supply that are electronic are literally not printed.

Borrowing on a credit card creates a credit card receivable, which is not normally considered part of most money supply figures. However, if it were part of a securitisation, it might eventually show up as part of the wider money supply aggregates (M3). (The securitisation ends up funded by a money market fund, and money market funds are typically part of "wide" money supply definitions.)

Are we collectively shooting ourselves in the foot as a result of this fabricated money?

If you think the only objective policy is to preserve the value of the currency unit, perhaps. The relationship between money supply growth and inflation is debatable, but it is seems safe to say that extremely rapid borrowing by the non-financial sector is associated with higher inflation.  However, if the objective is to enhance output and employment, not really.

Credit cards are just another form of credit. The growth of modern capitalist economies is associated with credit expansion. It may be possible to have a growing economy without credit growth, but it would be very difficult. Investment could only be funded by profits, and it would be difficult to offset the withdrawal of financial assets from circulation by the savings desires of households. Without credit, the only mechanism to recirculate savings to the business sector is via equity injections. In practice, direct equity investment is not a significant source of funding for the business sector. That is, stopping credit growth chokes off funding for businesses in practice.

In other words, we can say that society faces a trade-off between monetary stability and growth; the exact nature of that trade-off is somewhat fuzzy.


How can Factor Income paid to abroad be negative? There was a question in my book in which the factor income paid to abroad was given as negative .

I guess here negative means that we are not paying but receiving from them but how can it happen that we are receiving income from normal residents of other countries ?

Is it true that factor income paid to abroad can be negative or is it only in theory ?

I suspect that you are looking at an economic description which contrasts factor incomes with current transfers.  That is slightly old fashioned, and the contemporary terms are primary income and secondary income in the balance of payments accounts (a similar change in the national accounts involved going from what was called GNP to GNI - gross national income)

For example, for the United Kingdom, you can find data in the UK Balance of Payments Pink Book, for  primary income in Chapter 4 and secondary income in Chapter 5

Primary income includes:

compensation of employees (e.g. pay of cross-border workers and short-term migrants)
earnings on direct investment (e.g. profits of foreign subsidiaries - in theory this can be negative if they are loss-making)
earnings on portfolio investment (e.g. share dividends and bond coupons)
earnings on other investment (e.g. interest paid on bank loans and deposits)
taxes and subsidies on products and production (only recently reclassified to primary income and possibly not in your factor income)

By contrast, secondary income (so presumably not in your factor income) includes:

remittances by long-term migrants and current transfers by others
insurance premiums and claims
cross-border taxes on income and wealth etc. and social security contributions and benefits
overseas aid
other intergovernmental current transfers and international organisations

Exports and imports of goods and services are treated separately: in the UK Pink Book, goods are in chapter 2 and services in chapter 3

In each case there are credits (income from abroad) and debits (income due abroad), leading to a net figure which can be positive or negative.  Add all of these up and you get the current account balance


If interest rate increases and consumption in the present increases, is present consumption a normal good? I recently wrote an economics quiz and one of the questions was:

  Suppose "r" is the interest rate that prevails between the present and
  the future. If "r" increases and a household chooses to consume more
  in the present, then:

I answered that since the price of current consumption increases and the consumer consumes more, current consumption must be an inferior good.

However this was marked incorrectly for me and the correct answer was current consumption must be a normal good. I'm unsure of why this would be the correct answer, could somebody explain the reasoning?

Edit: The five options were:

  A) it is an irrational decision.

  B) consumption in the present must be an inferior good.

  C) consumption in the present must be a normal good.

  D) consumption in the future must be an inferior good.

  E) consumption in the future must be a normal good.

I chose chose B but the correct answer was listed as C.

First, the definitions:

A normal good is one whose demand rises when income rises.
An inferior good is one whose demand falls when income rises.

I will use $c_1$, $c_2$, and $y$ to denote current consumption, future consumption, and (lifetime) income.

Now, if $r$ rises, then as usual there are two effects, the substitution effect (SE) and the income effect (IE). We are given that the Total Effect (TE) is that $c_1$ increases or equivalently, that TE is positive.

Let us write $$TE=SE+IE>0.$$

We now look at each of the two individual effects:

Substitution Effect (SE). You correctly identified the cause of this effect -- "the price of $c_1$ increases". And so, the SE is that the consumer should substitute out of $c_1$ and into $c_2$. That is, the SE unambiguously says that $c_1 \downarrow$. We write $SE<0$.

However, you then made the mistake of concluding that this shows $c_1$ is inferior. But remember that whether a good is inferior or normal depends on responses to changes in income. So, the SE has nothing to do with whether a good is inferior or normal.

Income Effect (IE). We first note that since $$TE=SE+IE>0 \text{ and } SE<0,$$ it must be that $IE>0$.

Here there are two possibilities. I very much suspect the person writing this question overlooked possibility #2 (in which case the answer should be B) and went only with possibility #1 (answer C).

If the consumer is a lender (or saver), then an increase in $r$ implies an increase in $y$. In which case, $IE>0$ if and only if the good is normal. Hence, the answer is C.
However, if the consumer is a borrower,  then an increase in $r$ implies a decrease in $y$. In which case, $IE>0$ if and only if the good is inferior. Hence, the answer is B.


Multi-item multi-unit matching markets This is a reference request.
I'm interested in auction design problems of the following form:

- Consider one seller and many buyers.

- The seller seeks to sell multiple items where each item has multiple units.

- Each buyer is interested in getting exactly one unit from only one item.

- The seller wants to maximize the social welfare of all buyers.

Has this problem been studied in the literature? I have tried looking at combinatorial auctions, matching markets, and multi-parameter markets but so far haven't been lucky.
I'd appreciate any hints of direction where to look. Thank you!

I gave you an extremely vague lead in my other comment. Thinking about it a bit harder, I beieve you are right with having a look into the matching literature which I know a bit less.
Here is a setting that might be of interest: Kelso & Crawford, Econometrica 1982.
They study $m$ workers (=buyers in your setting) and $n$ firms (=items), where a worker can only work at one firm, but a firm can hire many workers. Firms pay salaries to workers (=accept payments for a unit). If that is a setting that appeals to you, go straight to "Matching with contracts" by Hatfield & Milgrom, AER 2005.


Does a store suffering increased theft generally cause higher prices? If a store suffers an increase in theft, will it generally lead to higher prices at that store?
My answer is that prices should have already been set to maximize the trade off between profit-per-sale and volume sold, so that if the store experiences increased costs of business, they cannot recover the loss by passing it onto consumers.  They HAVE to eat the loss, unless prices were set irrationally to begin with (in which case the theft only prompted the store to fix their mistake).
However, the majority of people and articles seem to take it for granted that a store will pass increased costs, such as theft, onto customers.

prices should have already been set to maximize the trade off between profit-per-sale and volume sold

But profit-per-sale depends on costs, which depends on the theft numbers, so if theft increases, the equation changes.


Finding pure-strategy subgame-perfect Nash equilibria I'm interested in finding the pure-strategy subgame-perfect Nash equilibria of the game below. What is confusing me is that after player A chooses between reducing and not reducing his end payoffs, the game is not sequential anymore, but simultaneous. How do I go about finding the subgame-perfect Nash equilibria?
I thought of first finding the Nash equilibria in the two simultaneous-move subgames and I got 4 equilibria in total (written as the outcomes):
$(2,4)$ and $(4,2)$ for the left subgame, and
$(1,4)$ and $(3,2)$ for the right subgame.
From this, I deduced what player A would choose in the first stage (don't reduce or reduce), based on possible payoffs, so I got the following two subgame-perfect Nash equilibria:
$ \{Don't\space reduce, a_2, b_2\}$, and
$\{Reduce,a_2,b_2\}$.
I'm not sure if this is correct. After determining the Nash equilibria in the subgames, I get confused trying to determine what player A will do in the first stage. Am I doing this right and can someone explain how to approach solving this?

Because you are looking for subgame-perfect equilibria, it is the correct approach to solve this game backwards. There are 2 proper subgames, and you identified the correct Nash equilibria there. However, note that you specified the payoffs, not the strategies. The correct formulation would be $(a_1,b_1)$ instead of $(2,4)$.
Next, you substitute the subgame perfect payoffs for the subgame and check for the optimal selection of A in the beginning. It is important that an equilibrium is always a full strategy profile. That is, it needs to specify an action for every information set, regardless of whether it is reached on equilibrium path. A has three actions, one at the beginning, one in the left and one in the right subgame. B has two actions, one for each subgame. So a strategy profile would be of this form [(first,left,right),(left,right)].
You have to check for all of the combinations. If you consider payoff (2,4) on the left and (1,4) on the right, you have a SPNE [(don't reduce,a1,a1),(b1,b1)]. Next, consider (2,4) and (3,2), you have a SPNE [(reduce,a1,a2),(b1,b2)]. You also have two more SPNE: [(don't,a2,a1),(b2,b1)] and [(don't,a2,a2),(b2,b2)]. That is, there are four SPNE.
If you do not specify what happens off path, you cannot evaluate what happens when player A deviates in the first stage and thus cannot determine whether no profitable deviations exist.


What is the purpose of measuring GNP? I know that the GDP (the value of all final goods and services produced within a country during a given period of time) is useful for determining the productivity of a nation, the size of the nation's economy, and the standard of living.  The GNP (the value of all final goods and services produced by individuals belonging to a particular nation, both domestic and abroad, during a given period of time), I believe, is used in very similar ways.
Overall, however, it seems that the GDP gives similar information and is easier to calculate  than the GNP.  That being said, what is the point of calculating the GNP?

In 1991, when the Bureau of Economic Analysis made the switch from GNP to GDP as "their primary measure of U.S. production," they indicated the continued importance of GNP this way:

  GNP, however, continues to be a useful concept. Because it refers to the income available to U.S. residents as the result of their contribution to production, it is appropriate for analyses related to sources and uses of income. For example, saving rates are normally expressed as a percentage of income, and GNP is the more appropriate measure for this propose. In addition, GNP is better than GDP for analyses that focus on the availability of resources, such as the Nation’s ability to finance expenditures on education.


Economies of scale: when is it disadvantageous? So, I watched a video on economies of scale. It makes sense to me but I'm wondering, is there a point where say doubling the production rate makes the product even more expensive? How can I figure out the equilibrium point and thus maximum useful rate for producing a product assuming certain restrictions on availability of product, maximum distance to customer, value of ingredients, and other factors? I imagine it would be something like this:

Exponential decay in price until certain point is reached

Stops decreasing right at relative price = 0

Exponential growth after the equilibrium point as relative price goes in the positive direction.

I would give you a simple answer: when the marginal cost is equal to the marginal income. This would be the equilibrium and beyond that the company would lose money.


Are savings necessary for economic growth? So, I've had this confusion for a long time. We all know how spending is absolutely vital for economic growth. However, at the same time, are savings necessary too?

My initial opinion was "no". In a very particular argument, someone argued with me that "since the money that goes into the companies as investment is nothing but the savings money,savings are important too"

I feel that if companies are getting all they want from direct profits (consumer spending), say with 100% consumer spending, they wouldn't need investments.

Would I be right in my argument? Or am I wrong?

I don't know if you're arguing a theoretical framework or whether saving is important for real economic growth. In theory a special case where all consumers would spend 100 % (MPC=1) of their income is possible to argue - the framework would be loaded with questions - it might, for example, make banks redundant.

In basic economic models savings is often considered equal to investment (you see a variation of S=I in many macroeconomic models) which means that all saved income is used for investment and therefore expected to expand the economy for future periods. In real life the relationship isn't quite this straightforward, but the basic idea still holds.


Why is VAR analysis all linear? Why not nonlinear? When doing VAR analysis, it is almost always a linear form that gets used. Is there any justifying reason (most DSGE models are non-linear unless linearized) to use a linear form?

First, it is important to note that there is a substantial literature both developing and using nonlinear VAR estimation (for example, see papers here, here, here, and here).

The reasons linear VARs are seen a lot, though, are similar to the reasons that least squares (in its varying forms) is seen a lot. The model is very transparent and analytically tractable. This is a benefit for both pedagogy (analysis can be done on linear VARs just using lag polynomials) and for interpretation of results. You also don't run in to the concavity and global vs. local solution issues you do with big nonlinear problems, which can make your results more credible in many circles.


Effects of an expected increase in the inflation rate on the market for loanable funds I am supposed to answer a question in my economics class and was wondering if someone could explain it out for me. The question is,

  What is the effect of an increase in the expected inflation rate on the loanable funds market?

This question goes against what I was taught. I was taught about the Fisher Effect where the real interest rate is not effected by changes in expected inflation and that the quantity of loanable funds does not change with this rise in effect inflation. So, my instinctive answer upon reading the question would be to answer no effect on quantity or real interest rate and that there would be a rise in nominal interest rate. However, this was a multiple choice question and that wasn't even close to one of the answers.

I think I got the answer right by saying

  It decreases the demand for loanable funds, thereby increasing the nominal interest rate.

All of the answers involved a shift in the demand curve for loanable funds. My question is if anyone could explain to me why there would be a shift in the demand curve instead of what we would expect based on the Fisher Effect?

The Fisher Hypothesis is a standard example of the approach that argues that nominal magnitudes just reflect the real economy, they do not affect it. Denote $r$ the real interest rate, $i$ the nominal interest rate, and $\pi^e$ the expected inflation. Then the Fisher Hypothesis states that

$$i = r+  \pi^e$$

I write it this way to emphasize that it is the nominal interest rate that depends on the real one. In this framework, the real interest rate is determined in the real economy, say the marginal product of capital. So an increase in expected inflation will have the effect of increasing the nominal interest rate, and nothing else.

How is this rationalized?

The demand schedule for loanable funds is drawn with respect to their price. The price of loanable funds is the nominal interest rate. Magnitudes like expected inflation, if they have an effect, is to shift the whole demand schedule.

In a standard diagram, and with supply curve assumed unaffected, your answer appears strange: since when a "decrease in demand" (shift to the left of the demand schedule), leads to an increase in the equilibrium price? Intuitively, when customers start to demand less for any given price, this will lead to a lower equilibrium price, not higher. But the second part of your answer asserts that the price, i.e. the nominal interest rate, will increase due to this downward shift in the demand schedule.

Before any re-equilibrium effect, a rise in expected inflation reduces the real interest rate that prospective borrowers face. They may pay the same nominal interest rate, but the financial burden is smaller, due to the inflationary expectations: loans have just become cheaper, in real terms (while the current purchasing power they represent has not been affected).

So inflationary expectations shift the demand schedule upwards-outwards.

Now, it would be arbitrary to keep the supply schedule fixed. If expected inflation increases, prospective lenders should have a tendency to increase their current consumption, thus reducing the available funds: the supply schedule shifts upwards.

The Fisher Hypothesis says that these movements will lead to an increase in the equilibrium nominal interest rate, and the increase will be equal to the increase in expected inflation, since the real interest rate "should" remain constant.

$$\Delta i^* =  \Delta \pi^e \implies \Delta r =0$$

Moreover, the equilibrium quantity of loans will be unaffected, (and so real magnitudes like consumption will be unaffected).

If no choice reflecting the above effects was given to you, and if "none of the above" was not an option, then the question was deficient, or it postulated some additional assumption.


Should Company B enter the market in the following cases Say Company A has a monopoly producing product E, at a constant marginal cost of $3$ USD. Say the ideal number of units produced is $1$ unit which produces a profit of $2$ USD (=$P_{A}$).

Next, Company B wants to enter the market and produce product E at a marginal cost $3$ USD, but it has initially invested $\frac{1}{2}P_{A}$ in order to enter the market.

Question:

$1.$ Under Cournot Competition, should Company B enter the market. Why/Why not?

$2.$ Under Bertrand Competition, should Company B enter the market. Why/Why not?

Ideas:

$1.$ No, since we are in Cournot competition, the price is determined by the total units that both Company A & B produce together. If Company B were also to produce, it would drive the price down as a result of excess supply, eventually forcing the price below the marginal cost, thus not profitable

$2.$ Yes, the price is driven down until the marginal cost. Although Company B will earn $\frac{1}{2}P_{A}$ less than company A.

Do my answers suffice, or rather, are they correct, and touch on the right point?

Knowing that demand is linear, we can deduce from the two points on the demand curve, $(q,p)\in\{(1,2),(2,3)\}$, that the demand function is $p=7-2q$, which is consistent with the Company A's profit maximizing quantity being $2$ units (assuming no fixed cost).

If B enters the market and competes in quantity, the Cournot outcome is $q_A=q_B=\frac23$ and $p=\frac{13}3$. Taking into account B's fixed cost of $1$ for entering the market, its profit is
\begin{equation}
\left(\frac{13}3-3\right)\frac23-1=-\frac19<0.
\end{equation}
Hence it's not profitable for B to enter.

If B enters the market and competes in price, the Bertrand outcome is $p_A=p_B=3$. In this case, revenue is equal to the cost of production, so B makes zero profit (absent the entry cost). However, given the positive cost of entry, B would be making a loss if it enters the market.


Why does entitlements leads to lower US productivity? In a recent Bloomberg interview, Alan Greenspan suggested that entitlements leads to lower productivity, can you please explain it?

What does 'capital stocks' mean?

Does he means that because we are spending a lot on health we don't have money to invest in other things?

Thank you

  ALAN GREENSPAN:  Well, it's unfortunately very simple but not a good story.  It's turning out that we're using more and more people at the
  margin to produce less and less.  Productivity, which is output for
  man hours as we conventionally measure it, is running at a very low
  rate of increase.  And that's the critical variable in the economy
  over both the short-term and the long-term.

  So what we are confronted with right now is a very serious problem
  caused by the fact that capital investment is falling far short of the
  requirements necessary to keep the capital stock growing, and
  therefore productivity.  It is not working.

  LIU:  So how do we reverse that?  What exactly is behind that,
  Chairman?

  GREENSPAN:  Well, I've on many occasions indicated that the best way
  to standard this is to track it backwards.  There's a very tight
  relationship between the stock of nonresidential, private stock and
  output per hour.  They move together parallel all the time for very
  good reasons.  But that capital stock requires capital investment.
  And capital investment, in turn, is being crowded out by a very
  substantial increase in government expenditures.  Basically,
  entitlements -- because both parties, both the Republicans and the
  Democrats, don't want to talk about it largely because it is
  considered the third rail of American politics.  You touch it and you
  lose.

  LIU:  Well, so that makes perfect sense.  So it might come down to
  cutting some costs, right, to cost controls, Chairman.  Top of your
  list, I know you've mentioned entitlement spending.  You know, you've
  got Medicare, Social Security.  The No. 1 thing that you think that we
  need to cut our costs on is what?

  GREENSPAN:  Well, the basic issue is the entitlements and the reason
  it's a problem is that people put money in their own funds and their
  employers' funds plus interest and that is what they perceive they et
  back , and therefore they are entitled to it because it is their
  money.

  The only problem is that's not what we are doing.  We're not creating
  enough funding for the Social Security trust funds, and the same thing
  goes for Medicare Part A.  And we're not funding this.  So long as we
  are not funding this, we are dollar for dollar crowding out capital
  investment.

"Well, the basic issue is the entitlements and the reason it's a
  problem is that people put money in their own funds and their
  employers' funds plus interest and that is what they perceive they et
  back , and therefore they are entitled to it because it is their
  money."

He's saying people think that they receive the income that they are putting into the program.  For example, a common perception that people have about social security is that it is simply a forced savings program: I put in \$50, that \$50 is put into a vault somewhere, then pulled out later, and given back to me for my retirement.

That's not how it works. I put in \$50, and we spend it immediately on someone's current retirement, or a number of other pre-approved (and sometimes seemingly unrelated) programs. We then hope that some new young person puts in another \$50 in time for my retirement.

This is particularly a problem as that the number of retirees is going to grow while the number of young people putting money into social security is going to shrink. In fact, this is a problem if productivity declines in any way, and the amount going in is limited or restricted, or fails to grow.

Questions 1/3: He is not saying that entitlements cause lower productivity in this statement-> he is saying entitlements will have problems -because- of lower productivity (probably from lower population, as has been popular to discuss for quite some time).

Question 2: Capital stock is the collection of tools available for production.  (Hammers, technical know-how, computers, assembly lines.)


Forward rate discounts I'm working with the following task:

"You are convinced that the bond market is dominated by long-term investors. Hence, you have your own view on the liquidity premium/discount that forward rates embody. Given that, do you think that a duration of 3 years for this portfolio is a good idea or a duration of -3 years would be better?" (The provided yield-curve is upward sloping).

First, liquidity discount and premium are in contrast to each other?

Second, could anyone explain why/if the forward rates embody a liquidity discount because the market is dominated by long-term investors?

What does it involve if the forward rates embody a liquidity discount, and what will this imply for the future expected rates?

This is the solution, but it doesnt make much sense to me:

"Market dominated by long-term investors ⇒ Liquidity discount ⇒ E[r] > f
Upward sloping yield curve ⇒ f > y0
In other words, forward rates above current yields. And, on top of that, we need to take into
account the liquidity discount to obtain the expected short rates. Hence, future interest rates are expected to increase and, thus, one would prefer a portfolio with a duration of -3."

What are your assumptions about a market dominated by long term investors?

For example if the market is dominated by investors does that mean demand outweighs supply so that yields are generally lower?
Does long term mean this level of demand for bonds will persist for a long time or that the investors are predisposed to buy maturities of durations longer than another?
Do your long term investors have the ability to buy short term maturities and roll them on an on going basis to allow them the possibility of investing for the long term via multiple short dated instruments?

  What is the liquidity premium/discount?

Is your market very large and liquid (like US or UK treasuries), i.e. you expect prices to be more transparent and have narrower bid-offer spread so that execution costs are small?
Is your market illiquid because your investors are buy-and-hold so that there is effectively no secondary market (like SEK or NOK corporate bonds).
what impact does each have on the supposed prices of securities.

  What about exogenous factors?

are you basing the answer to the question solely on this one aspect of knowledge and ignoring all other factors, such as current yield levels and view of the direction of interest rates?

I know this isn't an answer to the question but I have seen first hand how models do not reflect reality and this model seems incredibly simple for this type of analysis. I don't agree with the solution because I don't agree that the 'implications' will always be upheld, and there are 3 of them before the conclusion with scope for much argumentation. This is my own pragmatic view and not necessarily consistent with any of the academics that you are being taught so take it with a pinch of salt.