Can a currency with constraints on the amount a person can posses boost the economy? So there was the following proposition: Create a currency with the following contraints:

  Each person may only own x amount of this currency. Gaining more of this currency is not allowed. Using a cryptocurrency, such a system could probably be crafted.

So one could probably achieve a similar system by creating an appropriate tax-system. However, what would be the outcome of such a currency. Could such a currency boost the economy? The main target of such a currency would be to drastically reduce the gini-Coefficient.

Some implications I can think of:

A rich person would have to

Reduce work and hence let someone else work for him (increase employement)
Spend more money so he/she can keep up his/hers income (boost economy)

A poor/unemployed person would (could)

Profit from social security, since increasing cash flow leads to (possibly) higher tax-income.
probably get faster a new job, since profitable companies can only spend more cash on either assets or empolyees

Reduce work and hence let someone else work for him (increase employement)

But that won't necessarily work.  Say the person is Bruce Springsteen.  He's making enough from royalties to hit the max.  So he doesn't need to tour at all.  But if he doesn't tour, there isn't necessarily someone else that can tour instead of him.  It's just as likely that his fans will just stay at home and play recordings.

Even worse, remember that a Springsteen concert involves many other people that either don't make money from his recordings or not as much:

His band mates.  He's the face of the band and may well make the largest share of the proceeds.
Roadies.  They make no money from recordings and are only paid for their duties on the live show.
The venue crew.  Ticket sellers, concessions, security, cleaning, etc.  None of these get any money if he doesn't play live shows.

Beyond that, there are ways to get around such a limit.  Instead of buying things with the currency, barter your services directly for what you want to obtain.  Or have your employer pay you in benefits rather than salary.  So you and another person may have the same salary, but she or he gets driven to work by a limo paid for by the company while you drive your own car.

  Spend more money so he/she can keep up his/hers income (boost economy)

It seems unlikely that most rich people actually keep large cash balances.  They either invest or spend their money already.  So any boost from this is going to be minimal.  Another problem is that this boosts the effective money supply, which is going to cause inflation.  So the government will print less money in response, which of course removes the boost.

  Profit from social security, since increasing cash flow leads to (possibly) higher tax-income.

This seems unproven.  As I said earlier, it could just as well reduce employment.

  probably get faster a new job, since profitable companies can only spend more cash on either assets or empolyees

This doesn't follow from what you wrote, but let's assume that you do something else to make this so (e.g. limiting currency accrual of companies as well as people).  Then how do companies get investment capital?  If they can't pay dividends, then who buys stock in the company?  How does a company start and grow?  Realize that many companies have a minimum size.  FedEx is one of the most egregious.  They need to be nationwide.  They don't work as a local concern.  But other companies have a similar problem.  You can't build your own car and sell it to compete with Ford.  It would take one person years to manufacture a car and how would you pay for parts and materials?  Design?

So instead of getting a new job faster, this would mean that new jobs would be quite rare.  You can only get a new job if an existing company expands.  And it could only expand in fits and starts.  They'd have to buy land on the layaway plan.  Then put up the building in fits and starts.  Buy one machine here and another there.  Then, after months or years of preparation, they can finally start hiring employees.

Under this rule, a company can't save for a rainy day.  So if business is slow, it might go out of business entirely.  All of its employees are laid off.  The best find jobs quickly, possibly displacing other workers.  The lower quality workers stay on the job market.


The TYPICAL law of motion of capital Consider a typical macro firm set-up where the capital can be produced from output goods using a linear technology. It costs some X units of output good to make a unit of the capital, and the capital production is instantaneous. For simplicity, let the numeraire be the output good.

The typical law of motion of the capital is (with a geometric depreciation rate):

$k_t=k_{t-1}(1-\delta)+i_t$

The firm's technology meets the typical strictly concave, increasing, Inada, and TFP conditions: the amount of capital invested by a firm at time $t$ produces output $y_t$ at time $t+1$ where $A>0$ denotes the TFP.

$y_{t+1}=Af(k_t)$

$\textbf{My question}:$
How do you understand the $\textit{investment TIMING}$ in the law of motion of capital? I read it as the capital that is available today is the sum of what you have carried over from yesterday as depreciated capital plus how much you invest. But how do you interpret this rearrangement:

$i_t=k_t-k_{t-1}(1-\delta)$

So if I stand at $t$, then I have the following sources for capital, correct?:

(1) $(1-\delta)k_{t-1}$: This simply what I carried over as depreciated capital

(2) $k_t$: The capital I obatained from my linear production technology using the capital I used yesterday. (The remainder of unused capital is depreciated and carried over as in (1))

But why is (2)-(1), today's firm investment?

$k_t$ is your capital after investment, so if you subtract the capital you carried over from last period, $k_{t-1}(1-\delta)$, you obtain the amount that must have been invested in order to have $k_t$ of capital today.

Remember that $k$ is a stock variable, while $i$ is a flow variable. This is why the flow $i_t$ is the difference between the current and the former stock: $k_t-k_{t-1}(1-\delta)$.


Are there any drawbacks to a hypothetical climate policy?- Carbon tax for reducing Income tax Disclaimer: I do not have a formal education in economics

Here is the idea of my hypothetical policy: graduated over a period, say about 10 years or longer, the income tax is phased out and a carbon tax is implemented, such that the revenue lost from the income tax is gained by the carbon tax.

Possible strengths:

Increased consumption
Increased incentive for the public to invest in renewable energy
Increasing the weight of the penalty of wasted fuel.

Possible weaknesses

Reduction of the tax base
Unequal tax burden on oil companies, and those that rely heavily on oil
The potential that the graduated increase in carbon tax and decrease in income tax will not be fulfilled (non-cooperation).

Are there any weaknesses, that I, in my limited economic understanding, have overlooked?

Prominent economist Greg Mankiw has been a prominent advocate of the kind of change you describe (he invites people to join "The Pigou Club", named for Arthur Pigou who first proposed these kinds of corrective taxes).

You can find a nice, non-technical summary of his arguments here. In particular, Makiw deals with some of the weaknesses you identify above and argues that they shouldn't be too much cause for concern.

Wikipedia has an article that lists other prominent economists who have jooined the Pigou Club by publicly advocating for a shift towards carbon or similar taxes (including links to many articles where the issue is disccused. It is here.


In demand and supply chart, why is it assumed that import will only happen if domestic suppliers are unable to supply? First Review What I do understand,
The demand and supply chart shows once imports are allowed...

Tariff is added on imports resulting in loss of consumer surplus and increase in supplier surplus.

I get everything up until to this point. However...

Is this wrong? But this traditional textbook version. Green represents both, width represents imported quantity and area represents govt surplus. This is not what happens in real life. If there are two products both priced $10, I'd buy either one all things being equal regardless of what company or country it was made in. For most products I'm not going to care whether they were imported or domestically made. YET, this graph very clearly assumes import will stop where local suppliers are able to provide.
Correct version should be like this:

or maybe like this:

The standard supply and demand model is a model. Models by definition are distorted version of reality not reality by themselves. The model also ignores transportation costs and other real life issues as well.
However, think about the main message of the model that tariffs decrease overall welfare. Assuming that consumers randomly decide to either consume imported product or domestic product would indeed affect possible size of government tax revenue but not in any way change the main outcome that overall welfare has decreased as when you calculate area of all losses even in corner case where everything is imported taking into account higher government revenue there would still be net welfare loss. Hence adding this bit of 'realism' (I am using '' as randomly picking product is still not realistic either) would complicate math, make your exams more difficult and would not teach you much more. The point of every model is to be as simple as possible in order to be general but still complex enough to allow us to analyze the issue of interest in a way that exposes the underlying economic mechanism.
Of course, different people can disagree about where the dividing line between being too simple to be useful is - that’s an opinion based question, but it’s common for undergraduate models to be oversimplification. In undergraduate physics you will be constantly assuming perfect vacuum, massless points, zero friction etc. all of which is unrealistic in order to gain enough knowledge to understand more nuanced models. All fields use this method of ‘teaching beginners by oversimplified models’ for better or worse.
Later in your academic carrier at PhD or Master level you will encounter far more complex and also more realistic trade models. If you want to see them before you get there you can read Advanced International Trade by Feenstra or Applied International Trade by Bowen, Hollander or Viaene. Or published papers on these topics. Some of those models deal with geography, monopolistic competition and other issues that address international trade in more nuanced way than a Econ 101 could. For the sort of question you are asking here some industrial organization (IO) model with explicitly modeled competition would be more appropriate than assuming 50/50 split for example.
PS: Your last picture is actually not correct. The Government revenue, in this model, will always be a rectangle since it is by definition $Q_{import}*t$.  A correct way of visualizing government revenue if you assume half of the quantity would be imported no matter what would be this:


Does GDP count both the investment and the house rental? Suppose you bought a new house in the year of 2010. Then the price of the house in counted toward the 2010 GDP. Say then you live in the new house in the following years. So in these years, the GDP includes the housing rental you paid yourself. But then why is it not an overcount? I mean, when we counted the house price into GDP in2010, we have already counted all the utility of the house in one year and there is no need to count the de sequent rental.

You are correct that what you describe would be an overcount, but fortunately, your description of what is counted in GDP is incorrect. When a new home is constructed and sold, the full sales price is not counted in GDP. Instead, only the value of the construction put in place is counted in GDP— when the construction is completed. Then, the value of the stream of housing services (i.e., the imputation for owners' equivalent rent) is counted annually as an output of the asset.

Quoting "How BEA Accounts for Investment in Private Structures":

  In the NIPAs, private investment in new construction
  is measured mainly as the sum of the costs of inputs
  of all construction “put in place,” that is, all
  construction activity completed in a given period. For
  individual projects, BEA’s measure of investment in
  structures includes the following:

  Cost of materials installed or erected
  Cost of labor and the cost of construction equipment
  rental for the period
  Cost of architectural and engineering work
  Miscellaneous overhead and office costs incurred
  by the project’s owners
  Interest and taxes paid during construction
  Contractors’ profits

Houses are therefore counted just as any other capital asset is. Just as a machine that makes bolts first appears in GDP when the machine is constructed then later its output is also counted, a house appears in GDP as output when it is constructed (or renovated) and its output— housing services— is also counted.


What does it mean by Portugal having a negative inflation? Portugal is experiencing a negative inflation rate for 2020. This means that the prices of basket-of-goods are decreasing this year.

My first question is: is it a good sign for Portugal's economy?

Secondly, If Portugal's economy is not so strong, why are they experiencing a negative inflation rate?

Regarding whether negative inflation is a good sign: Deflation is generally speaking not a good sign for an economy. Most economist argue that it is good for an economy to have on average about $2\%$ inflation per year. There are many reason for this one example is that wages are sticky and hard to adjust but inflation can help to bring them down in real terms even if they dont change in nominal terms.  This is especially crucial during the times of economic crisis when it can help prevent unnecessarily high unemployment.

Regarding the potential causes: Inflation depends on many factors. Generally speaking the price level (changes of which are called inflation) is given by:

$$P=MV/Y$$

So the price level $P$ is increasing in money supply $M$ and velocity of money $V$ and decreasing in real output $Y$ (also note its driven not just by the variables itself but also by expectations of how they evolve). Moreover, Portugal is member of the euro-zone so its inflation rate depends on only situation in Portugal but across whole euro-zone.

Currently Portugal is experiencing recession, due to covid so one would expect that this would ceteris paribus lead to inflation as $Y$ drops. However, an important caveat is that during the recession velocity of money also drops as people are more reluctant to spend and prefer just saving their money 'under their mattresses' and that is what creates a lot of deflationary pressure. However, thats just an back of an envelope analysis of the situation.


How do you stop Hyperinflation in a Nation? In history, I learned that the Weimar Republic had hyperinflation as a consequence of leading and striving war during World War I and placed a new currency named German Rentenmark which would be about 1 trillion German Mark to stabilize the purchasing power. Would it be therefore that more money will not be printed, just put worthless money in another currency to then reboot the purchasing power of real currency? How does someone actually get out of Hyperinflation and do Hyperinflation have any, really any positive factors as in the Weimar Case the Economy boosted later on?
Note: I am new to economics and I'm grateful for any contribution to this question whether long or short and accept if the question is taken down when not with guidelines of Economics SE or other specific reasons.
https://www.spiegel.de/geschichte/hyperinflation-1923-a-948427.html

You can generally stop hyperinflation in very similar way as any inflation. It is generally accepted by economic profession that price level $P$ (change in which is by definition inflation) in an economy is determined by money market equilibrium. In turn a simplified model of money market equilibrium can be given by the following equation of exchange (see Mankiw; Principles of Macroeconomics pp 87):
$$P= MV/Y $$
where $M$ is the money supply, $V$ velocity of money (i.e. how much one unit of currency is used on average) and $Y$ real output (also note this is a simplified version - more complex ones depend also on expectations of these quantities, but given that you are non-economist I think it is better to stick to this simple one - in case you would be really interested in the more complex versions Romer Advanced Macroeconomics is a leading macro handbook).
Next, hyperinflation does not have exact definition, but typically people consider inflation higher than $50\%-100\%$ per month a hyperinflation (e.g. see Sachs, 1987). Consequently, to stop hyperinflation you just need to make sure that the (expected) change in the right hand side $\Delta(MV/Y)$ is less than $50\%$ per month.
Government issuing its own fiat currency has complete control over $M$ so one option would to decrease the rate at which new money is created. Government can also to a certain degree affect velocity of money $V$ since it does depend on nominal interest rate (increasing nominal interest rates will lower $V$). In addition government has also some control over real output to the extend it can make some structural reforms that help economy grow or various policies that can expand $Y$. In addition as mentioned in the second paragraph this model is simplification and in real life expectations matter as well. This is why often countries that try to combat hyperinflation resort to monetary reform where they replace their currency with new one (this is meant to signal to the public government is serious about the issue thereby lowering their inflation expectation). Naturally, some combination of the above is always an option. Of course, this is just very broad and brief explanation. One could write whole tome on this issue, but exhaustive review would be too long for SE (for more in depth treatment you can have look at above mentioned Romer and Mankiw textbooks as well as  Sachs (1987, Kiguel (1989), Reinhart & Savastano (2003)   - in addition Cagan (1989) has whole book on hyperinflation - and sources cited therein).
Regarding whether there are any benefits of hyperinflation, there are generally only very few. One big benefit is that it can help country to inflate away public debt. Also, hyperinflation actually does not help economy to grow.  Regular inflation can help economy grow, but when it comes to hyperinflation, it is generally agreed that its effect on output is on net negative as any benefit that it has in terms of boosting export through exchange rate, or through removing nominal friction are smaller than the negative effects on output which are caused by uncertainty it creates, and due to other costs of inflation, as well as due to the fact that hyperinflation often leads to people abandoning the currency altogether, in worst cases resorting to barter which is very inefficient form of exchange (see the sources recommended in previous paragraph for discussion on this).


Do minimum wage laws bring more bad than good? Let me begin by saying I know nothing about economics.

In the past couple of days I've been listening to some lectures by Milton Friedman. They are of non-technical nature. In one of them he makes an argument which I have understood approximately as follows:

  Having a minimum wage law is harmful to workers who compete for low paying jobs and are relatively less skillful because it deprives them of their "only weapon" - working for less.

Do minimum wage laws increase unemployment? Is there any information enabling this comparison?
Are there purely economic arguments, or empirical evidence, favoring minimum wage laws? Have they in any sense improved the economy?

There is ample evidence that increases in the minimum wage in the magnitudes that we've seen in the last 20-30 years have caused no or very small decreases of low-skilled employment. In that sense, the predictions of competitive labor market models like the one Friedman probably had in mind are clearly wrong.

A classic reference here is Card and Kruger 1993 (http://davidcard.berkeley.edu/papers/njmin-aer.pdf). A more recent contribution is Allegretto et. al. (http://ftp.iza.org/dp7638.pdf). There are many more.

Some recent minimum wage increases have been much bigger than the ones discussed in these papers (for example the 15$ minimum wage in California) and the effects of these increases may be more substantial.

The argument for minimum wages is mostly about redistribution, and modest minimum wages probably achieve this goal.


Calculating monetary base from given data I need to some data for Pakistan's monetary base. Searching through the website of State Bank of Pakistan (SBP), I found the following pdf on Monetary Statistics.

I wanted to ask that can I calculate monetary base from the given values.

Following is a list of values given in pdf in case pdf is not opening for you.

Currency in Circulation
Other Deposits with SBP
Currency in Tills of Scheduled Banks
Banks' Deposits with SBP

Regards

Looking into monetary base definition:

  Monetary base is the total amount of a currency that is either circulated in the hands of the public or in the commercial bank deposits held in the central bank's reserves.

So this means that M0 is actually the monetary base. So I really don't have to calculate anything.


What is a Stock exchange? What is a stock exchange, I understand that it is a place where one buys and sells shares but I would like to know in more detail.

Generally, it's the place (e.g. NYSE) where the equity portion of company's capital structure trades publicly. The exchange creates a market for buyers and sellers of equity to meet and trade (think Ebay but for equity).

Equity is in contrast to the debt portion of a company's capital structure, which is often comprised mainly of term loans and revolvers provided by banks as well as as secured and unsecured bonds of the company purchased by investors.

To understand a stock market, it's important to understand priority of payments in a capital structure. Imagine a company goes bankrupt - this is the order in which stakeholders lose money (first to last): equity, unsecured bonds, secured bonds, 2nd lien term loan, 1st lien term loan.


Demand functions homogeneous of degree zero in prices and income - how this relates to budget exhaustion (solving a consumer's problem) I have the following demand system:

It appears to me that each demand function is homogeneous of degree zero in prices and income as:

Why would this demand system not satisfy the following budget equation?

where I is exogenous. I would have thought the budget constraint would not have been satisfied only if one of the demand functions was not homogeneous of degree zero in prices and income.

I would have thought the budget constraint would not have been satisfied only if one of the demand functions was not homogeneous of degree zero in prices and income.

You should look into this claim. It is true that demand functions are homogeneous of degree zero in prices and income, but not all functions that are homogeneous of degree zero in prices and income are demand functions.

Some examples with only one good, so where $p_x x = I$ should hold:

$
x= \frac{I}{7p_x}
$
is homogeneous of degree zero, but with this the consumer does not spend all their income.

$
x= 0
$
is homogeneous of degree zero, but with this the consumer does not spend all their income.

$
x= - \frac{p_x}{I}
$
is homogeneous of degree zero, but there is definitely something weird going on here.


Absolute Value of Total Factor Productivity in an Aggregate Cobb-Douglas Production Function A standard formulation of the Cobb-Douglas production function (e.g. here) is:
$$Y=AK^{\alpha}L^{\beta}$$
Have there been estimates, at aggregate level for any large economy, of the absolute value of total factor productivity $A$ (at a defined date, and for defined units of measurement of output $Y$, capital $K$ and labour $L$?).  Even a rough order of magnitude would be of interest.

From searching the web, there have been many studies that estimate changes in total factor productivity over time, but I could not find any that focused on its absolute magnitude.

Applying a regression model

$$\ln Y = \ln A + a\ln K + b\ln L$$

on a standard macroeconomic time-series data set from a country would immediately provide an estimate for $A$, essentially an average over the sample.

The problem is that experience has shown us that we don't have $A$ but $A_t$, i.e. it is time-varying. As such, estimates of $A$ as though it was a constant seem rather meaningless or even misleading.

More-over, in a time-varying coefficient framework, what is important is the change, rather than the absolute value, since it is essentially a mark-up index on the production function, and not something that can be meaningfully measured in absolute units. In this case, we take $A_0=1$ (the first period in the sample) and we track the percentage change over the sample.


Classical Theory of Inflation - Money Supply, Money Demand and Prices In every textbook, website I read when talking about the classical theory of inflation,  I see the diagram below which depicts the value of money, prices etc. This one below is from Spark notes (https://www.sparknotes.com/economics/macro/money/section2/) or Mankiw (chapter 28 Money, growth and inflation).
These sources all go through a shift in the MS to the right to demonstrate inflation. No problem with that conceptually. Makes sense.
But what about the demand curve? If the demand curve SHIFTS to the right (due to a thriving economy and an increase in transactional demand for money) and the central bank keeps the money supply the same, the result would be deflation? An equilibrium with lower prices than before. i.e. A higher point on the supply curve (see my doodle below).
It would seem that no source considers a shift in the demand curve like any other S & D diagram. And I can't rationalise it for myself.
It seems totally counter intuitive. Could anyone explain the logic of this model when it comes to shifts in the demand curve (keeping money supply fixed).

If the demand curve SHIFTS to the right (due to a thriving economy and an increase in transactional demand for money) and the central bank keeps the money supply the same, the result would be deflation?

Yes, this would result in deflation ceteris paribus. In fact Mankiw Macroeconomics 8ed also mentions that in passing on pp 335, but you are right it does not explain intution.
The intuition is that if money demand shifts to the right and money supply is fixed that means that each individual unit of money will have higher value (e.g. this is equivalent to standard supply and demand model - fix supply of houses, increase demand for houses and you get that they have both higher value and price in equilibrium). Increase in value of money means that purchasing power of money increases which decreases the price level. New equilibrium interest rate will be higher because interest rate is essentially a price at which you can obtain money from banking sector (I am oversimplifying a bit to give you an intuition). Consequently, shift in money demand to right will increase interest rate, value of money and lowers a price level.
Conversely, if demand shifts to the left and money supply is fixed the value of each unit of money will drop, the interest rate drops as well and price level increases.
In addition, it is not true that no source discusses this. It is true Mankiw focuses on money supply in his Macroeconomics, but in Blanchard et al Macroeconomics an European Perspective there is whole sub-chapter that focuses just on change in money demand (see chapter 4.2 pp 62).


Leontief input output model with column sum greater than 1 In a linear algebra textbook I came across the following question (not included in the answer key):

Consider an open economy with a consumption matrix
\begin{equation}
     C =
     \begin{pmatrix}
           0.5 &  0.25  & 0.25 \\
           0.5 &  0.125 & 0.25 \\
           0.5 &  0.25  & 0.125 \\
     \end{pmatrix}
   \end{equation}
If the open sector demands the same dollar value from each product-producing sector, which such sector
must produce the greatest dollar value to meet the demand? Is the
economy productive?

This textbook defines productive as:
"Economies for which $(I − C)^{−1}$ has nonnegative entries are said to be productive.".
Below is a theorem from the textbook.

If $C$ is the consumption matrix for an open economy, and if all of the column sums are less than $1$, then the matrix $I − C$ is invertible, the entries of $(I − C)^{−1}$ are nonnegative, and the economy is productive.

Immediately I notice that the column sum of $C$'s first column is greater than $1$, and from what the textbook says that means the given sector requires more inputs than its output, thus it's not profitable. However, it turns out that this given matrix is invertible and its inverse has nonnegative entries.
I understand mathematically in the cited theorem that the column sums being less than $1$ is not an if and only if condition and thus exceptional circumstances are possible.
However, in economic terms the question seems odd, in other words, asking whether an economy with an unprofitable sector is productive.
If the question is not faulty: how would you explain this in economic terms? Or if it is, what is wrong with the question?

In terms of if and only if statements according to Peterson & Olinick (1982);

A substochastic matrix A is productive if and only if $I-A$ is
nonsingular.

In substochastic matrix the sum of entries by row or columns will not be greater than 1 so it is part of the condition but in addition the matrix $I-C$ should also be nonsingular. The nonsingularity is important for the invertibility of the matrix.
Consequently, I do not think that there are exceptions where the industries are unprofitable but the matrix is still productive. Rather there are exceptions where just because the entries sum to less to 1 and matrix is non-negative but it is singular and so we cannot invert it, in which case it would not satisfy conditions to be productive.


CES v. Leontief Aggregator in Production Consider a production process with two distinct capital types such that there is a capital aggregator. You could view $k_v$ as a more versatile capital (e.g. can be converted into many different production processes) as opposed to $k_u$ which is a unique factor of production exclusive to a particular production process. Hence $J=\{v,u\}$.

  A CES aggregator is:  ($\gamma$ is substitution coefficient, $\sigma_j$ is factor share such that $\sum_\limits{j\in J}\sigma_j=1$)
  $$k\equiv(\sum_{j\in J}\sigma_j k_j^\gamma)^{\frac{1}{\gamma}}.$$

Similarly,

  a Leontief aggregator is:
  $$k\equiv\min\{\frac{k_v}{\sigma_v},\frac{k_u}{\sigma_u}\}.$$

My Question:

  When and why (i.e. economic intuition) is it appropriate to use one aggregator over the other? Are there other aggregators that are also commonly used?

I guess it depends on the application in question. Leontief function presumes that there is no substitution between the arguments, i.e. no amount of increase in one argument can compensate the decrease in another to keep output at some original level. In contrast, the general CES does allow some degree (as captured by the parameter $\gamma$) of substitution between the arguments. Note also that Leontief is obtained by taking $\gamma\to\infty$, thereby rendering the elasticity of substitution between the arguments $0$.

If you were doing a simulation exercise, you should usually "let the data speak" first, namely, estimating the value of $\gamma$ (and $\sigma_j$) from some existing data. However, if you have some a priori reason to believe that $\gamma$ is of a particular value, then you would assume that value and carry on with the analysis.


Does the UK have a trade agreement with Australia? Since the UK was a member of the EU, I'm assuming the EU was responsible for any kind of trade arrangements between the UK and Australia, but I'm not entirely sure. Does the UK have an agreement with Australia for trade and if so, when did this agreement take place? Many thanks.

No, the UK does not have a trade agreement with Australia.

Since it is still a member of both the European Union's Single Market and Customs Union (EU SM&CU), it is covered by all of the EU's trade deals. However, the full EU-Australia trade deal is, at the time of writing, still being negotiated.

Should the UK decide to go ahead and become the first country in history to impose economic sanctions on itself, withdrawing from EU SM&CU, then its own home-baked trade agreements will come into force. The embarrassingly unimpressive list of trade agreements that the UK has negotiated is listed here.


What is the difference between marginal cost and average cost? Marginal Cost is
$$MC(y) = \frac{\partial C(y)}{ \partial y}$$
Average Cost is
$$AC(y) = \frac{ C(y)}{ y}$$
Average Variable Cost is
$$AVC(y) = \frac{VC(y)}{ y}$$
Note:
Cost is
$$ C(y) = FC + VC(y)$$
I don’t understand what the differences are. Like I understand the definition of cost function, fixed costs, and variable costs, but I don’t get how marginal cost, average cost, and average variable costs are related.

Can someone explain?

Suppose initially there are no fixed costs.

What does it mean to take an average?

Consider a cost function $C(y)$. What does it mean to take the “average” of this function? Mathematically, it is just $$A(y) = \frac{c(y)}{y}$$

Let’s suppose we are considering $C(y) = y^3$. Suppose we now consider $y = 5$. Then $$A(5) = \frac{5^3}{5} = 25 $$
This is just saying that, for each unit I buy, I am buying them at $25$ each on average. So I could have paid
$$ \frac{15 + 39 + 46 + 14 + 11}{5}$$
or
$$ \frac{17 + 3 + 78 + 23 + 4}{5}$$
What information does the average cost give us?

The 'cost per unit' given by an average cost function isn't like taking an average by adding up the cost of each unit we bought. When we are given a cost function $C(y)$, this just tells me the total cost. I don't know how much my first TV cost me from this equation alone. And the average doesn't tell me that either. Note how above we have two sets of 5 TVs that yielded the same average cost. Thus, the average cost function doesn't tell me how much I paid for each specific TV.

What does marginal cost tell me?

This is exactly what marginal cost provides. Marginal cost provides the specific cost of each successive infinitesimal amount of good. Consider again $C(y) = y^3$.
$$MC(y) = \frac{d C(y)}{d y}= 3y^2$$

Suppose I have purchased $3.5$ units of TV. Then the MC equation thus says, for $c(y) = y^3$, each additional infinitesimal amount of TV costs me $$3(3.5)^2 = 36.75$$ at that point. If I purchase an additional $0.1$ amount of TV, then my MC changes and now I am at $$3(3.6)^2 = 38.88$$

Thus, this concept is a bit trickier because it involves a continuous amount of TV and the cost per infinitesimal unit changes as you buy more. So you really can't just consider how much $MC(1)$ is and $MC(2)$ is. You are considering it for some infinitesimal additional amount $dy$ at a given point (e.g. $y=2$). The trend is easier to think through if you don't restrict yourself to integers. Note, we are assuming you can have noninteger quantities of goods, otherwise we wouldn't be working in $\Bbb{R}^n$ and the integration later might be trickier.

Example to Clarify Marginal Cost

So suppose I want to buy $5$ TVs. For the $k$th TV purchased, the $$MC(k)= 3k^2$$ Going back to our example above, let's now suppose $k \in [0,5]$. To find the average cost, we simply do the addition formula used above for the 5 TV example, except now summed over each infinitesimal amount (of which there are an infinite number). This gives us

$$A(5) = \frac{3(0)^2+\cdots + 3k^2+ \cdots + 3(5)^2}{5} = \frac{\int_{0}^{5} 3y^2 dy}{5}= \frac{(125-0)}{5}=\frac{c(5)}{5}=25$$

$$A(5) =25$$
the same as we calculated earlier.

Summary

Marginal Cost is
$$MC(y) = \frac{d C(y)}{d y}$$
Average variable cost is

$$A(y) = \frac{\int_{0}^{y} MC(y) dy}{y}$$

Note, since we assumed $FC = 0$, this formula also thus defines AC but would not be true for $FC \neq 0$.

AVERAGE COST VS AVERAGE VARIABLE COST

I have been sloppy about the distinction between AVC and AC up until now. I have avoided this distinction by assuming $FC = 0$. Now I will try to clarify this point by assuming $FC$ can be anything.

Fixed costs ($FC$)are costs the firm pays that do not vary with the amount produced. For example, suppose I work for Uber and I buy a car. That money is spent and doesn't change with the amount I drive. But the amount of gasoline I consume does change as with the amount I drive. Costs that scale with production are known as variable costs ($VC(y)$).

$$AC(y) = \frac{C(y)}{y}=\frac{VC(y) +FC}{y}= \frac{VC(y)}{y} + \frac{FC}{y}=AVC + AFC $$

Hyperbolic Behavior of AFC with y >0

As production goes up ($y\rightarrow \infty$), AFC goes down ($AFC \rightarrow 0$) in an inversely proportional fashion. But note, as production goes down ($y\rightarrow 0$), AFC goes to infinity ($AFC \rightarrow \infty$). Thus, the plot of AFC will always be a hyperbola unless $FC = 0$ in which case AFC is just 0.

How does AFC affect AC?

Without specifying $VC(y)$, we cannot know the behavior of $AC(y)$ as $y$ moves away from $0$. There will be some $y_{0}$ such that, for $y > y_{0}$, $AC(y)$ can essentially be anything. Of course, as $y \rightarrow 0$, $AC(y) \rightarrow \infty$. This is because AVC cannot be negative and so we are guaranteed any variable costs will not lower the average cost below AFC. Therefore, $AVC \geq 0$, so since $AFC \rightarrow \infty$ as $y\rightarrow 0$ (remember it is a hyperbola), thus AC must go to infinity as well.

Thus, since the behavior of fixed costs are always known, AVC is the missing ingredient needed to specify the behavior of AC.

AC and AVC can't be exactly equal for $FC>0$

Since $AFC \rightarrow 0$ but does not ever equal 0 (for $FC >0$), we know that $$AC \neq AVC$$ for any $y$ and $FC >0$. But since $AFC$ approaches 0 for large enough $y$, AC approaches AVC asymptotically.

AC and AVC can't be exactly parallel for $FC>0$

If $AVC$ and $AC$ are parallel, then their derivatives should be equal. But notice that $$\frac{dAFC}{dy} = -\frac{FC}{y^2}$$
so $$\frac{dAC}{dy} = \frac{dAVC}{dy} + \frac{dAFC}{dy} = \frac{dAVC}{dy} - \frac{FC}{y^2} \neq \frac{dAVC}{dy}$$
So they aren't parallel because their derivatives aren't equal. That said, for large enough $y$, the derivatives will be very close to each other so they may appear nearly parallel over some portion of the curves.

MC intersects AC at minimum point of AC curve

See Alecos's answer.

MC intersects AVC at minimum point of AVC curve

Consider the average variable cost curve. Find $y^*$ that solves

$$\min_{y} AVC(y)$$

So at this point,
$$\frac{dAVC(y^*)}{dy^*} = 0$$

This means by quotient rule

$$\frac{VC'(y^*)y^*-VC(y^*)}{(y^*)^2} = 0$$
and since $y^*$ can't be 0, this implies $$VC'(y^*)y^*-VC(y^*)=0$$ which rearranged gives
$$VC'(y^*)=\frac{VC(y^*)}{y^*}$$
Recall,
$$C(y) = FC + VC(y)$$
Note, since $FC$ is a constant,
$$C'(y) = VC'(y)$$
Therefore,

$$C'(y^*) = \frac{VC(y^*)}{y^*}$$

EXTRA STUFF

Why do we define the firm's longrun shutdown point in terms of average cost not marginal cost?

Recall a firm's profit function is $$\pi = py - C(y)$$

I am not defining the behavior of $p$ here or who controls $p$. I am just considering for what $p$ will the firm shut down, and ignoring everything else because it's irrelevant.

So we can easily see that since $$AC(y)= \frac{C(y)}{y}$$ for $p=AC(y)$, this yields $$\pi = \left(\frac{C(y)}{y}\right)y - C(y) = C(y)- C(y) = 0$$
So the firm will shut down if $p <AC(y)$ because then $\pi < 0$.

So consider the function $C(y) = y^3$. Note, $$MC = 3y^2 > AC = y^2$$ We know the firm profit maximizes at $MR = MC$. So since, for $y > 0$, $MC(y) > AC(y)$, the firm would always produce if $p = MC$ since this would mean for $y>0$,

$$ MC(y)y-C(y) = \pi_{p=MC}  > \pi_{p=AC} = \left(\frac{C(y)}{y}\right)y - C(y) =0$$
$$\pi_{p=MC} > \pi_{p=AC} = 0$$
So, for this $C(y)$, at $p=MC$, $\pi >0$ for all $y$.

So this example clearly shows you would never shut down at $p=MC$ for $y>0$ for $C(y) = y^3$. Although this isn't the most thorough explanation, this example clearly invalidates that train of thought and makes clear firms shut down for $p< AC$

Does average cost necessarily equal marginal cost at some point?

See Alecos's answer.

Takeaway Rules

In long run, firms produce if $p \geq AC(y)$. They shut down for $p < AC(y)$
Firms always produce at $MR = MC$


Firm Sizes over the business cycle There has been a lot of evidence about the firm size distribution (as measured in employment) being Pareto (see for example Luttmer 2007), but what are the properties of this distribution over the business cycle?

These guys (paper) claim the distribution is still power-law, but steeper in recessions and flatter in booms.

[Content added after suggestion]

  While it is well known that the distribution of firm sizes (in the US
  at least) looks like a power law distribution, these guys look at
  whether it changes in shape over the business cycle.

  They show that (in log-log space) the distribution is actually a power
  law in both recessions and expansions, but its not the same power law,
  its steeper in recessions and flatter in booms, meaning that large
  firms become relatively larger in booms than in recessions, or
  alternatively that there is  a lot of entry of small firms in booms.


Hedging with volatility swaps? I'm studying financial derivatives, and became curiosity in volatility products, more specifically volatility swaps. It always intrigued me how can you create products based on volatility. Who is interested in buying them? Other than traders who want to speculate with the volatility I can't image how a large corporation could find a seller/buyer for this kind of product.

How can volatility swaps be used to reduce the risk of volatility in the markets (hedging strategies)? How is their fair value calculated?

What are volatility swaps?

Before the introduction of what is now volatility swaps, investors gained exposure to the market's volatility (yes, they already wanted to) through call and put options, products that depend on volatility, but also heavily on the price level of the underlying asset.

A volatility swap is a forward contract on future realized price volatility. Similarly, a variance swap is a forward contract on future realized price variance, variance being the square of volatility. It is basically an agreement between two parties on exchanging $N_{var} (\sigma_{realized}^2 - \sigma_{strike}^2)$ after a given period.

  How is the fair value calculated?

A good way to catch the meaning of that fair value is to suppose both actors had to make a consensual prediction on volatility. For example, they expect a realized variance of $\sigma^2$ and they agree on $B$ giving $A$ $N_{var} (\sigma_{realized}^2 - \sigma_{strike}^2)$ at expiry. Then the fair value would be $N_{var} (\sigma^2 - \sigma_{strike}^2)$.

The strike is usually chosen such that the fair value of the swap is zero, i.e. $\sigma_{strike} =\sigma$. This is not always the case, though. This was for the second, simpler question.

  How can volatility swaps be used to reduce risk of volatility in the
  markets?

Let's take the example of a life insurance company. The company offers many products with guaranteed benefits and these expose them to short volatility positions, that is, they are better off if volatility is low than if it is high. To balance this risk (they are insurance companies after all), they will buy long positions, that is, volatility swaps that gives them green notes if the volatility is higher than they expected. This does not modify their expected outcome, however it contributes to risk reduction. As they are risk-adverse, they may be willing to lower their expected value in order to bring risk down, which mean they are prepared to pay more than the fair price for a volatility swaps, which means other players will be interested in buying them whatever the composition of their portfolios, hence giving birth to the volatility market, which now-a-days has a daily trading volume of about $30-35 million.

Reference: https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/3967/pricing_hedging.pdf


How to derive firm's cost function from production function? I recently learned how to solve the following type of problem using the method of Lagrangian multipliers:

Given a consumer with utility function $u(x,y)$, wealth $w$, prices $p =(p_x,p_y)$, budget constraint $w = xp_x + yp_y$. Find the demand function for $x$ and $y$. I also learned how to find cost functions by plugging these demand functions into my budget constraint and rewriting to give a cost function.

But those cases all involved having $w$ and somehow budgeting with respect to that budget.

Problem Setup:

Suppose a firm is a price-taker with market price for the good in question $p$. Suppose the firm has a production function $F(K,L)$. Derive the firms cost function.

My Question:

How should I approach this problem?

My Ideas / Thoughts Relevant for Solving Problem:

I am not given wealth $w$ although I suppose I could assume any firm who is purchasing has some budget. All previous problems I have done involved two goods, but this involves one. Perhaps I could therefore have a budget constraint $w = qp$ where $q$ is the quantity and $p$ is the price as given to the price-taking firm. But Lagrangian multplier problems I have seen involve two variables and this is just a function of one.

Remark:

The specific production function I am using is $F(K,L) = \sqrt{k} + \sqrt{l}$. I only include this in case it's relevant. I want to solve the problem myself.

"I am not given wealth $w$ although I suppose I could assume any firm who
  is purchasing has some budget."

No. This is exactly where the fundamental microeconomic theory of the firm differs from the microeconomic Consumer Theory: the firm is not constrained by a budget. The reason is that this fundamental theory deals most and foremost with the "long-term" view, or even better, with the "planning view". So we assume that the amount necessary to cover expenses, will come from sales, since the firm won't enter production at a loss (remember also, this is a deterministic set-up, there is no uncertainty). Working capital considerations (the fact that usually first you have to actually pay expenses and then to actually collect revenues), does not enter the long-term view, justifiably, it is a short-phenomenon. Also, in the long-term or planning approach, there are no fixed costs, all factors are variable.

Now, the "cost-minimization" approach to solve the firm's optimization problem, is an alternative behavioral assumption to the profit-maximizing setup, and it is very relevant in many real-world cases: public utilities that exist mainly to satisfy demand, and their motive is not to maximize profits -rather they want to minimize cost for the given level output, as determined by demand, in the context of efficient use of the always scarce resources.

But also, the case of a price-taking firm that is too small compared to its market, is closer to a cost-minimizing behavior rather than profit maximizing, since the firm has not really control over its production (except downward by direct decision).

In both of the above cases, an exogenous variable appears: the level of output itself. So we solve the problem by treating the level of output as a "constant" or better, we solve it for any given level of output, and the solution we obtain has the level of output as one of its components.

So

$$\min_{K,L} C\equiv rK + wL \\
s.t. F(K,L) = \bar Q$$

with the Lagrangean

$$\Lambda = rK + wL +\lambda[\bar Q - F(K,L)]$$

The first order conditions are

$$r = \lambda F_K,\;\;\; w=\lambda F_L  \tag{1}$$

which gives, at the optimum,

$$rK + wL = C = \lambda\big(F_KK + F_L L) \tag{2}$$

Now assume that the production function is homogeneous of some degree $h$ (not necessarily homogeneous of degree one, i.e. exhibiting "constant returns to scale", but homogeneous -and yours is, of degree $h=1/2$.). From Euler's theorem for homogeneous functions of degree $h$ we have that

$$F_KK + F_L L = hF(K,L) = h\bar Q \tag{3}$$

the last equality holding given the constraint of the initial problem. Inserting $(3)$ into $(2)$ we obtain

$$C = \lambda h \bar Q$$

The multiplier $\lambda$ is optimal marginal Cost, denote it $C'(\bar Q)$, so we arrive at

$$C = C'(\bar Q)\cdot (h\bar Q) \implies C'(\bar Q) + [(-1/h\bar Q)]\cdot C =0$$

This is a simple homogeneous differential equation with solution

$$C = A\cdot \exp\left\{-\int(-1/h\bar Q) {\rm d}\bar Q \right\} = A\cdot \exp\left\{(1/h)\ln \bar Q\right\}$$

$$\implies C^* = A\cdot (\bar Q)^{1/h} \tag{4}$$

for some constant $A >0$. To complete the solution, we need to express the object of interest, $C^*$, in terms of the exogenous entities: $r,w,\bar Q$.
To do that derive the optimal marginal cost (which is equal to the multiplier)

$$(4) \implies \lambda^* = (1/h)A(\bar Q)^{1/h-1} \tag{5}$$

Inserting $(5)$ into the first-order conditions we have

$$r = (1/h)A(\bar Q)^{1/h-1} F_K,\;\;\; w=(1/h)A(\bar Q)^{1/h-1} F_L  \tag{6}$$

It is time to use the specific functional form of the production function

$$F(K,L) = K^{1/2} + L^{1/2} \implies, F_K = \frac 12 K^{-1/2},\;\; F_L = \frac 12 L^{-1/2} \tag{7}$$

Inerting $(7)$ into $(6)$ together with $h=1/2$ we obtain, after manipulation,

$$rK = \frac {A^2}{r}(\bar Q)^2,\;\; wL = \frac {A^2}{w}(\bar Q)^2 \tag{8}$$

Sum the two to obtain an alternative expression for the Cost function

$$rK+wL = C^* = A(\bar Q)^2\cdot \left[\frac Ar + \frac Aw\right] \tag{9}$$

But inserting $h=1/2$ into $(4)$, we also have that

$$C^* = A(\bar Q)^2 \tag{10}$$
So

$$ (9),(10) \implies   A(\bar Q)^2\cdot \left[\frac Ar + \frac Aw\right] = A(\bar Q)^2$$

$$\implies \frac Ar + \frac Aw = 1 \implies A = \frac {wr}{w+r} \tag {11}$$

Inserting $(11)$ into $(4)$ we conclude obtaining

$$C^* = \frac {wr}{w+r}\cdot (\bar Q)^2 \tag{12}$$

Three things:
A) Verify that the second-order-conditions hold for all this to indeed lead to the optimal cost-function.

B) Solve the unconstrained profit-maximization problem with the same production function, normalizing the price of output to $p=1$ (i.e. treating the exogenous prices, $w,r$ as expressed in real terms), to verify that it will lead to a cost level that it is consistent with $(12)$.

C) If you are interested in the theory of the firm under a budget constraint, a related paper is
Lee, H., & Chambers, R. G. (1986). Expenditure constraints and profit maximization in US agriculture. American Journal of Agricultural Economics, 68(4), 857-865.


Taxes and the economy as a whole Does reducing taxes generally lead to better economic performance? Does it lead to slowdowns in the economy?

It is much more complex than just saying yes.
You need to look at different factors and then you can answer your question.

Generally, high taxes have a negative effect on businesses, the more taxes a business pays - the less money it has to growing itself.

The lower the taxes the less money the government has (this is not necessarily as there is a Laffer curve to take into consideration).

It also differs depending on how you measure economic performance, GDP? GNP? job growth, unemployment rate - these are all very different.

If you look at most major economies - you will see that generally the lower the taxes, the better the economy performs. However there are many countries - such as the Scandinavian Social democracies, that have high taxes but generally good economies.

In my opinion, high taxes are not a major factor in economic performance (although they are a factor), and Free market and less regulations is much more important.
Simplifying tax code is also more important than lowering taxes, as complex tax codes are waste of time and money.

If the taxes are low, the budget is balanced, and the tax code is simple - it is  generally better than the same economy with higher taxes.


Taking the derivative of capital per effective unit of labor in the Solow model I'm taking an intro macro course, and my calculus is pretty rusty.  I'm going through some lectures notes right now where they derive the growth rate of capital in the Solow model like so:

I'm wondering what the process is for getting to the very first step where they take the derivative with respect to time.  Generally, are there good resources for learning how to do this, as I imagine I'll be doing it a lot?

I've tried to "fill the blanks", hope this helps.

$$\tilde{k} = \frac{K}{AL}$$
$$\frac{d[\tilde{k}]}{dt} = \frac{d}{dt}\left[\frac{K}{AL} \right] \quad (1)$$
Now we use the quocient rule: to differentiate $f(x) = \frac{g(x)}{h{x}}$ (for $h(x) \neq 0$) we can apply the formula $f'(x) = \frac{h(x)g'(x) - g(x)h'(x)}{[h(x)]^2}$. In your problem, $f(x) = \dot{k}$, $g(x) = K$ and $h(x) = AL$, but instead $x$, you have $t$. So, applying the rule in (1), we have:
$$\frac{d[\tilde{k}]}{dt} = \frac{AL\left(\frac{d[K]}{dt}\right) - K\left(\frac{d[AL]}{dt}\right)}{(AL)^2} \quad (2)$$

The second term in the numerator has the derivative of a product ($AL$), so we need again to use the appropriate rule: $(f(x)\cdot g(x))' = f'(x)\cdot g(x) + f(x)\cdot g'(x)$

So, using the rule in (2) we have:

$$\frac{d[\tilde{k}]}{dt} = \frac{AL\left(\frac{d[K]}{dt}\right) - K\left(L\frac{d[A]}{dt}+A\frac{d[L]}{dt}\right)}{(AL)^2}$$

Now we re-write using dot notation - $\dot{x} \equiv \frac{d[x]}{dt}$:

$$\dot{\tilde{k}} = \frac{AL\dot{K} - K(L\dot{A}+A\dot{L})}{(AL)^2} \quad = \frac{AL\dot{K}}{(AL)^2}-\frac{KL\dot{A}}{(AL)^2}-\frac{KA\dot{L}}{(AL)^2}$$

Since $\frac{\dot{A}}{A} = g$ and $\frac{\dot{L}}{L} = n$, we have

$$\dot{\tilde{k}} = \frac{\dot{K}}{AL} - Kg -  Kn = \frac{\dot{K}}{AL} -K(n+g)$$

ps: I'm not sure why your textbook is using dot notation over $\tilde{k}$ before taking the derivative.

EDIT:

I'm adding an alternative way to achieve the same result.

Starting with $\tilde{k} = \frac{K}{AL}$, you can rewrite as $K = \tilde{k}AL$.

Now, take log on both sides and remember that $log(ab) = log(a) + log(b)$:

$log(K) = log(\tilde{k}AL) = log(\tilde{k}) + log(A) + log(L) \quad (1)$

Now we are going to take the derivative (in t), using the log rule: if $f(x) = log(x)$, then $f'(x) = \frac{1}{x}$. But now we have to use the chain rule, because all variables are in reality functions of $t$. The chain rule is: if z depends on y and y depends on t, then z depends on t: $\frac{dz}{dt} = \frac{dz}{dy}\frac{dy}{dt}$. Using $log(K)$ as example, we have: $\frac{d}{dt}[log(K)] = \frac{d}{dK}[log(K)]\cdot \frac{d}{dt}[K]$.

(1) then became:
$$\frac{d}{dt}[log(K)] =  \frac{d}{dt}[log(\tilde{k})] + \frac{d}{dt}[log(A)] + \frac{d}{dt}[log(L)]$$

Which is...
$$\frac{d}{dK}[log(K)]\cdot \frac{d}{dt}[K] =  \frac{d}{d\tilde{k}}[log(\tilde{k})]\cdot\frac{d}{dt}[\tilde{k}] + \frac{d}{dA}[log(A)]\cdot\frac{d}{dt}[A] + \frac{d}{dL}[log(L)]\cdot\frac{d}{dt}[L]$$

Now we substitute all derivatives of logs and use dot notation:

$$\frac{1}{K}\dot{K} = \frac{1}{\tilde{k}}\dot{\tilde{k}} + \frac{1}{A}\dot{A} + \frac{1}{L}\dot{L} = \frac{\dot{\tilde{k}}}{\tilde{k}} + g + n$$

In the SS we have $\frac{\dot{\tilde{k}}}{\tilde{k}} = 0$, so:

$$\frac{\dot{K}}{K} = g + n$$


Exam question implies that a perfect labour market can have wage differentials? My understanding is that wage differentials should not exist in a perfect labour market for occupations, but the following exam question seems to imply that this can be the case. A brief marking scheme also implies this.

and its marking scheme explanation:

I have always thought that if occupations belonged to a perfect labour market, it would mean that due to the assumptions of perfect mobility and homogeneity of labour, wages will always adjust so that wages are always equal across industries. The marking scheme seems to imply that this does not have to be the case.
One possible caveat I suspect would make the question's situation possible would be if the firms do not operate in perfectly competitive product markets, though I am not sure about this, and neither did the marking scheme mention this.

The question (implicitly) assumes that there are relevant skill differences in the population. As you say, it is true that in a perfect labor market there are no wage differences if workers can move freely across sectors.

If your course defined perfect labor markets as having homogeneity of labor and perfect mobility, then the given answer is wrong. However, typically these two factors are not necessarily a feature of perfect labor markets. That usually just means there is no market power on either side.

As the question asks about the case of different labor supplies, there can be no homogeneity of labor nor perfect mobility. Different labor supply is only possible if not everyone can do each type of work, meaning there are more available workers for certain jobs, thereby implying not all workers have the skills to do all jobs. Hence, to the extent that the question assumes supply differences are possible, it also assumes that workers cannot move freely across sectors. That is the reason wages do not equalize according to the answer.


Why is the long-run average production cost not necessarily the same as the minimum average total cost? As you can see from the graph, the LRATC doesn't touch the SRATC curves when they're at their minimum. Why is this so?

Denesp's comment is your full answer: it's a badly-drawn chart which fails to do its one job, that was to illustrate that the long-run cost curve consists of joining up the minima of the short-run cost curves.


Are all fixed capital public goods? fixed capital: any kind of real or physical capital (fixed asset) that is not used up in the production of a product

public goods: goods that are non-rival and non-excludable in consumption

Both of the terms above seemed like they are talking about something similar so can I say that fixed capital all belong to the category of public goods?

I agree with @BBKing, just to put it here as an answer: if we go back to your two definitions you can find quiet easily some counter examples. Let's take a firm, which uses a machine as capital. Let's assume also that this machine can only be used by one man at a time. Do you think this machine is a non-excludable / non-rival good ?


Putting a Price on Happiness When I was in college, a classmate of mine working two jobs mentioned that his/her job working at at a local fast food restaurant was causing undue stress and dissatisfaction.

My response was to ask "What is your price on Happiness?"

If your income from the other job can satisfy your basic needs (rent, food, clothing, etc.) and the income from your fast food job was 'extra' aren't you valuing your happiness at $10/hr?

In a short time I learned that my classmate decided to quit the fast-food position. But in hindsight, I never gave much thought as to my advice.

With this said, can it be realistically said that a price can be put onto happiness?

There are several approaches to this problem, none of them accurate as the human happiness is internal subjective experience and thus not verifiable by people other than the afflicted (it is not intersubjectively verifiable).
Please see below several methodologies for pricing the non-economical values such as happiness developed by economists:

Willingness to pay

This problem can be viewed as ‘what is the market price of an item not sold on the market’. To solve it, economists can look whether happiness cannot be, at least in theory, bought on the market. For example, if a pharmaceutical company wants to test some drug that causes unhappines and has to pay USD 1000 for a person to take the test and willingly be unhappy at some level, then the price of this level of unhappiness is USD 1000.

Cost-base valuation

This can be applied when the lack of happiness is directly connected with measurable expenses, like therapy bills, antidepressant drugs, lost income, etc. In this methodology, if a decrease of a happiness is connected with cost of USD 1000 in some period, its value in this period can be measured at not less than USD 1000.

Comparability with damages won in courts

In this method you must find a statistical sample of court judgments, in which compensation was granted for non-pecuniary damages (e.g. for work related undue stress and dissatisfaction) under similar circumstances. As the circumstances can never be the same in different cases (happiness always is subjective and have different economical and social context for each individual), you rank the judgments (e.g. from the weakest to the strongest undue stress and dissatisfaction) and try to place your case on the X axis against court cases. This should result in a point or a range at which unhappiness at question should be valued.

The methods above are connected with many technical problems and are highly criticized. For example, such issues are usually tackled in economics by analyzing the relationship between the marginal cost and one unit of happiness. But what would be a unit of happiness? I recommend further reading of some legal papers on this issue as well as Steven Kelman criticizm in his paper ‘Cost-Benefit Analysis: An Ethical Critique’, where he argues against putting dolar values on non-market benefits and costs at all.

Hope this helps.


A few variables expressed in units of a standard normal distribution in a regression I am using three of the Worldwide Governance Indicators (WGI) estimates. They represent broad dimensions of governance for countries. All indicators range from -2.5 to 2.5 approximately. They are expressed in units of a standard normal distribution.

For your information: here is the link to the website: https://info.worldbank.org/governance/wgi/Home/Documents#doc-intro

I want to use these indicators in a panel regression as control variables. All my other variables are not expressed in units of a standard normal distribution. Is it a problem? Do I need to convert the governance indicators (-2.5, 2.5) to another scale (0, 1)? Will the 'econometrics' make sense?

In general, there is no expectation that right hand side variable in a regression are in the same units. We often have combinations of variables like years of education, price, regional dummies, etc. that are all included together. So in principle, there’s no reason why you should have to convert your controls to some other scale.

From a numerical standpoint, it can be useful to normalize variables to maintain numerical stability. The eigenvalues of the covariance matrix can be a little funky if the relative scales are way different (for example, one variable ranging between 1-4 and another variable ranging between 1-4 billion). It can also be useful to normalize variables to help with interpretation of the coefficient values (easier to compare 1 and 2 than it is to compare 1 and 0.000000002).

From your example, though, if you’re just considering adjusting from something that ranges on the order of -2 to 2 to something that ranges from 0 to 1, neither of these reasons would probably hold. As such, based on the info you’ve given, I would probably just leave the RHS variables as they are.


Why is Ricardian Equivalence Important? Ricardian equivalence is a result regarding the ineffectiveness of government due to consumption smoothing behavior of consumers. A primary reason why it fails is due to population turnover (i.e people have finite lives).
In spite of these issues why is Ricardian equivalence important to know about in terms of its use as actionable information.

This link to a 43 page paper: Ricardian equivalence: an empirical application to the Portuguese economy CarlosFonseca Marinheiro
https://core.ac.uk/download/pdf/6978949.pdf
Introduction on page 3:

The fiscal policy may be used with a stabilising role if the government finance decisions are able to influence private consumption (i.e., aggregate demand) and saving. This influence depends on the degree to which consumers treat government debt as net wealth.

If Ricardian equivalence holds then the government cannot stimulate aggregate demand by increasing spending and/or reducing taxes. So history of economic debate over the effectiveness of fiscal policy includes this theory called Ricardian equivalence.

According  to  the  Keynesian  consensus  consumers  treat  government  debt  as  net  wealth. Therefore, a substitution of debt for taxes has a positive influence on private consumption and  aggregate  demand.  However,  the  consequent  decrease  in  private  and  national  saving, implies  an  increase  in  the  real  interest  rate,  which  crowds  out  private  investment.  The reduction  in  the  capital  accumulation  then  leads  to  a  reduction  of  the  long-term  growth prospects of the economy. This negative long-run effect offsets some of the positive short-term effects of the government deficit.

The  Ricardian  thesis  has  a  complete  opposite  view.  It  states  that,  for  a  given  expenditure path, substitution of debt for taxes has no effect on aggregate demand nor in interest rates.The  government’s  inter-temporal  budget  constraint  implies  that,  for  an  unaltered  level  of government outlays, a tax cut now implies a tax increase in the future. As borrowing only postpone  taxes  for  the  future,  consumers,  who  are  simultaneously  taxpayers,  anticipating the increase in future taxes, do not consider the current tax cut and the consequent increase in  disposable  income  as  being  permanent.  Their  inter-temporal  budget  restriction  is  left unaltered.  Therefore,  consumption  is  also  unaffected.  The  increased  disposable  income  is entirely saved.

Then there is another historic economic debate over the concept called "crowding out."


How can you profit from junk bonds and selling treasuries, if the junk bond doesn't default? Junk Bond/Treasury convergence
Typically junk bonds, given their speculative grade, are undervalued as people avoid them. Therefore the spread over treasuries is more than the risk of default, by buying junk bonds and selling treasuries, to hedge interest rate risk. Often profits can be achieved by buying junk bonds and selling treasuries, unless the junk bond defaults.

Wikipedia doesn't detail this interest rate hedge. Assume that a junk bond never defaults and the semistrong-form of the EMH:
Zvi Bodie, Alex Kane, Alan J. Marcus. Investments (2018 11 edn). p 338.

      The semistrong-form hypothesis states that all publicly available information regarding
the prospects of a firm must be reflected already in the stock price. Such information
includes, in addition to past prices, fundamental data on the firm’s product line, quality
of management, balance sheet composition, patents held, earnings forecasts, and accounting
practices. Again, if investors have access to such information from publicly available
sources, one would expect it to be reflected in stock prices.

Correct me if I'm wrong, but Treasury bonds' interest usually $<$ junk bonds' interest. So

why would anyone rational sell you junk bonds and buy T-bonds from you (so that you can long junk bonds and short T-bonds)?

wouldn't this spread over treasuries always be forthwith arbitraged?

You assumed that junk bonds do not default. They do default. So people will price junk bonds at a greater yield than Treasuries.
It can’t be arbitraged since the probability of default (and associated loss) is unknown. An arbitrage implies locking in an abnormal profit at no risk. You cannot hedge out that default risk without using an instrument like a credit default swap. if you did hedge losses with a credit default swap, the cost of the swap cancels out the yield advantage on the bond (assuming everything priced at fair value).

If we ignore transaction costs - which we cannot in practice - the breakeven spread point for a high yield bond portfolio is where the average spread approximately equals the expected annual loss (= probability of default times loss given default). E.g., a 500 basis point spread (5%) will offset credit losses of 5% a year. (We would need to do a detailed cash flow analysis to map credit losses to spreads, but the approximation is typically quite good for bonds trading near par.)

The credit loss rate is unknown, and opinions differ wildly about them. Observed spreads represent some kind of “average” of market participant’s views (assuming no other factors influence pricing). The first quote just says that the actual credit losses tend to be below what spreads discount across the cycle.

However, high yield bonds are illiquid, and have greater transaction costs, and so need to offer an additional spread to compensate. Meanwhile, markets can be disturbed, such as forced liquidations, and so spreads can trade wider than most market participants’ expected credit losses.


If $\succsim$ is rational, then $B \mapsto C^*(B, \succsim)$ satisfies the weak axiom, and $\succsim=\succsim^*$ If $\succsim$ is rational, then $B \mapsto C^*(B, \succsim)$ satisfies the weak axiom, and $\succsim=\succsim^*$

Previously in the same theorem actually, they proved the following:

  If $C$ is a choice rule satisfying the weak axiom, then $\succsim^*$ is rational, and for all $B \in \mathcal{P}(X), C(B) = C^*(B, \succsim^*).$

Note: $C^*(B) = C^*(B, \succsim) = \{ x \in B: \forall y \in B, x \succsim y \}$, and the weak axiom is referring to the weak axiom of revealed preference which a choice rule satisfies if $[x \succsim^* y ] \Rightarrow \neg (\exists B)[y \succ_B x]$

My try of the proof:

First suppose $B \mapsto C^*(B, \succsim)$ does not satisfy the weak axiom, then $\succsim^*$ is not rational by the earlier part of the theorem, so if we can prove $\succsim = \succsim^*$ we have a contradiction which will prove the statement.

As $\succsim$ is rational, then there is a utility function $u: X \to \mathbb{R}$ that represents $\succsim$, then $\{x \in B: \forall y \in B, u(x) \geq u(y) \} = C^*(B, \succsim)$ but then $\exists B$ s.t. $x,y \in B$ and since $B \mapsto C^*(B, \succsim)$ then $u(x) \in C^*(B, \succsim)$ so $x \in C(B)$ hence $\succsim = \succsim^*$

Here is an attempt at a direct proof:

Let all the assumptions hold, and further assume that $x \succcurlyeq^* y$. Then for some $B \supseteq \{x,y\}$, $C^*(B) \supseteq \{x\}$ (by definition of $\succcurlyeq^*$), which further implies $x \succcurlyeq z$ for all $z \in B$, and therefore $x \succcurlyeq y$ (by definition of $C^*$). (This shows that $\succcurlyeq^* \subseteq \succcurlyeq$; the other direction follows from looking at doubleton sets $B = \{x,y\}$).

What is left to show is that $C^*$ satisfies the weak axiom. So take any $B' \supseteq \{x,y\}$, such that $y \in C^*(B')$. If no such set exists, then $y$ is not revealed preferred to $x$ and we are done. If such a set exists then by definition $y \succcurlyeq z$ for all $z \in B'$. We already know $x \succcurlyeq y$ so by transativity $x \succcurlyeq z$ for all $z \in B'$ and hence $x \in C^*(B')$. Again,  $y$ is not revealed preferred to $x$ and we are done.

Notice, while we used transitivity, we did not use completeness. This hints at the fact that the statement can actually be generalized to pre-orders (reflexive and transitive), by allowing $C^*$ to be empty. This point is somewhat lost by appealing to the second result.


Income effect for inferior goods question When you are only told in the question that the price level of the inferior good decreases, how can you draw the indifference curve accurately? The size of Substitution effect depends on the curviness of the curve. Thus when I draw my diagram, it is not matching with the one in the textbook.

When do you prevent this when no figures about the exact consumption is given?
Thanks

Could you clarify what your your question is? If Ramen is inferior then an increase in wealth (parallel shift of the budget line) should cause the consumption of ramen to go down. Hence $B$ should be to the left of $A'$. Then income effect is the distance on the x-axis from $A'$ to $B$.

(Edit in response to the comment)

Let me try.

The slope of the budget line is related to ratio of prices. So $A'$ is the point of tangency of between the old indifference function and a budget line with a new ratio of prices. Essentially what it is saying is what would be your basket if the price of ramen was reduced but some of your money was taken away, so that you are no better and no worse off. The change from A to A' is pure substitution effect.

Then, since your money was not actually taken away from you, you have to consider income effect. This is achieved by shifting the dased line upwards. So A -> A' is substitution effect. A' -> B is income effect.

Direction of substitution effect is always the same. Higher relative price means less consumption. Direction of income effect depends on the type of goods.


How to measure quality of education across countries? For my research, I need a measure of the quality of education that I could apply to multiple countries. It must include quality of tertiary education.

Standard measures like HDI Education Index are not precise enough. For example in HDI Education Index, Kazakhstan is ranked along Hong Kong, Belarus above Singapore, etc. Such absurd discrepancies destroy any hope for good results for my model.

Please, if you have an idea (no matter how wild it is) what I can use as a proxy for quality of education, please share it.

A good reference is the Barro-Lee Dataset wich gives educational attainment
for 146 countries from 1960 to 2010. The data are disaggregated by sex and by 5-year age intervals. Their estimates of educational attainment provide a reasonable proxy for the stock of human capital.

An older reference is hosted by the World Bank.

In case you need more recent data, you may apply their methodology.


How effective is progressive tax at regulating monopoly? Regardless of the morality of progressive taxes, the economical benefit of progressive tax is at least debatable. But could a highly progressive tax replace at least some of the american/european anti-trust regulations?

Progressive income taxes on individuals is not very likely to have any real impact on market power, but progressive income taxes on corporations can certainly have this effect. The key idea is that in many industries (for example, the financial industry), there are geniune economies of scale: having a big balance sheet allows an investment bank to take advantage of various synergies, meet demand from customers at lower costs and therefore at lower prices. This means that there is a natural pressure towards concentration in the financial industry. High levels of concentration, however, allow firms to price out their competitors from the market due to their size and the aforementioned scale effects, and can lead to a scenario of oligopoly.

The government can try to deal with this problem by introducing negative incentives for corporations to get bigger. This can be in the form of an explicit limit on the size of corporate balance sheets rel to GDP, as advocated by Stiglitz, or it can be in the form of income taxes, or capital requirements, which are "progressive" in the sense that they impose higher marginal costs on larger and more complex firms over smaller ones. Such a measure can offset the natural incentive towards aggregation in the financial industry, for example. This is already done to some extent by Dodd-Frank (perhaps unintentionally) in the US, which raised capital requirements for SIFIs (which are well-integrated financial institutions with large balance sheets). The adverse effect is that by doing this, a country can effectively price its financial institutions out of international markets.

In turn, a policy which reduces market power can have positive effects on the income distribution, as it would lead to lower prices and higher wages. The problem is to find the right balance between the benefits (lower costs) and costs (market power) of concentration in the marketplace.


Find value of $\beta$ for which there is a strictly dominant strategy The question is as such: $N$ firms are lobbying for subsidies. Let $h_i$ be the number of hours spent by form $i$ for lobbying, with cost $wh_i^2$ where $w$ is a fixed constant. The subsidies granted to each firm will be $\displaystyle\alpha\sum_i h_i+\beta\prod_i h_i$, where $\alpha$ and $\beta$ are constants. We are supposed to find value of $\beta$ such that there exists a strictly dominant strategy for each firm, and with this value of $\beta$, find the Nash equilibrium.

My attempt so far: for firm $i$, the payoff will be $\displaystyle\alpha\sum_i h_i+\beta\prod_i h_i-wh_i^2$; by FOC, we have $\displaystyle\alpha +\beta \left(\prod_{j\neq i} h_{j}\right)-2wh_i=0$.

My question is: do I attempt to find $\beta$ from here? There will be $N$ such equations, with a product of $N-1$ terms, so solving the system of equations do not seem that feasible. However if I take value of $\beta$ as it is, then there will be many different values.

I feel that the value of $\beta$ should be zero here, but I am not sure how I can show this.

Hint
Let $h_i^*(h_{-i}$) be firm $i$'s best response to the other $N-1$ firms' strategy profile $h_{-i}$. If $h_i^*(\cdot)$ is a dominant strategy, then it must be independent of the other firms' strategies, i.e. $h_i^*(h_{-i})=h_i^*$ for all $h_{-i}$.


What are the main differences in a macroeconomic model, i.e. New-Keynesian DSGE, under a currency substitution (full dollarization) scheme? I have searched arround the web and economic journals trying to find out research related to a macroeconomic model in which the country is fully dollarized, but I haven't had any luck. My main concern is how to deal with exchange rates and the monetary authority. Maybe I just have to forget about them.

You are not likely to find New Keynesian DSGE models where money or currency plays an explicit role. These models mostly abstract from these considerations altogether and monetary policy is simply represented by the interest rate. I understand your situation as I myself have tried to write papers and searched for literature where dollarization plays a role.

If you can, try to circumvent the explicit use of currency in your model. Think about what the currency's role is in your model, e.g. if it is to have different inerest rates in different countries or in different currencies, then simply use different interest rates instead of different currencies.

Another way would be to go outside of the standard DSGE framework and use other international finance, open economy models, as you would find in the Obstfeld/Rogoff book.

If you really want to stick with DSGE, I would recommend looking into open economy DSGE models as well as DSGE models with "Money in the Utility Function".


Real GDP Computation and Justification How does one really compute inflation? I just now quickly looked up how the real GDP was computed. It is using the base year price to multiply the number of products traded. Is that meaningful? Is a ten year inflation computed on the base of the zeroth year price? The change in demand and supply would have made a huge change in the price when there is no inflation. The Motorola flip cell phone price now must be less than 1/100 of the price when it first came out. Does that mean there is severe deflation? On the other hand, the price for it could explode because it could have become a collector item. What about the price of a quantum computer --- the real one, or just something akin to DWave --- when it comes out? Are we going to compare its price against Von Neumann's Maniac or Allan Turing's Bombe or Intel 40386? This is nonsense and absurd. One rescue I can come up with right now, is we divide a finite time interval into multiple periods and computing recursively. We must assume the inflation speed is faster than the change of the supply and demand in each interval. I do not even know if that makes mathematical sense. Is there a proof of legitimacy for this or any other remedies, at least mathematically?

luchonacho has provided some sources below in his answer, particularly hedonic regression, for estimating the inflation. I have expressed my doubt over the efficacy of method. Here I would like to criticize the method further on the technicality.

The hedonic regression does not answer my question for distinguishing the change in supply and demand including that caused by the technological change. It seems the proponents of hedonic regression claim that it could make the distinction. Hedonic regression assumes the price of a good as the linear function of its attributes. Suppose the attributes have not changed over the period under consideration. However, the supply and demand for this good have changed due to, say, technological innovation that either has made the good obsolete or more valued or made useful in completely different ways than before, as well as inflation. Unless one already know extraneous information either on the change in supply and demand or the inflation, there is no way one can distinguish inflation from the change in supply and demand.

Your criticisms of GDP are valid, and have long been recognised in the literature and by statistical offices. For example, one of the issues your question deals with is quality changes. The case of hardware is particularly visible.

Several agencies do adjust for quality changes. A common method to do so is using hedonic regressions. The aim here is to obtain a "valuation" of all the different components of an item, like a PC. For example, using these regressions you can get an idea of the value consumers give to memory, graphic card, DVD reader, speed, etc. Then, new products can be adjusted using these values. An example of such regression for computers is here.

The ONS (which computes GDP for the UK) do attempt to adjust for quality. In fact, they consider "volume" of a product as a combination of both quantity and quality. They differentiate between two methods to evaluate volume. For some homogeneous goods like agricultural grains or energy products, where quality is less relevant, you simply compute the physical volume. Yet, for most of the products, heterogeneity makes such calculation impossible. The quality adjustment then comes from prices. The ONS uses the hedonic regression method for goods with "frequent model changes", but uses other methodologies too. For example, there is a major challenge in measuring change in quality of public services (like health care and education). For a detailed description on the ONS quality adjustment, check this article. Check here for public productivity measurement.

For other formal references, see this one. The latest UN System of National Accounts, in which most of countries are based to compute national statistics, also offer some guidance on quality adjustment (section 4, page 361, in particular).


What would be the likely economic consequences of the "trillion dollar coin" idea to eliminate all government debt? Taken from this question over at politics.se, consider this article by Business Insider which describes a scenario in which the treasury mints a trillion dollar coin to pay off all the debts of the U.S. government.

  The premise of the idea is this: Although the Treasury can't just create money out of thin air to pay its bills, there is a technicality in the law that says the Treasury has special discretion to create platinum coins of any denomination, and the thinking is that Tim Geithner could make the coin and walk it over to the Federal Reserve and deposit it in the Treasury's bank account.

What would be the likely consequences of this type of action by the treasury? Specifically:

What would be the impact to inflation?
What would be the impact to the value of treasury bills? Particularly: a) those currently in issue and b) those issued in the future?
Could the answer to the question of how to pay for all future spending proposals simply be to mint another coin?
If you were an economist advising the administration on economic policy, would you advise in favor or against such a policy action. What would be your reasoning for your policy advice?

Quite obviously, the act of creating and depositing the coin can't possibly impact anything of economic interest (except for creating an imperceptibly small increase in demand for platinum and hence an imperceptibly small increase in its price).

The impact comes when the government starts to make withdrawals and spend money.  And the nature of the impact depends on a thousand things you haven't specified, most notably:  What does the government do with the money it withdraws?  Does it pay down existing debt that it had not previously planned to pay down?  Does it buy more missiles that it had not previously planned to buy?  Does it expand a welfare program  that it had not previously planned to expand?  Does it cut taxes that it had not previously planned to cut?  Does it trade the coin for a bathtub full of $10,000 bills for the president to bathe in?

It's no use assuming that it does none of these things with the money, because it has to do something with the money.  So let's take the simplest example and suppose that they buy bonds (or cut taxes, which will have more or less the same effects).

In this case, you're swapping money for bonds, which is going to increase the price level.  The impact on inflation depends, once again, on things you haven't specified.  Does the government buy a trillion dollars worth of bonds at once?  If so, there is a jump in the price level but essentially no new inflation.  Do they spread the purchases out over a couple of years?  If so, that's going to be a very inflationary couple of years.

Could all future government spending be paid for this way?  Sure.  Here are some other things you could use to finance all future government spending:  A tax on food.  A tax on labor.  A tax on savings.  A head tax.  A tax assessed on random people in random amounts at random times.  What you're proposing is, in effect, a tax on holding money  (because it's the people who hold money who will lose when the price level adjusts).  Each tax has some advantages and some disadvantages.  In each case, the disadvantages grow nonlinearly as the tax increases, so it's very unlikely you'd want to just choose one tax to finance all government expenditures.  You probably want a mix, which is what we have now.  Whether we have exactly the right mix is open, of course, to a great deal of debate.


Economic Effects of Presidential Candidate Proposal: Pay the same % in taxes no matter what you gain There's a presidential candidate in USA that promises to change IRS laws in order that everybody pays the same % in taxes, i.e., the rich will pay the same percentage as the poor. This would seem to generate more income inequality in the long run.  Another effect would seem to bleed the Government treasury . I do not how much it accounts for, but I don't think it's at all negligible...

What type of impacts can we expect if this measure is implemented. I'm not interested in politics, just economics.

Any help would be appreciated.

Looking at the matter from a strictly positive and not normative or political view, then

1) Ignoring "Laffer-curve" effects, bleeding the Government treasury may not happen, if the flat tax rate is set to a suitable level (the specific politician has exactly in mind to bleed the federal government treasury, but that's discussing politics)

2) As regards income inequality, if indeed the current taxation system is effectively progressive and not just nominally, then it will indeed increase inequality, since this flat tax rate should be expected to lie above the current minimum tax rate implemented, and below the current maximum tax rate implemented.

A plausible anticipated effect is that lower incomes will reduce their saving (i.e. we should expect that the loss in disposable income will hurt savings more rather than consumption), while higher incomes, which will now have more disposable income, will increase savings. While the overall effect on the "consumption/savings" mix may be ambiguous, this will affect also the distribution of wealth, increasing also wealth inequality.

Is inequality bad for economic performance? Check some recent work by S. Turnovsky, that models links between inequality and growth.


In which country does my money have the largest purchasing power? To be honest i have literaly zero economic knowlegde so please treat me as a noobie in this case. Here is the questin: I live in Poland where my native currency is polish zloty (PLN), and i want to buy some comon product like 1 liter of milk, but i'm not bounded by national boundary. So i have let say 100 PLN, and my goal is to buy as much milk as possible in one selected country that maximizes the amount of milk purchased.
How to acchive this? How can i compare immanent value of my 100 PLN around different countries, and select one country that alows for maximal milk purchase? In this whole process i must convert my 100 PLN into national currency (in optimal country) and then go to shop (in that country).

Money does not have any 'immanent value'. Value of money will fluctuate across time and also different regions (1USD does not have the same purchasing power in New York as it has in Arizona). This being said there are ways of doing international purchasing power comparisons that go beyond simple market exchange rate that can sometimes be misleading.
Purchasing power parity (PPP) is one of the ways that purchasing power can be compared across different countries. There are also other ways (see discussions in textbooks such Krugman et al (2012). International Economics: Theory and Policy) but PPP is one of the few ways that does not require extensive research.
PPP works in a very similar way to an exchange rate. In fact PPP is sort of an exchange rate built under the assumption that the law of one price holds (Krugman et al (2012). International Economics: Theory and Policy). Data on PPP can found from multiple sources one of them being OECD (however, not all countries are always included in some it is simply too dificult to collect data). Next PPP is by convention reported as $\frac{\text{local currency}}{USD}$. However, we can change this by dividing all individual PPPs for different countries by the Polish PPP as that will allows us to express everything per PLN (e.g. $\frac{\text{local currency}}{USD}/ \frac{\text{local PLN}}{USD} = \frac{\text{local currency}}{PLN}$).
Using this you can collect data on milk prices across all nations for which PPP data is avaiable and then compare the different prices directly. For example, if in China milk costs $20¥$ then you could adjust that with Chinese PPP expressed in terms of PLN (based on OECD data it would be approximately $2.4$)  using  $\frac{20¥}{2.4\frac{\text{¥}}{PLN}} = 8.33PLN$ and then simply compare this cost of milk in China expressed in PLN in terms of PPP to cost of milk in your local store.
I don't have any data on different milk prices across different countries (and I collecting them would be too much effort for SE answer), but just glancing at the PPP statistics it looks like PLN would have highest purchasing power in Indonesia. This being said, to be sure you should actually take the basket of goods you are interested in and make the comparison as described above.


Help interpreting a Taylor rule I need a bit of help interpreting this version of the Taylor rule I stumbled across recently:

$$\ln\frac{1+i_t}{1+i} = X_i \ln\frac{1+i_{t-1}}{1+i}+X_{\pi}\ln\frac{\pi_t}{\pi}+X_y \ln\frac{Y_t}{Y}+X_s \ln\frac{S_t}{S}+X_{\theta}\ln\frac{{\theta_t}}{\theta}$$

I think that S is the exchange rate and theta is a money growth factor. Other than that, I am not very sure. I am hoping this uses some standard notation so that anyone here more familiar with economics research might be able to give me more thorough understanding of what is happening here.

$i_t$ should be the interest rate at time $t$. $\pi_t$ the inflation at time $t$. $Y_t$ the income at time $t$. The variables without indices are the targets of the central bank. The interpretation of this Taylor rule is therefore that the current interest rate is a function of the past deviation of the interest rate from the target, the current inflation deviation from target, the current output gap, the exchange rate deviation from target, and deviations from the current money growth target.


Can holding interest rates at zero (ZIRP) for a very long time cause the deflation it is trying to prevent? The fisher equation is nominal interest rate = real interest rate + inflation rate.

If nominal interest rate is kept to zero, and real interest rate remains constant positive in the long term, then the inflation rate will be negative, representing deflation!

When the central bank drops nominal interest rate at 0%, the negative delta in the nominal interest rate increases money supply and increases the price level - for a period of time. The boost in demand is because demand is brought forward due to the fall in interest rates. Producers increases production to match this surge in demand, and in doing so, increasing supply of goods come into the market. If there are no more negative deltas in interest rate coming, as is the case under a zero interest rate policy where the nominal interest rate is zero bound, the increased supply is going to cause a decrease in price level due to decreased demand that was consumed to produce the earlier demand surge from the negative interest rate delta, causing deflation.

I'm sure there is a flaw to the logic above, and to the fisher equation, otherwise it would mean a ZIRP, held for a long time, would produce the deflation it was implemented to prevent! Can you point it out?

While my answer would depend on how, why, and what the central bank said about why they pushed nominal interest rates to zero, I suspect in most situations the answer is no.

Consider the simplest case of quantitative easing. Continuously injects cash into the economy and uses it to purchase public debt and if that is exhausted private debts. With this massive increase in the money supply, and the expectation that the money supply would continue to increase in the future, it would be unlikely that prices would be falling (deflation) in such a situation.

Why? Recall Milton Friedman's quip that "Inflation is always and everywhere a monetary phenomenon." While it may not be an iron law, there does seem to be good evidence that when the money supply increases prices are likely to go up after.

  Is inflation always a monetary phenomenon? Many economists believe
  that the link between money growth and inflation in the U.S. has
  weakened over the last two decades due in part to the Federal
  Reserve's policy experiment in 1979–1982 and innovations in the
  financial sector of the economy. I find that the long-run relationship
  between money growth and inflation is strong in a statistical sense
  and important economically. The key result is that the trend or growth
  component in CPI inflation is entirely due to the trend component of
  monetary base growth.

THE LONG-RUN LINK BETWEEN MONEY GROWTH AND INFLATION (CROWDER (2007))

Since most zero interest rate policies are likely to hold rates down by increasing the money supply, it is unlikely they will be deflationary.

My major caveat is that a zero interest policy may be accompanied by overt or implicit indication that the central bank has a inflation target that is near zero. If the central bank tightens rates whenever they go above 0 percent they may have zero or even negative average nominal rates and deflation. But in that situation it it is the expectations of low future inflation and aggressive inflation fighting that hold down prices and the low inflation holds down the interest rates. Scott Sumner and others have argued that this was essentially the Japanese central bank's policy for many years.


Regression of Real GDP on Intellectual Property Products Problem I have a question regarding regressing the log growth of Real GDP on the log growth of Intellectual Property production which contributes to GDP (through using the expenditure method of calculating GDP). My question is does this regression make sense? I used the dollar values initially and I had an absurdly high R^2. After refreshing my knowledge of Time Series regression I changed the model as well as adding a lag for the log growth of IP production. The values I get seem as if they are economically and statistically sound. However, I am not sure if my model makes sense as IP production is a component of calculating Expenditure based GDP.

My goal for this was to find out what effect IP production will have on economic growth in order to quantify some type of relation that I can add in a report regarding to a project which proposes an increase in IP production of a state.

I apologize if the question seems rather trivial. I'm possibly undertaking more then what is required for this project but I'd like to gain some knowledge through doing this. Thank you in advance.

It is never a good idea to regress something so complex as GDP on a single variate. There may be myriad confounding factors.

I can think of two suggestions here:

1) Lookup Barro's and Sala-i-Martin book on Growth, the empirical part, to get an idea of what kind of factors seem to appear to influence growth (or what kind of factors growth can be decomposed into). They can be used as control variables, in order to check whether in their presence IntProp remains a statistically significant variable, and even if it does, what is the magnitude of its effect (so that one can assess its economic significance also).

2) Consider detrending your variables, either linearly or non-linearly using for example the HP-filter, and regress the cycle components and perform the usual correlation analysis of real business cycle models, in order to see whether IntProp leads or lags the GDP cycle. If it leads, an argument could be made that in the short-run at least IntProp pushes the growth cycle out of its trough.