Maximization with disposable income Consider a welfare system u dear which a single cash transfer(guaranteed income ) is given to every citizen. Then for each dollar the person earns the payment is reduced to by a where 00 you get a transfer. If t<0, you pay taxes. If t=0, you don’t pay taxes or receive transfers.

Suppose that te wage rate is $w>0$. And so a person who works H hours gets $y_e=wH$. A typical individuals utility function is $$u(y_d, H)=y_d/(1+H)^2$$

The question has multiple part. I tried to do most of them. But I’m not sure please check my solutions also I cannot do some parts.

First of all I write an expression for individual’s disposable income $y_d$ as a function of $y_g$ and $y_e$ and other parameters.

$$y_d=(1-a)y_e+y_g$$

secondly I try to draw indifference curves for that utility function and his disposable income line as follows

I only put this image to show the graph.

Thirdly, I try to drive utility maximizing labor supply function $H^*$ by assuming that $(1-a)w-2y_g>0$

$$u(y_d, H)=y_d/(1+H)^2$$

$$u(y_d, H)=((1-a)y_e+y_g)/(1+H)^2$$

Derivative with respect to $H$

$${(1-a)w(1+H)^2-((1-a)wH+y_g)2(1+H)\over (1+H)^4}=0$$

$$\iff$$

$$(1+H)[(1-a)w(1+H)-2(1-a)wH-2y_g]=0$$

Since H>0, $(1+H)≠0$

So,
$$[(1-a)w(1+H)-2(1-a)wH-2y_g]=0$$

$$H*={[(1-a)w-2y_g\over (1-a)w}>0$$

Additionally,

$$\partial H^*/\partial y_g=-w/((1-a)w)<0$$

By intuition, as the guaranteed income $yg$ increases labor supply will decrease.

$$\partial H^*/\partial a=-2y_g/. ((-a)^2w)<0$$

So for each dollar the person earns the reduction amount of a in the single cash transfer increases iff the labor supply decreases.

these intuitions are enough? What do you say about these results ?

Then,

Fourthly What is the utility maximizing labor supply when  $(1-a)w-2y_g\le 0$

In this case I said that

$$H*={[(1-a)w-2y_g\over (1-a)w}\le 0$$

Thus, the labor supply will be optimally zero.

I am stuck at this point. Is what I said true?

And then,

Assume that the government wants to choose its policy $(y_g, a)$ in such a way that a citizen utility is maximized subject to the constraint that the net transfer is zero   How can I derive the optimal policy? I tried to derive it. But I guess my solution is not true. How do you derive it? Is it correct? This point is really important.

$$u(y_d, H)=Y_d/(1+H)^2=((1-a)wH+y_G)/(1+H)^2$$

Subject to $ T=Y_G-aY_E=0$

So $y_g=aY_E=awH$

So
$$u(y_d, H)=Y_d/(1+H)^2=((1-a)wH+awH)/(1+H)^2=wH/(1+H)^2$$

Derivative w.r.t. H;

$$(w(1+H)^2-wH2(1+H))/(1+H)^4=0$$

$$(w(1+H)^2-wH2(1+H))=0$$

Iff

$$w+wH-2wH=0$$

So $H^*=1/2$

So, $y_g^*=aw/2$ and $a^*=2y_g^*/w$

I am really stuck at this part.

And my last question is based on above assumption. But different citizens earn different wages. What do you think about the merit of this policy?

Thank you in advance.

Disposable Income $Y_D$ as a function of $Y_G$ and $Y_E$ is:
$$Y_D = Y_G + (1-\alpha) Y_E$$
Given wage rate $w$, and $Y_E = wH$, the budget equation can be written as:
$$Y_D = Y_G + (1-\alpha)wH$$
Preferences of the individual over $Y_D$ and $H$ are represented by the utility function
$$U(Y_D, H) = \dfrac{Y_D}{(1+H)^2}$$
So the utility maximization problem is :
\begin{eqnarray*}\max_{Y_D, H} && \ \ \dfrac{Y_D}{(1+H)^2} \\ \text{s.t} &&  \ \ Y_D = Y_G + (1-\alpha)wH \\ &&  \ \ H\geq 0 \end{eqnarray*}
Here is the picture to demonstrate optimal solution :

Solving the above problem we get the optimal labor supply as
\begin{eqnarray*} H^*(w, \alpha, Y_G) = \begin{cases} 1-\dfrac{2Y_G}{(1-\alpha)w} & \text{if } (1-\alpha)w - 2Y_G > 0  \\ 0 & \text{if } (1-\alpha)w - 2Y_G \leq 0 \end{cases}  \end{eqnarray*}
So the optimal utility as a function of $w, \alpha, Y_G$ is as follows:
\begin{eqnarray*} U^*(w, \alpha, Y_G) = \begin{cases}  \dfrac{((1-\alpha)w)^2}{4((1-\alpha)w - Y_G)} & \text{if } (1-\alpha)w - 2Y_G > 0  \\ Y_G & \text{if } (1-\alpha)w - 2Y_G \leq 0 \end{cases}  \end{eqnarray*}

Now the Govt. chooses $(Y_G, \alpha)$ by solving :
\begin{eqnarray*}\max_{Y_G, \alpha} && \ \ U^*(w, \alpha, Y_G) \\ \text{s.t} &&  \ \ Y_G = \alpha wH^*(w, \alpha, Y_G)  \end{eqnarray*}

Solving it we get
$\alpha^* = 0$ and $Y_G^* = 0$


Why GDP series always has an unit root problem? In one of the lecture slides of class that I am currently taking our professor mentioned that when it comes to the GDP is it safe to always assume it has unit root and testing for it is just superfluous. However, why is this the case? Is that just an empirical regularity or is there some reason why GDP will always have unit root?

I suppose this could be due to the economic growth, but we did also learn about trend stationary series. I also understand that the reason why any series has unit root is that the shocks to the series never die out, but why wouldn't that hold for GDP? In our macroeconomics class we were always taught that business cycle shocks are transitory and ultimately GDP grows around its balanced growth path.

Whether GDP has a unit root depends on whom you ask, and what they believe about the nature of business cycle.

The seminal paper that first applied a unit root test (the ADF test) to macroeconomic time series and extracted economic implication is Nelson-Plosser (1982).
They were unable to reject the unit root null hypothesis for GDP and other standard macro series. They offered the following conclusion:

"...macroeconomic models that focus on monetary disturbances as a source of purely transitory fluctuations may
never be successful in explaining a large fraction of output variation and that stochastic
variation due to real factors is an essential element of any model of macroeconomic fluctuations."

These are fighting words in the debate of Real vs. New Keynesian Business Cycles. They interpret their finding as evidence against the latter. Or at least that variation in output is more attributable to permanent real shocks rather than transient shocks to aggregate demand ("monetary disturbances").

Later, however, in a subsequent milestone result Perron (1989) found that a trend-stationary series with a break in its deterministic trend may be mistaken as unit root. In particular, he overturned Nelson-Plosser's non-rejection result for GDP (and other series), after taking into account the 1929 crash and 1973 oil price shock.

Another possible example of such trend-stationary series with structural break is the CBO GDP data series covering the Great Recession shown in answer by @1muflon1.

Today, the suggestion that, say, US GDP of the last 20 years has a unit root would probably not be too controversial.
In general, the answer you get depends on the data, the unit root test being applied (there are many), and whether the economist has a strong RBC or New Keynesian bias.

(For example, Nelson and Plosser were already RBC advocates before publishing their finding.)


Is modern monetary theory sustainable? I am looking around at a lot of the central banks around the world (primarily ECB, Fed, and BOJ) and they all seem to be simply printing their way out of any issues with their economies. As far as I understand, this is the central component to MMT. Is this sustainable without collapsing currency? I can't understand how massive supply increase doesn't led to reduction of purchasing power of a currency.
Additionally, will the low-rate environment remain permanent? I can't imagine the Fed, for example, raising rates substantially as 1. It would tank most assets and 2. It would make the already incredibly unwieldy sovereign debt that much harder to manage. It would seem we are locked into an endless money printing path that essentially can't be stopped without immense pain. Am I right in this understanding?

MMT is propounding to be a theory. A theory can't be sustainable or unsustainable.  However, I think you meant to ask if the policy proposals of MMT-ers would be sustainable so I will answer assuming that is your question.
Now MMT is not a proper scientific economic theory* as it is not rigorously defined (Mankiw 2020), so it is not actually clear what MMT policy implications are but many MMTers generally claim that central bank should monetarily finance government spending, and that generally any amount of real spending can be funded by monetary expansion. Moreover they generally claim that countries that borrow in their own currency should not worry about government deficits because they can always create money to finance their debt.
These claims of MMT are rejected by virtually all professional economists. For example, recently IGM forum made poll among top US policy economists to gauge how many economists believe in the above mentioned propositions of MMT,  and the results shows that none of the top economists polled (all economists in the poll are a representative sample of Ivy league economists) did agree with any of the stated MMT propositions (see here). But then even MMT proponents generally do not agree on what MMT is. I seen people claiming it is a monetary theory and others claiming it is whole new economic paradigm. Moreover, the MMT is generally criticized for its policy prescriptions and even generally as a theory itself in the academic literature (e.g. see Mankiw 2020 or Palley 2014)).
Furthermore, you should note that I do not know of any central banker at Fed or elsewhere that would be supporter/adherent to MMT (I suppose some might exist but nobody who is publicly known).

Additionally, will the low-rate environment remain permanent?

This is a good question without a good answer. It might be. Summers (see Summers 2014 in  Teulings and
Baldwin  (2014) or Summers 2015) argues that we will live in low rate environment due to secular stagnation and overabundance of savings (indeed Fed is forced to keep interest rates low due to enormous supply of savings). The secular stagnation hypothesis has its proponents but it is far from being completely accepted by profession.  To an extent we really live in secular stagnation and there is permanent over-supply of saving due to aging populations, slow technological growth and so on it might be permanent. However, it might as well be just transitory phenomenon caused by the sheer magnitude of Great Recession (indeed before pandemic hit Fed and other central banks were already planning to hike the interest rates but then pandemic hit - see this Dec. 2018 news article).

I can't imagine the Fed, for example, raising rates substantially as 1. It would tank most assets and 2. It would make the already incredibly unwieldy sovereign debt that much harder to manage. It would seem we are locked into an endless money printing path that essentially can't be stopped without immense pain. Am I right in this understanding?

Fed can do it in small steps in order to avoid popping potential bubbles. In fact that was the plan before covid-19 hit, to slowly rise interest rates instead of dramatically hiking them. See this NY times article on what Fed officials were claiming they planned to do, from before covid hit,   here.

 * from the mainstream perspective on demarcation of science where theories have to be rigorously defined and testable to be considered scientific, of course there might be some alternative interpretations of what science is see discussions in Reiss Philosophy of Economics


Never a Best Response and Belief Consider a game in static, complete information environment, and the following definition of a strategy never being a best response to a player:

  A strategy $\sigma_i\in\Delta S_i$ is never a best response if there are no beliefs $\sigma_{-i}\in \Delta S_{-i}$ for player $i$ for which $\sigma_i\in BR_i(\sigma_{-i})$.

I want to understand the role of belief in this definition correctly. The definition of belief is given as:

  A belief of player $i$ is a possible profile of his opponent's strategies, $\sigma_{-i}\in \Delta S_{-i}$.

My understanding is:

  In situations where there is no strictly dominant strategy, a player asks herself "what do I think my opponents will do?". To resolve this uncertainty, the player assigns probability distribution over the set of pure strategies of opponent. One particular distribution produces a belief, one possible opponent's profile which is $\sigma_{-i}\in \Delta S_{-i}$.
  Now, I look at my simplex and say, is my particular strategy $\sigma_{i}\in \Delta S_{i}$ a BR to that of opponent? I strike out my $\sigma_i$ if I cannot find any probability distribution over the opponent's pure strategies such that $\sigma_i$ would be my BR.
  So, technically, I would have to compare my particular $\sigma_i$ against every possible probability distribution over the opponent's pure strategies to identify it as Not-BR, but in simple games, you often face with a situation where one of the pure strategies a player might have, say Column L of player 2, never gets underlined when you work out which ones for Player 2 is BR. This helps the process of eliminating all the strategies that are never a best response.

Is my understanding of belief and its role in finding the set of rationalizable strategies correct?

Your understanding is mostly correct, but the following sentence is not:

  in simple games, you often face with a situation where one of the pure strategies a player might have, say Column L of player 2, never gets underlined when you work out which ones for Player 2 is BR.

Consider the following counterexample:
\begin{array}{|c|c|c|c|}
\hline
 &L&C&R\\\hline
U&1,3&3,4&3,0\\\hline
M&2,3&0,1&0,4\\\hline
D&0,0&1,2&2,1\\\hline
\end{array}
In this game, $L$ is never a BR to any of player 1's pure strategies. However, if player 2 believes player 1 will play a mixed strategy that assigns $\frac12$ probability to $U$, $\frac12$ to $M$ and $0$ to $D$, then $L$ becomes a BR.


Pareto optimal and Walrasian equilibrium There are 100 units of good 1 and good 2 in a economy. Consumer 1 and consumer 2 have 50 units of each good.
Consumer 1 only wants good 1 whereas consumer 2 only wants good 2.

Note: Neither of these are lexicographic preferences.

Question: Find Walrasian equilibria

Here is what I have reached:

Can someone explain why red lines are WE..and why not F and G?
And P is Pareto optimal I understand, but is it Walrasian equilibrium as well?

Is every Walrasian equilibrium Pareto optimal and every Pareto optimal point Walrasian equilibrium?

We have two Consumers 1 and 2, and two goods 1 and 2 pure exchange economy. The following utility functions can be used to represent their preferences:

$u_1(x_{11}, x_{12}) = x_{11}$
$u_2(x_{21}, x_{22}) = x_{22}$

Equilibrium price vector $(p_1, p_2=1)$ and allocation $((x_{11}, x_{12}), (x_{21}, x_{22}))$ satisfy the following:

Optimality Conditions (Allocation must solve the utility maximization problem of the two consumers, i.e. it must lie on their demand functions)

$(x_{11}, x_{12}) = \left(\frac{50p_1 + 50}{p_1}, 0\right) $
$(x_{21}, x_{22}) = \left(0, 50p_1 + 50\right)$

Market Clearing Conditions

$x_{11} + x_{21} = 100$
$x_{12} + x_{22} = 100$

Solving the above gives price vector $(p_1, p_2) = (1, 1)$ that supports the allocation $((x_{11}, x_{12}), (x_{21}, x_{22})) = ((100, 0), (0, 100))$ in equilibrium. This allocation is the only competitive equilibrium. It is also the only Pareto efficient allocation in this economy.


What guarantees that for every credit there is a debit in an electronic fund transfer? I'm worried about the difference between seeming honest and actually being honest.  I know banks rely in part on a good reputation to stay in business.  But it seems to me that as long as a bank has a plausible argument that they acted in good faith, they are free (and perhaps indeed it might be greatly in their interest) behind the scenes to be arbitrarily dishonest.

Double-entry bookkeeping guarantees that for every credit there is a debit.

It's not really different for a bank than for you or I.

I can claim that I've got an account with myself for 10 squillion pounds, but everyone will ignore me. The only balances that matter are the physical currency that I hold, and the accounts I have with other people or institutions; e.g. my bank account.

It's the same for a bank: the balances that matter are the physical currency that it holds, and its accounts with other people and institutions. Predominantly, other banks, including Central Banks.

Clearing Houses are institutions, or groups of institutions, that act as intermediaries to ensure that when one bank has a bunch of transactions with another, the net balance is transferred correctly while minimising counterparty risk. And the Central Bank offers a settlement service: for example, banks with sterling deposits will (typically) have an account with the Bank of England, which carries out settlement between banks.


How can banks pay interest to the central bank? If the central bank is the only institution that can increase the monetary base (create both, digital and paper money), how can any institution that borrows from it (mostly banks) satisfy its interest requirements? In other words, how can you pay back more than what left the central bank?

A dumbed down example would be: Only I can create money, I (the central bank) loan you (the banks) 10 dollars expecting 11 dollars back (10 dollars principal + 1 dollar interest). Where will you get that 1 dollar from to pay me the interest if there are only 10 dollars in existence?

This question can be easily answered if there were any way in which new money can leave the central bank without being paid back. Are there such transactions I don't know about?

You anticipate the answer when you ask:

  This question can be easily answered if there were any way in which
  new money can leave the central bank without being paid back. Are
  there such transactions I don't know about?

Indeed, there is always a way that money leaves the central bank without being paid back: the central bank does something with its net interest earnings, usually sending them to the central government, which treats them as part of its revenue, and is therefore able to get by on a little less tax revenue than it would otherwise need. For instance, in 2013 the Federal Reserve remitted $78 billion in profits to the US Treasury.

Let's incorporate this observation into an augmented version of your example. Suppose that the central bank keeps the supply of money at \$10, with a corresponding loan of \$10 to banks, and the annual nominal interest rate is 10%. Suppose that the central government spends \$5 per year and runs a balanced budget.

Each year, banks pay \$1 in interest to the central bank. This is profit and is sent to the central government, which then only needs to raise \$4 in taxes to pay for its \$5 in spending. The net effect of this is to put \$1 in the hands of the public, which ultimately finds its way to paying for the \$1 in interest that banks owed to the central bank. (After all, these banks are presumably lending out the money and collecting interest from the public themselves.)

One can make the example much more intricate, but the key point is that we don't get an exponentially growing debt owed to the central bank by the rest of the economy - because the central bank sends its profits to the government, and then they're recycled into the rest of the economy.

(As user4385 points out in a comment, the situation is similar for any kind of debt. Suppose, for instance, that Connecticut is a net creditor to the rest of the country - where does the rest of the country get the money to pay interest to Connecticut? The answer is that Connecticut eventually spends its interest earnings on goods and services from the rest of the country - funds flow in both directions.)


Source of commodity production statistics? What would be a recommended source of historical data for commodity production amounts which is current up to the previous year or better?

For example, if I wanted to know the annual global production of steel (metric tonnes), timber, cotton, soybeans, aluminum, salt, sulfuric acid, asphalt, paperboard, wheat, kaolin, copper, silica, etc etc, where could I find that information. Note I want physical amounts (tonnes, bushels or whatever), not prices or dollar volume.

I work for Quandl and on our site I can recommend two free historical databases that you may want to check out:

The United Nations Industrial Commodities Database, I believe, shows production amounts for various commodities like steel, petroleum, glass etc. in metric tons for different countries: https://www.quandl.com/data/UINC

The United Nations Energy Statistics Database also shows production for other things like alcohol, gasoline etc. in metric tons: https://www.quandl.com/data/UENG

When you go to each database above, just search for "production" within each database. Hope this helps!


What are some good Phd or research programs for Economic History / Economic Thought History? Please correct me if I am wrong, but my impression is that most "mainstream" economics programs are now focusing less and less on economic thought history. So, in order to do research on economic thought history or some comparative studies on economic development, perhaps history department is a better place to study? What are some good programs for that? Thank you!

What are some good Phd or research programs for Economic History / Economic Thought History?

The RePEc/IDEAS website publishes various rankings in economics. I would suggest checking out their ranking of authors working in Business, Economic & Financial History or History & Philosophy of Economics and see if there are people that you'd like to work with. Usually you can find a list of recent publications or working papers on their website/CV. See if any of those are to your interest. The ranking of departments in those fields (HIS, HPE) may also be relevant.
In addition, there are specialized journals for the fields you mention, such as the Journal of Economic History and Journal of the History of Economic Thought.
Their recent publications should give you a sense of who's currently active in those fields and what they are working on. Also, papers on economic history do get published in mainstream journals. You should be able to find them by searching for articles with the appropriate JEL codes. In your case, codes "B" (History of Economic Thought, Methodology, and Heterodox Approaches) and "N" (Economic History) are relevant.
There is also "A Guide to Graduate Study in Economics: Ranking Economics Departments by Fields of Expertise". Table 3 in this article ranks economics graduate programs in the US by JEL codes. Keep in mind, however, that this is a 13-year-old paper. So information therein may not be up to date, since people may have moved/retired/etc.


How to handle change in base year of index? I have monthly IIP data from 1996-2016. But the issue is the change of base year. For the year 1996- 2011 the base year is 1993-94 and the index is disconnected from Feb 2011. For the year 2005-2016 the base year is 2004-2005.

I intend to use the IIP monthly index from April 1996 - March 2016 but as you can see their exists two set of different index. Can you please help suggest some technique/method so that the entire index is on the same base year of 2004-2005?

For your reference I have attached the data.

Edit: see the data and the necessary calculation here.

You need to rebase the oldest series, using the base from the new series. This is an example of how to do this, with annual data (same for monthly data):

So, basically, you need to find a period in which both series have an entry, compute the ratio between them, and then transform the old series using the ratio just calculated. This is how you link two series in different base years.

Remarks: you will have several months in which the series have values. If you have reasons to believe that the newest series is better, then I would make sense to take the earliest month in which the two have data (probably January of 2005). Nonetheless, the two series might be in fact different (e.g. sector composition or definitions vary). Compare the rate of monthly growth of both indexes for the months in which both have data (probably January 2005 to Feb 2011). Are they very different? If so, you might try to adjust the old series. Perhaps, there is a persistent difference, which you can account for when expanding the newest series backwards. See more in this document.


why has the GDP per capita of Ireland grown of almost 30% between 2014 and 2015? I came across these graphs today :

https://data.oecd.org/gdp/gross-domestic-product-gdp.htm

https://data.oecd.org/lprdty/gdp-per-hour-worked.htm

In both, something doesn't make sense for me: the GDP per capita of Ireland had a 30% growth between 2014 and 2015. None of the other country seems to have such behavior.
Does anybody know why? Is there any bank/debt/accounting reason for this sudden increase? A political reason?

It is an national accounting reason, rather than the Irish people have higher incomes or being more productive

It seems that some companies previously deemed to be foreign are now deemed to be Irish, and so their profits now count towards Irish GDP (and, to the extent they are not a subsidiary of a foreign company and retain their profits, also to Irish Gross National Income).  The Irish Central Statistics Office said a 26.3% increase in GDP and 18.7% in GNI from 2014 to 2015 at constant prices

What may have happened is inversion where United States companies are notionally taken-over by Irish companies (though the old US shareholders remain shareholders of the new merged company), largely to take advantage of Ireland's generous corporation tax regime.  That makes their production/value-added/profits appear to be Irish this year, boosting Ireland's GDP compared with last year

Further reading from 10 months ago when this was noticed:

http://www.irishtimes.com/business/economy/ireland-s-gdp-figures-why-26-economic-growth-is-a-problem-1.2722170
https://www.theguardian.com/business/2016/jul/12/irish-economic-growth-revised-figures-foreign-investment-aircraft
http://uk.reuters.com/article/uk-ireland-economy-idUKKCN0ZS0ZC


Which elements to forecast/estimate Oil/Pretroleum derivatives, would you consider? I mean, if you had to forecast the price or production volumes of polyethylene or polyurethane, for example, which elements would you include to the model, in addition to oil crude prices/volumes?

The idea was to biuld an econometric model, but I have doubts of which factors I could add into the model, since the focus is to predict oil derivatives and not crude oil per se.

Often people will first find a spread between the derivative products and the base one. This spread, is likely to be a reflection of the marginal cost of refining that last unit of the derivative product. Therefore it is likely to depend on demand relative to supply of refining capacity: If there's a new refinery for this product coming online, then you'd expect the spread to fall. If the demand for construction goods that use this refined product is increasing, then you'd expect and increase in the spread.

Often several plastics and refined produces are substitutes of each other, like natural gas and gasoline are somewhat substitutable for each other. I would use the recent price of the other refined products to predict the price of polyethylene or polyurethane or its spread w/respect to crude oil.

This wikipedia article has more on the spread and how people think it is determined.


Would a Job Guarantee impact Cost of Living? What effect would a job guarantee, a method of achieving full employment often suggested by modern monetary theorists, have on the cost of living?

In the case of student loans offered by the government, all this has really done is push up the price of tertiary education (simplification for the purpose of example, I'm not really looking for discussion on this topic). Would a job guarantee inflate the cost of living? I suppose this question would also apply to universal basic income.

The answer depends on whether the provision of full employment is a public good that corrects for a negative externality (poverty). Suppose it is and we wish to create full employment.

First, we should consider what makes government provision of jobs different from policies like unemployment insurance? Instead of hedging against business cycles causing cyclical unemployment, we are now trying to effectively eliminate it. Then, we should consider if the government providing jobs as an employer of last resort would be any different than normal public sector jobs. Presumably, providing such undesirable jobs shouldn't crowd out the private labor market, but at the same time, what is to say that people wouldn't just reject these and continue to seek out jobs in the private sector?

The main route I see for making the government an employer of last resort would be to replace black markets, or to provide competition in inefficient markets. The former option has a prohibitively expensive political cost (and if allowed would be blockaded to the point of gross inefficiency). The latter option is harder to parse through. Most monopolies or inefficient markets we think of today are in technology or other places where monopolies benefit from large economies of scale. Treating the provision of goods in those markets as utilities and then subsidizing them is the go-to option. The other thing that could happen is that the government abuses its power to become a monopoly itself in the market it tries to provide employment for.

All that said, let's put those complications aside. Say the government tries to provide more public sector jobs (of some low perceived quality perhaps). The quantity is fixed to always provide jobs for every applicant at exactly the price where the worker would be indifferent between working and taking the public job. Thus, everyone searching can find employment, and in fact, everyone will be induced to join the labor market in this scenario. Note that the government has changed the number of people in the labor market.

You can form an economy with one representative private good, and one collective (public) good. The government levies taxes on consumers to freely to fund their jobs program if needed. The private sector produces the private good, while the government can produce the private or collective good. The government has the same technology as the private sector.

Thus, we have the different components of our economy:

$$
\begin{align}
\text{Utility:} & \qquad U(x_p, x_c, e) \\
\text{Prices:} & \qquad p(\sum x_p), p(\sum x_c) \\
\text{Production:} & \qquad f_p(\sum e), f_c(\sum e) \\
\text{Private Sector Profit:} & \qquad \pi(x_p) = f_p \cdot p_{x_p} - c(w, e)\\
\text{Government Profit:} & \qquad \pi(x_p, x_c, t) = f_p \cdot p_{x_p} + f_c \cdot p_{x_c} - c(w, e) + t\\
\end{align}
$$

You can add in the appropriate subscripts for the collective good to indicate what you desire about how the benefits or costs of the collective good are captured. We have $e$ as effort, $c(w, e)$ cost given wages and effort, $t$ as the tax, in this a case a simple lump sum. Solving for the equilibrium in the case with or without any government intervention here and then applying Shephard's Lemma would get you the consumer's expenditure function, which you can use to compare the cost of living in each case. If utility for each agent increases with the government provision or stays the same, then although the cost of living may increase, we would say in this scenario it is a Pareto improvement to have the government provision. Obvious extensions to the model could be changing the type of tax, making it so that you can levy a tax on production rather than consumption, or changing the competition so that you can use game theory to analyze price setting.

If this all seems rather theoretical (we have not specified the functional form of these equations), it's because your question is very broad. There is no way to succinctly analyze the effects of full employment on the cost of living. I gave my opinion above that I think it sounds infeasible, but if you wanted to set up a model and investigate for yourself, that might be a noble effort. My official answer thus is that it's unclear what effect a government provision of jobs would be on the cost of living.

(Boring safe answer, I know.)


Why does the Dutch disease cause the value of the currency to increase? I was just reading about the Dutch Disease and it causes that the value of a country's currency increases when said country suddenly finds natural sources of oil. Why is that?

How well do you know what you mean with "currency increases"?

The term Dutch disease describes an event where a single sector's boom (your example, finding oil) causes the said sector to grow and other sectors to decline as revenues increase in one sector. The booming sector causes the value of the currency (for example, the Dutch guilder) to appreciate (grow in value) compared to other currencies. This makes exports from non-booming sectors more expensive for other countries and therefore the booming of one sector causes a negative competitive effect on the other sectors.

So the effect is:

Oil is found
Oil (manufacturing) sector booms
Currency value of the Dutch guilder increases as demand for Dutch guilder increases (to pay for Dutch oil. Can cause/be due to an inflow of foreign currencies)
Exports from other sectors become more expensive (due to currency value increase)
Other sectors become less competitive.


Do tax cuts to the rich lower interest rates? The rationale for giving tax cuts to the income brackets is that this money is then invested in new businesses which increases jobs.

If the saved money is being saved/invested instead of being spent, this would increase the amount of lending capital available and decrease interest rates.

Given that changing tax rates is a distinct and frequent occurrence around the world in a variety of contexts, there must be a lot of data available to perform a regression on.

Do tax cuts to higher income brackets cause a subsequent lowering of interest rates?

You may want to look at the literature of the effects of taxation on savings. A survey is given in: Sandmo. A. (1985) The effects of taxation on savings and risk-taking, in: Auerbach & Feldstein, Handbook of Public Economics, Elsevier.

In this survey, the (simpler) problem of the overall effect of taxation on saving behavior is analyzed. A change in tax progression is much more subtle and harder to measure.

The survey states the problems associated with estimation of this simpler problem and the author comes to the conclusion that the empirical results are inconclusive. Since then there may have been some move in the literature, however.


Doesn't the semi-strong form of the EMH conflict with expecting stock indices to increase in the long run? I willfully don't define "long run", as I'm certain you economists can do this better! Please edify me on a reasonable number, and I can edit this post.

I quote Malkiel's definition of "semi-strong" beneath. As he doesn't believe in the EMH's strong form, and he knows far more about finance than I, I too don't believe in it.

Doesn't the EMH's semi-strong form jar with explanations on Personal Finance SE on why stocks can be expected to rise in the long run?

Burton Malkiel. A Random Walk Down Wall Street (12 edn 2019). Anyone know the page numbers?
THE SEMI-STRONG AND STRONG FORMS OF THE EFFICIENT-MARKET HYPOTHESIS (EMH)
The academic community has rendered its judgment. Fundamental analysis is no better than technical analysis in enabling investors to capture above-average returns. Nevertheless, given its propensity for splitting hairs, the academic community soon fell to quarreling over the precise definition of fundamental information. Some said it was what is known now; others said it extended to the hereafter. It was at this point that what began as the strong form of the efficient-market hypothesis split into two. The “semi-strong” form says that no public information will help the analyst select undervalued securities. The argument here is that the structure of market prices already takes into account any public information that may be contained in balance sheets, income statements, dividends, and so forth; professional analyses of these data will be useless. The “strong” form says that absolutely nothing that is known or even knowable about a company will benefit the fundamental analyst. According to the strong form of the theory, not even “inside” information can help the investors.
      The strong form of the EMH is obviously an overstatement. It does not admit the possibility of gaining from inside information. Nathan Rothschild made millions in the market when his carrier pigeons brought him the first news of Wellington’s victory at Waterloo before other traders were aware of the victory. But today, the information superhighway carries news far more swiftly than carrier pigeons. And Regulation FD (Fair Disclosure) requires companies to make prompt public announcements of any material news items that may affect the price of their stock. Moreover, insiders who do profit from trading on the basis of nonpublic information are breaking the law. The Nobel laureate Paul Samuelson summed up the situation as follows:

If intelligent people are constantly shopping around for good value, selling those stocks they think will turn out to be overvalued and buying those they expect are now undervalued, the result of this action by intelligent investors will be to have existing stock prices already have discounted in them an allowance for their future prospects. Hence, to the passive investor, who does not himself search for under- and overvalued situations, there will be presented a pattern of stock prices that makes one stock about as good or bad a buy as another. To that passive investor, chance alone would be as good a method of selection as anything else.

      This is a statement of the EMH—the efficient-market hypothesis. The “narrow” (weak) form of the EMH says that technical analysis—looking at past stock prices—cannot help investors. Prices move from period to period very much like a random walk. The “broad” (semi-strong and strong) forms state that fundamental analysis is not helpful either. All that is known concerning the expected growth of the company’s earnings and dividends, all of the possible favorable and unfavorable developments affecting the company that might be studied by the fundamental analyst, is already reflected in the price of the company’s stock. Thus, purchasing a fund holding all the stocks in a broad-based index will produce a portfolio that can be expected to do as well as any managed by professional security analysts.

The two propositions here are:

EMH: I can't predict which stocks will do better than average.
The average stock will increase in the long run.

1 does not contradict 2.

Analogy: I am in a room full of babies.

EMH: I can't predict which of these babies will be the tallest in 20 years.
Nonetheless, I can predict that in 20 years, these babies will be taller than they are today.


What is the value of something? What is the worth of something?

I was thinking that it is either how much someone is willing to pay, or is it how much someone is willing to sell it for? Or is it the point where those two meet?

What if it doesn't meet? Say I had an object and would give it up for \$100, but if no one wants to buy it for that much, only say \$90, then what is it worth? Because I won't be selling it and no one will be buying it.

There is a lot to be said about this subject, and I will only give a partial insight.

First off, value is subjective. Everyone will place different values on different things, depending on such things as personal preferences, their economic status and income, and thoughts about the future such as expected future income and wealth, and the future worth of the item. Your reservation price is the highest price you would theoretically be ready to buy or sell something for. This may or may not correspond to the actual price you would be getting on the market. If the price of the product is lower than your reservation price ($ P > P_{r}$), then the difference is your surplus value, which is what you gain beyond what you think the actual value is. For example, on the market for goods, let's say that the price of a good is $ \$ 100 $. Your reservation price is $ \$ 110 $, so that means that you think the product is worth $ \$ 10 $ beyond what you pay. The total value to you, is $ \$ 110 $. On the other hand, the seller's reservation price is $ \$ 90 $ – i.e. the seller would be ready to let go of the product for that amount. On a very efficient market, that price might be what it cost to make the product. So $ \$ 90 $ is the value of the product for the seller. $ \$ 100 - \$90 = \$ 10 $ is the surplus value for the seller, if it sells for that price.
If your reservation price is $ \$ 100 $ to sell something, but the best offer you can find is $ \$ 90 $, then you should distinguish between the personal value that you attach to the product, and the market value. In the public world, we usually value things by its market value. So if $ \$ 90 $ is the best offer you can find, then that is its fair value.
This assumption means that a building that cost $ \$ 1\ million $ to build, can actually be worthless ($ \$ 0 $) on the market if nobody wants to buy it. This could of course change in the future, perhaps people will get around to see the value you see, with time. So how is it that a building can be considered completely worthless, even though it's "obviously not"? Well, it can also be said, from a more financial perspective, that a value of an asset is worth the future income that it will provide. So if the market doesn't believe that the asset can create future income, then it's basically of no use. In market crashes, fear may drive investors to undervalue assets, or simply not be willing to engage in transactions at the time, driving prices down.
We can create a measure of something's value by calculating its present value. Typically, the formula would look something like:

$ PV = \frac{FV}{(1+i)^{n}}$

where $ FV $ is the future value (what you can sell it for in the future), $ i $ is the best alternative rent you would be able to get per period during that time (e.g. by investing in a risk-free bond), and $ n $ is the time periods until payment. The formula discounts the future value to give a comparable present value, that you can use to compare it with other investments. $ (1+i)^{n} $ is the compounding effect of the rent over time.

So let's say that you own a nice painting, and you think that it will be worth $ \$ 500$ in 10 years. Given that you could sell the painting today, and place the money in a bank account which pays $ i = 1 \%$ per year in interest rate, you should be willing to sell it for $ \frac{\$ 500}{(1+0.1)^{10}} = \$ 193 $ today, meaning that you either can get $ \$ 500 $ by selling the painting in 10 years, or the same money in 10 years by selling it now and keeping the funds in a bank account until then. Again, market value is what should be used here to value the asset in transactional terms. But for you personally, the painting may be worth more than $ \$ 193 $ because it brings pleasure looking at it every day. In that case, you might actually value it in such a way that you would rather keep the painting for 10 years, rather than sell it now.


What is market economy status? After reading several articles on China losing WTO dispute against EU for market economy status, I could not understand what is the market economy status in this case?
One such newspaper article is here
My question: Does WTO assign economy status?

Market economy status that World Trade Organization (WTO) uses is not really an economic status per se. Rather its a 'legal' status that determines how other WTO members are allowed to treat country with regards to imposing tariffs or other protective measures. The reason why this status exist is that in past non-market economies such as
Union of Soviet Socialist Republics (USSR) were considered to be engaged in dumping since they heavily subsidized their economically nonviable industries.
WTO has created some special provisions made in case such economy would want to join WTO, and such economies with non-market status could be subject to some extra protectionists policies (in this case especially anti-dumping policies) in contrary to original WTO mission of promoting the free trade.
Such status has nothing to do in principle with whether the country is actually predominantly based on market economy or not. Its rather just a term WTO uses in its policy. A legalistic language does not need to conform to economic reality, for example often many taxes from economic perspective are legally not considered taxes but have different status such as social contributions in many countries.
According to professor Li Jinshan:

The term “non-market economy state” originally appeared in the 1930 Tariff Act of the United States, as opposed to “state-controlled economy”. For the US, socialist countries totally monopolized the national economy and controlled prices of all merchandises. Hence, the prices of exported goods were untrue, and importing countries needed to seek a third country’s data to be a reference to calculate the market price for anti-dumping investigations and for determining anti-dumping duties on goods from the socialist countries. .... In accordance with these criteria, all socialist countries were listed as “non-market economy states”. The EU, Canada and other WTO members followed the US in defining the concept of “non-market economy” and relevant criteria in their anti-dumping laws.

Also yes the WTO can decide whether economy has market economy status or not as its a legalistic term that does not need to correspond to whether economy is actually a market economy or not. In fact until recently countries could choose themselves how to treat China. As further argued by Li Jinshan:

In its WTO accession agreement, China agreed that other WTO members could treat it as a non-market economy until 2015. This classification was agreed in the US-China 1999 bilateral agreement and was multilateralized as part of China’s WTO entry protocol. This classification is vital to one area of trade policy: dealing with dumping allegations against Chinese firms.

So not only WTO can give the economy such status it can even let some countries decide whether they will treat an economy under such status or not. In fact as the article you link mentioned this is all about EU treating China as non-market economy. Of course, countries might dispute this at WTO (it’s in some ways similar procedure to having dispute at a court), but in this case China lost the dispute.


By what steps and contracts does new money enter the economic system? Like many noneconomists who read about economic history and finance, I always remain somewhat baffled by the opaque generation of currency under the federal reserve system. My understanding is that the banks "loan" money to the government, which prints a federal reserve note or IOU signed by Treasury. But then what?

How do the banks actually receive federal currency and/or credit... and determine the amounts they receive? My understanding is that banks can effectively receive as much money as they can "justify" by credit contracts, ratings, and a given ratio of leverage or fractional reserve. Apart from market forces and assumed prudence, are these the only factors that legally limit the amounts of money banks can receive? Can banks essentially get as much money as they say they can securely loan?

The phrasing of your question (the same is true for your description of your understanding) suggests to me that what you need to understand about money creation in banking is much more basic than "steps and contracts". As a full treatment of money creation would not be appropriate on a Q&A site (it'd be really long!), I will instead recommend that you first read about the different types of money (specifically, the difference between base money and broad money), and then that you read "Money Creation in the Modern Economy", which will answer your question about how banks create money.

The short answer to your question is that banks don't "receive" money to loan out as a part of any formal arrangement, rather, they are allowed to lend out a large fraction of the money that is deposited with them. Importantly, when they give someone a loan, the money that is loaned will tend to be deposited at a bank (because banking is a mostly closed system), which gives the bank that receives the deposit the option to loan out more money. That's how money creation happens— loans that, through the magic of double-entry accounting, result in the bank swapping one kind of asset (reserves) for another (an outstanding loan), while the borrower suddenly has a new liability (the loan they owe to the bank), and a new asset (cash).

When we talk about money creation, we are not saying that banks literally create money in the sense of asking that some be printed up for them, it's that the banking system acts in a way that generates total liabilities (or claims on others) that are much greater than the monetary base. Because all money is really just claims on others, this is, in effect, money creation.


Has income inequality ever been solved in societies in the past in terms of what people make to cost of living? One thing I've seen many on here whether life style is increasing or poor's wealth is, income inequality in terms of things like food, water, healthcare keep going up, but wages aren't keeping up.  This includes education sadly since if someone can't afford schooling, they can't escape poverty likely?

Have countries in the past ever faced these issues and solved them?  Is it possible for places like America these days?

America has faced staggering income inequality during the Great Depression.

http://thinkprogress.org/economy/2014/03/31/3420998/wealth-inequality/

In 1933 unemployment was 25%. President FDR's "New Deal" policies of fiscal stimulus, massive government spending on infrastructure, increased financial regulation and the creation of a social safety net (welfare, unemployment, pension) helped millions of people out of poverty and minimized the wealth gap.

Whether such a "New Deal" is politically feasible in today's America is debatable. We have to wait until November 3 to see who wins the election.


What have been the main developments in macroeconomics and financial economics since the 2008 financial crisis? In the aftermath of 2008 economists were, fairly or not, blamed for a failure to foresee the coming crisis. Ideas such as "The Great Moderation" and market efficiency were openly ridiculed as hubristic.

Now, almost a decade later, seems like a good time to take stock and ask: What have been the main developments in macroeconomics and financial economics research that have emerged in response to the financial crisis?

are there lines of research that have been discredited or essentially abandoned?
are there new topics that have received much more attention?
are the new approaches to modelling (or approaches that have come to be used more than previously)?
have any big new ideas emerged in our understanding of recessions / financial crises?

Or perhaps there is good reason to think that everything was fine before and so nothing has to change.

Well, in macroeconomics, namely in DSGE modelling, VOXEU has recently published a report on its uses by Central Banks (CBs), and future lines of improvement, which academics have been tackling but still hasn't found its way into CBs policy analysis. There's no space to explain all the new topics, nor do I think it's the intention of this question. So, I'll just enunciate the topics, with some references. More can be found in reading the report. Also, I'll focus on the theoretical considerations, i.e., it's known that, empirically, the the VAR obtained by solving the DSGE model can be considered as misspecified (see here). This is a WP, but you can easily find many articles on this subject, increasingly so since the crisis)

Financial Frictions (an example)
Forward Guidance(extending low-rates period), due to the presence of a ZLB (see here; this was already being studied before the crisis.)
(Incomplete Markets) Heterogeneity across households in
the transmission of monetary and fiscal policy (see here). I would also add firm heterogeneity (example here)
Systemic fragilities, i.e., economy more prone to crisis due to increasing leverage (an example)
Allowing for structural (long-run) changes, instead of a simple sequence of short-run shocks, this allows for fluctuations of for example the natural rate of interest (see here and here).

Finally, one critique, with which I agree, and Romer has written very funny and interesting 'WP' on, is the degree of exogeneity, through shocks, that is needed to explain the economy.

Behavioural economics (2017 Nobel prize winner was from this area) may supply us with an answer. It allows to endogenize some of the shocks. Here's an article on VOXEU with many references, and analysis of an example of how it's done.

Edit: To complement Kitsune answer, I find this image from the wikipedia page really good. In a very succint way, it explains the difference between macro and micro prudential perspectives.


College enrollment probability model Im working on college enrollment linear probability model where enrollment is regressed on income.

I have the following regressions

$$y=\beta_0+\beta_1x_1+u$$
$$y=\beta_0+\beta_1x_1^2+u$$
$$y=\beta_0+\beta_1x_1+\beta_2x_1^2+u$$

where $x_1$ is Income and $y$ is a binary variable which indicates

In cases (1) and (2) I have statistical significance at the 1% level ( *** ), but in regression (3)I have no significance at all in these variables.

How do I remedy/ interpret this?

Model (1) is a regular linear probability model. Your results say that $x_1$ is significantly correlated with $y$.

Model (2) is strange. It means that the probability is quadratic in $x_1$ and the turning point is exactly $x_1=0$. You will have difficulty justifying the restriction.

The coefficients in Model (3) being insignificant may be a symptom of multicollinearity, i.e., $x_1$ and $x_1^2$ are strongly correlated. To see if that's the case, you can test $H_0: \beta_1 = \beta_2 = 0$. I am quite confident they are jointly significant considering the significant results in (1) and (2). If they are jointly significant but individually insignificant, it's a typical symptom of multicollinearity.

Plotting the fitted probabilities for (1) and (3) often helps. Also see if the range of $x_1$ contains the turning point ($-\frac{1}{2} \beta_1/\beta_2$) in Model (3). You usually have insignificant quadratic terms if the turning point is not in data range, because $y$ is already explained well by the linear model, and then the linear term also becomes insignificant due to multicollinearity.


Why do wars increase the public debts? This should be a very simple question for most of you, but I can't seem to get an answer so I decided to ask the question here. So please be as simple as possible and excuse my ignorance.

This is a chart of the US debt as percentage of GDP versus time. It is obvious that WW1 and WW2 have greatly increased the debt. Let's take the WW2 case as an example. the US military/defense spending reached 38% of GDP in 1944-1945, and as far as I understand, GDP is value of the all the products and services in a country within a specific time, a year in this case.
So my question here is, why does the debt increase during a war ? And why can't governments "direct" the products and the services they already own and which are already accounted for in the GDP to their war effort instead of borrowing ?

In other words, what could have happened if the US spent on the war entirely from its production and services (GDP) without borrowing a penny ?

Countries don't wage war, Governments do.
GDP is the economic production of a country, which is usually much larger than what the government has as available annual income. Historically government expenditure in the US has amounted to ~20% of GDP since 1940 (and was lower than that previously). (Source)

In general, if a government needs to spend more on a war effort, it has three options: print money, which is going to inflate the money supply and might work for a very short time period but will backfire quickly, raise taxation (which may not be possible once taxes get to a certain point, and the US did do this over the course of WWII) but once you reach a certain point, taxation will slow your production down, at that point you'd have to seize assets from the private sector (which obviously wouldn't go down well in the US). Lastly, the government could go into debt.

To answer the second part of your question, since we know that the US was spending 38% of GDP but was only raising 18% of GDP in taxes (and if you look at the graph it's probably safe to say that it was raising an average of 12-15% over the course of the war) that means there's somewhere in the ballpark of 26-20% of GDP worth of money that has to come from somewhere. Since printing more money isn't going to work, realistically the US government would have had to triple taxes from 1930 levels to pay for the war without going into debt, or it would have had to drop the size of it's military by two-thirds, or some combination thereof, say double taxes and half the size of it's military.
This also leads to some problems: if we had to half the size of the US military, would the allies have been able to win the war? Keeping a balanced budget as a priority over that of winning the war doesn't seem like a wise course of action.

Any increase in taxes would also have a dampening effect on the economy itself, (and would also indirectly increase the costs of some of the purchases that the U.S. government would be making), so while the government might get more revenue this way it might end up with a less cost-effective military.

If the government wanted to avoid that, it could just seize assets from the private sector-- if it just stole from multimillionaires, the rail and coal tycoons etc. it probably would be able to finance the expansion without too many short-term effects, but I doubt it would ever have been a politically viable option. Also, arbitrary seizure of private property is generally a bad thing if you want an economy to run well.

So all of this kind of argues for taking on debt.

Of the three choices going into debt is more palatable for most people. It has the advantage of taking wealth from citizens NOW with the promise of them getting money later, when the government desperately needs money now (to win the war) and couldn't care less about how it will pay the citizens back later.


Can 10% of the population provide super-abundance for the entire world? In a discussion at the Watson Institute for International and Public Affairs on Nov 9, Mark Blyth, a political scientist, said that

  We live in a world where literally 10% of the population could provide super-abundance for everyone.

Despite not being defined by Blyth in that talk, I'm assuming that super-abundance in this means:

3500 kcal (14.6 MJ) per day in nutritionally complete food
100 sq meters of appropriate shelter
clothes
entertainment (including vacations)
healthcare, education, sanitation and everything else related to the first two levels on Maslow's hierarchy of needs

Can 10% of the population working full time or the entire working population (I'm assuming that 50% of the population is work capable) working only 20% of the time provide for the entire world ?

Listen to the 30 seconds leading up to that claim. To me it is clear that he is talking of factory jobs. And there he is right. The top countries have no trouble producing more than 10 times the per capita consumption of industry goods per worker.

What he is saying is that production of goods is very efficent. He then goes on and mentions Germany and the US. I looked up the numbers of my home country, Sweden. In Sweden, the number of factory workers has decreased by more than a third since 1970, but production is way up. His point is that lack of production capacity isn't the reason why not everyone has a car, tv, washing machine, etc. We have the technology to produce the same material wealth (things, not services) for the entire world using just 10% of the population.


Understanding Bond Yields According to Bloomberg, the coupon rate on a 10-year UK government bond is 4.75%.

Bloomberg also states that the yield is currently 0.55%, and the market price £143.51.

But if the following formula is correct:

Then the yield should be $\frac{4.75}{143.51} \approx 3.31$%

Clearly this isn't the case. So what did I do wrong?

You did not apply your formula correctly.

Your top formula is correct. But in your bottom formula, the numerator on the left side of the equation is a percentage. It should, instead, be a monetary unit of £ in this case.

The annual coupon payment should be denominated in £. Not a percentage. Otherwise, the units don't balance each other and don't match the units of the original equation.

Edit:

I noticed in your comment you include some information that was left out of the original question: that the par value is £100.

That's why I asked for a link to the source of the Bloomberg report. These numbers would make more since if the par value were £1,000


In GDP growth studies, are factors of production measured as stock or flows? Consider the following cases:

One machine (capital) is used by multiple producers within one year. For instance, farmers renting tractors from the same company. In this case, in terms of GDP, there is one unit of capital which was used to produce value added by many producers.
One worker (labour) which have two jobs. For instance, in a factory during the day, and as a Uber driver during the night. In this case, in terms of GDP, there is one unit of labour, used to produce value added in different goods/services.

The common feature is that the same factor of production (stock) is employed in more than one activity over a given period (flow).

Is the measurement of capital and labour used in the standard "determinants of growth" studies based on the stock or flow approach?

In other words, are capital and labour measured in terms of the flow of services that these factors produce, or in terms of the stock of factors available in an economy over time? It is clear to me that the latter approach is plagued with problems, and the former is clearly more accurate.

My experience is that the use of stock is more common.

In Nicholas Stern (1991)'s The Determinants of Growth first equation (I a), without preconceived ideas, one reads

$\frac{\dot{K}}{K}
= \frac{d K}{d t} \frac{1}{K}$

Which means explicitly (in discret values)

$= \frac{K_{t+dt}-K_{t}}{dt} \frac{1}{K_{t}}$

If $t$ is in years, and that we are interested in the variation of $K$ over $1$ year (i.e. $dt=1$), one obtains

$= -1 +\frac{K_{t+1}}{K_{t}}$

Even if the above equality could represent either the variation of a stock or the variation of a flow, the story behind this is about stocks. To summarize

$K_{t}$ is the stock of capital in the economy at year $t$
$dK = K_{t+dt}-K_{t}$ is a flow of capital occuring at year $t$, differently put an investment in capital.
$\dot{K}=\frac{d K}{d t}$ is the absolute dynamic of investments in capital in economy $\forall t$
$\frac{\dot{K}}{K}$ is the relative dynamic of investments in capital in economy $\forall t$

Depending on the object you are looking at, it can be both measured in flow or in stock. To know with what you are dealing with, you must understand the story behind equations.

To the practice side of the issue, you cannot make realistic analogy between Solow's capital and, say, tractors. The least abusive perception of $K$ would be cumulated flows of investment in terms of money since, for example in micro-based CGE modelling, it is conceived as representative of the shareholding structure of the economy, and is thus linked to income formation via dividends (see the zero profit condition). In this non-realistic framework, although non-abusively linked to the everyday-life object, $L$ is very similar to $K$, is a self owned stock, and gives right to wages, that are flow objects, as dividends are. Still on the practice side of the issue, the difference between $L$ and labor force is the fact that the former is effectively employed, while the latter is not. Put differently, the link between the two is the labor market, $L$ is a demand, while labor force is a supply, and both form jointly a labor market whose equilibrium is reached via deflation/inflation of wages.

Finally, to my knowledge, the fact that  the same factor of production (stock) is employed in more than one activity over a given period (flow). is not really a neoclassic native notion, I would say, once again when one refers to CGE modelling, because of the capital market clearing condition. It is more a monetary-macro-financial object, and is, e.g. all what debt is about when dealing with capital. However I do not see any analogy with $L$ in this case.


Soft Question: Economic measurement in a post-industrial economy I have a colleague who is a mathematician by training and currently works in Risk Analysis. He has issues with current Economic theory and I have debated him over coffee a couple of times.

One question he asked stood out to me as I could not answer it.

  In terms of economic measurement, how does one know if the variables economists are looking at are relevant to the economic health of a country in a post industrial economy?

  i.e.people and firms consume and produce many services that barely make a dent in the GDP, like how some medications and computers today are much cheaper today than when they first arrived on the market.

Your friend is right that GDP and similar measures are flawed—or, at least, incomplete. But this isn't exactly news to economists!

For example, Richard Easterlin was arguing in the 1970s that GDP is a poor measure of national well-being. The specific issues with GDP that you point out in your question (failure to account for the value of innovations or for free products, etc.) are so well-known that they now make it into tutorials aimed at high school students. For a more recent take on the issue, here is a discussion paper on the topic of technology and GDP measurement (the author also has a book on the topic of GDP as a measure).

To be a little bit more concrete about how economists know the measure is flawed, let's look at how economic theory helps us to set objectives and guides us in measuring our performance in a simple example.

Economics as a body of knowledge suggests variables of interest to a policymaker. Suppose, for the sake of illustration, we are concerned only with maximising peoples' material well-being. We know that we can get a measure of material welfare by computing the area bounded by the general equilibrium demand curve and supply function. So, in an ideal world, we would just measure this total surplus and pursue policies that increase it. For a variety of reasons, this quantity is difficult to measure—especially at the aggregate level over time.

The 'next best' alternative is to use the economic model to tell us what variables influence this surplus, and then try to measure those variables instead. Obvious examples of such variables are income (which expands demand possibilities) and technology (which expands production possibilities). Broadly speaking, if income is going up and technology is improving then the surplus (which is what we are actually interested in) should also be increasing.

It is important to keep an eye on both variables because the theory tells us that surplus can rise as income falls if, for example, technology is improving fast enough (just think about the extreme case where technology is so good that we can produce everything costlessly; then price and income would be zero, but surplus from consumption would nevertheless be very high).

With this framework in mind, it is very natural to look at GDP and say: "This is a measure of income, which is a part of the picture. But it is missing another component (technology) that we know, from theory, is also important."

If measures like GDP are known to be so flawed, why are they used? It is important to understand that no serious economist cares about GDP per se. Instead, economists stress the importance of a portfolio of policies that work together to improve overall well-being of the populace. There are many factors that weigh on well-being. These include income and productivity (which will show up in GDP), but also technological innovation, environmental improvement, improved health outcomes, reduced inequality, and so on.

Given these objectives, some way is needed to measure the efficacy of policy. Because the agenda is multi-faceted, we need enough indicators to measure the various dimensions we are interested in. GDP is useful because it is a widely-available measure of one part of what economists are interested in (material wellbeing). But this should not be confused with a situation where GDP is the objective in its own right. Nor should it be thought that economists have no interest in improving upon this measure.

The monomaniacal fixation with GDP is really a trait of the media and politics rather than practicing economists.


Value Added Approach of GDP calculation Suppose I sell bread loaf for 20 dollars, the cost of raw material like oil,flour,electricity.... is 13 dollar, I pay 2 dollars to my workers, 1 dollar to transportation company to transport it to someplace , finally I make 4 dollar profit. Whats things will be considered for the GDP calculations through value added approach.

Value added GDP measures the total market value of all final goods and services produced in the same country. Intermediate goods (goods or services that are input in the production of other goods) are not included in Value added GDP to avoid double counting.

The making of bread( raw materials) would be the cost of the initial inputs to include transportation services.  In the Transportation statistics annual report of 1996 transportation services are components of both final demand and production.  However, a large share of transportation activities, like freight, is identified as intermediate inputs.

https://books.google.com/books?id=r3sgAQAAMAAJ&pg=PA42&lpg=PA42&dq=intermediate+inputs++trucking+service&source=bl&ots=2OtHjJ5qhp&sig=ACfU3U31CxEpI6jMe3hQiNIZzbhXGg1nbQ&hl=en&sa=X&ved=2ahUKEwi35tbZ07npAhX-mHIEHf0bCqEQ6AEwA3oECAUQAQ#v=onepage&q=intermediate%20inputs%20%20trucking%20service&f=false

components of Value Added (VA): Labor Income (LI)[cost of workers], Other Property Income (OPI),[capital costs] and Taxes on Production and Imports (TOPI).
So I listed labor separately to be accounted for value added.

Valued Added would omits the following:

the cost of raw material (13 dollar)

1 dollar to transport it to someplace


a risk lover agent preferences and the preference of risk natural agent may be the same Consider two lotteries $N$ and $M$. Agent $i$ is risk-averse and prefers $N$. Agent $j$ is risk-neutral and prefers $M$. Would any risk-loving agent $k$ also prefer $M$? That is, would $j$ and $k$ have the same preferences in this scenario?

My attempt:

For example, I can easily show that a risk averse agent can behave as if it is risk natural. I can show this on indifference curves by using the equal marginal rate of substitution.

Then I consider and follow the same way to demonstrate a risk lover agent behave as if risk natural agent by using MRS. But I cannot a result that does make sense.

But I know and assume that I need to use MRS and indifference curve. After that point, I am glad if you give any help. Thanks a lot!

Don't commit the cardinal mistake of equating preferences with choices.

In the context of Expected Utility Theory, the fact that a risk-averse agent ($RA$) would choose $N$ over $M$ implies that

$$E[u_{RA}(N)] > E[u_{RA}(M)]$$

The fact that a risk-neutral agent ($RN$) could choose $M$ over $N$ implies that

$$E[u_{RN}(N)] < E[u_{RN}(M)] \implies E(N) < E(M)$$

A risk-lover is a person that could choose $M$ over $N$ even if $E(N) > E(M)$. So here that the opposite inequality holds, it is certain that it will also choose $M$ over $N$, given also the fact that there appears to be no other lotteries to choose from.

But never say that the risk-neutral and the risk-lover have "same preferences". They don't -it just happens, given the available lotteries, that they choose the same lottery, even though they have different preferences.


Lucas Cost of Business Cycles I am trying to understand the logic behind Lucas attempting to analyse the potential benefits of eliminating business cycles by attempting to calculate the percentage of income that individuals would be willing to pay to eliminate such cycles/fluctuations;
My understanding is that Lucas proposed measuring the cost of business cycles as a percentage of consumption that would make a consumer indifferent between a world with and without business cycles - and that, this was found to be an unrealistically small proportion, from which it may be concluded that business cycle fluctuations are not very harmful for welfare(?), economic growth(?) etc.

However, how exactly is the impact of business cycles quantified in such a framework? In other words, if business cycles are so severe that many people lose their jobs, then if they were aware of this possibility, they'd pay a far greater insurance not to lose their jobs, i.e. to live in a world with no business cycles.

The Lucas model does not address at all the points that you address of people losing jobs, as it utilizes just one agent that simply has a perfectly steady (perhaps growing at a constant rate) consumption path. A model with heterogeneous agents where they have the possibility of losing their jobs and having some periods with, supposedly, very low consumption, would give a much higher cost of business cycles.

Further, in a paper using robust preferences Sargent and some coauthors find that if the agent has fear that his model of where income fluctuations are drawn from is misspecified, the costs of business cycles are much higher.


equilibrium, optimum, and decentralizing the optimum I'm reading a paper on parking:
Anderson & de Palma, 2003, The economics of pricing parking.

The authors repeatedly refer to either 'decentralizing the optimum' or 'the optimum can be decentralized'....

Here is an example:

  The optimum involves unequal treatment of equals in the sense that
  different individuals get different utilities at the optimum.  Those
  who are allocated to park closer to the [central business district]
  get higher utility than those who park further away.  The optimumm can
  be decentralized via pricing of parking.  Since parking is more
  desirable closer to the center, the optimum parking tariff increases
  with closeness to the CBD in order to counteract this effect and
  reduce the over-congestion that is more pronounced closest to the CBD.
  We next derive the optimum parking tariff.

Q1: In general in economics literature and/or in the context of this paper, is "optimal" generally accepted as referring to Pareto efficiency?

Q2: What does it mean to "decentralize the optimum" ?

Q1 Optimal usually means one of two things:

Pareto optimal (there's no way to change the outcome such that everyone is at least as well-off, but someone is strictly better-off).
Optimal in the utilitarian sense (we maximise the sum of everyone's profit/utility).

If utility/profit is quasilinear then the two concepts coincide.

This paper appears to be using the utilitarian standard: the optimum is the allocation that minimises the sum of everyone's costs (which, in this case, are the time spent travelling and parking).

Q2 To understand what is meant by decentralisation, it is useful to first know what we mean by centralisation. We say that a decision is centralised if there is one agent (often called a "social planner") who makes all of the decisions and imposes them on society.

We know from experience that governments are not very good at centrally planning things (cf. the USSR). Thus, an interesting question is whether we can set up a market, system of prices, or other kind of mechanism such then we can leave each individual to his/her own devices and still end up with the optimal outcome (such as how we get the efficient outcome under perfect competition, without any kind of central planner).

When everyone is left to their own devices like this, the market is said to be decentralised. We say the optimum is decentralised if we find a way to decentralise the market such that the end result is optimal.


What is used more: economic growth rate compared to previous quarter (GPSA), or growth rate compared to the same quarter of the previous year (GYSA) For my thesis I'm writing about the Baltic states and why they didn't vote out their incumbent governments despite undergoing severe austerity. As part of that I'm looking at their growth rates from quarter to quarter, but the OECD website gives me two options to do so:
Growth rate compared to previous quarter (GPSA)
Growth rate compared to same quarter of previous year (GYSA)

I'm not sure which is used more often in academic literature, or is more useful for my purposes. I've seen both being used in newspapers, and so I'm not sure which is better. GPSA seems more volatile, but I think I've seen it being used more often as well.

Any ideas?

QOQ (quarter on quarter) GDP growth is more common, at least in the US and the UK.

See the press releases by the US BEA and UK ONS. For both, the headline rate is the QOQ rate.


Are these preferences consistent with rationality? Suppose there are three kinds of commodities, X Y and Z. We ask an agent about his preferences and receive the following answers:

"I prefer Z to Y and Y to X".

"For every $n$, I prefer one unit of Z and $n-1$ units of X to $n$ units of Y".

Are these preferences consistent with rational preferences, according to the "rationality" axioms of von-Neumann and Morgenstern?
Initially, I thought that "obviously yes". von-Neumann and Morgenstern only talk about preferences on lotteries, but here, the agent's preferences are only given on sure sequences, so obviously there should be some rational preference relation on lotteries that is consistent with them.
However, one of the rationality axioms is "continuity". It says that there exists a probability $p\in(0,1)$ such that:
$$ p Z + (1-p) X \sim Y $$
The preference relation can be represented by a function $u$ such that: $u(X)=0, u(Y)=p, u(Z)=1$.
But then, if we take $n>1/p$, if the agent receives $n$ units of Y, his utility is more than 1, so the agent should prefer this over receiving one unit of Z and $n-1$ units of X...
What is wrong with these preferences?

You implicitly assume that the utility of $n$ units of $Y$ equals $n$ times the utility of 1 unit of $Y$, and there is no reason for that. For instance, if $Y$ is a fridge, the gain in utility from having 1 fridge compared to 0 is certainly larger than the gain in utility from having 2 fridges compared to 1. The formula $U("nY")=n*U("Y")$ that you use does not make sense: there are utility functions other than $U$ that represent the same preferences over $\{X,Y,Z\}$, and you will reach different conclusions if you make the same computation with these utilities.

The Von Neumann-Morgenstern theory does not make any assumption on how to value $n$ units of a good. A Von Neumann-Morgenstern representation attributes a utility level to all the consumption goods in the choice set. In your case, the representation would include objects such as $U("Y")$ (the utility of one unit of $Y$), $U("nY")$ (the utility of $n$ units of Y), $U("Z \text{ and  }(n-1)X")$ (the utility of $1$ unit of $Z$ and $n-1$ units of $X$), etc. There is nothing that allows you to relate these values with each other. The only behavioral restrictions of the Von Neumann-Morgenstern theory concern preferences over lotteries induced by these goods.

You need other tools to understand whether preferences over a finite set of commodities are rational. These tools are the Weak Axiom of Revealed Preferences and the Generalized Axiom of Revealed Preferences.

On a historical note, the reason why Von Neumann and Morgenstern developed a theory of preferences over lotteries is precisely because they wanted to identify a notion of "how much the good $Y$ is preferred to the good $X$". An obvious possibility was to observe preferences over pairs of goods such as: $n$ units of $Y$ versus $m$ units of $X$. But this is problematic for the reason stated above: nothing relates the utility of one unit of $Y$ to the utility of $n$ units of $Y$. Their trick was to consider preferences over lotteries that deliver $Y$ with a certain probability and $X$ with the complementary probability: the answer to the question "how much are you willing to pay to increase your chance of receiving $Y$ by 1%?" gives a good measure of "how much you prefer $Y$ to $X$". In contrast, the answer to the question "how many units of $X$ are you willing to sacrifice to receive one additional unit of $Y$?" does not make any meaningful sense.


prove that $M_xM_1 = ?$ Let $\mathbf{y} = \mathbf{X_1}\mathbf{\beta_1}+\mathbf{X_2}\mathbf{\beta_2}+\mathbf{u}$.

Let $\mathbf{X} = [\mathbf{X_1} |\mathbf{X_2}]$.
Define $\mathbf{M_i}$ to be the complementary projections for $i = 1,2$.

Then, $\mathbf{M_xM_1} = \mathbf{M_x}(\mathbf{I} - \mathbf{P_1}) = \mathbf{M_x - M_xP_1} = \mathbf{M_x-[I-P_x]P_1} = \mathbf{M_x-[P_1-P_xP_1]} = \mathbf{M_x - [P_1-P_1]} = \mathbf{M_x}$.

Could you check if this is okay?

The only assertion here that goes beyond self-evident matrix algebra and substitutions, is that

$$P_XP_1 = P_1$$

Since the columns of $X_1$ are in $X$ it follows that

$$P_X X_1 = X_1$$

because in general it holds that

$$P_X X = X$$

Namely the projection matrix operates as the identity matrix for the columns of the matrix from which it has been constructed. But then

$$P_X P_1 = P_XX_1(X_1'X_1)^{-1}X_1' = (P_XX_1)(X_1'X_1)^{-1}X_1'$$

$$=X_1(X_1'X_1)^{-1}X_1' = P_1$$


What is the effect on GDP when foreigners buy lots of domestic bonds? I am trying to figure out the effect on GDP of foreigners buying lots of domestic bonds. From what I understand, when foreigners buy lots of domestic bonds:

They need to convert their foreign currency into the domestic currency. This increases the demand for the domestic currency, leading to appreciation of the domestic currency. This appreciation of the currency makes domestically produced goods more expensive to foreigners, while making foreign goods cheaper. Exports fall and imports rise. Net exports fall. Therefore, GDP decreases.

The influx of foreign money into bonds causes bond prices to rise, and bond yields to drop. The increased demand for bonds leads to lower bond yields. As a result, domestic firms will find it easier to borrow money. This leads to an increase in investment. Therefore, GDP rises.

Is my understanding correct? What am I missing? In the real world, when foreigners buy lots of bonds, what happens to the GDP?

For every buyer there is a seller. If a foreigner buys a bond, that means a domestic investor sells it to them (or issuer). Why should the identity of who owns the bond matter?

In practice, there are many moving parts. One feature of financial crises is that investors buy U.S. Treasury bonds as a flight to safety. This means that purchases coincide with the weakening economy created by the financial crisis.


Why has gold dropped during the same week as Deutches Bank faces great difficulties I chose the phrasing "great difficulties" to be polite. The "capital release unit" seems to be a bit of a desperate action from the bank, coupled with further complications involving bad press made things even worse for DB.

Wouldn't all of that be a fairly unmistakable signal to buy gold as a hedging instrument?

Question

Is there anything in economic theory that can explain why gold would drop when a bank looks to be in big trouble? Have I missed something? Or is this a case of "market irrationality?" I wonder if there are studies on how long markets can remain "irrational."

As Brian Romanchuk commented, there are a number of factors that can affect the daily price of an asset.  Gold is one of the most traded futures contracts on the CME so the performance of one bank (assuming you mean Deutsche Bank) might not be enough to offset those other factors.

But there is a strong correlation between gold and fiat currencies.  This is because gold is used to hedge against inflation.

Regarding your question about economic theory:

In a fractional reserve banking system, the supply of money is controlled by a central bank such as the Federal Reserve.  According to the Quantity Theory of Money, the supply and demand of money determines inflation.  However, John Maynard Keynes rejected this theory because it doesn't account for interest rates.

Keynes suggested that governments could offset recessionary / inflationary periods by directly decreasing / increasing interest rates.  According to Keynes, lowering interest rates in a recessionary period will create an incentive to borrow (cheaper capital) and short-term demand for money increases.  Prices change slowly in response to the change in interest rates as lenders increase the money supply to meet demand.  This slow change allows money supply and changes in interest rates to encourage or discourage borrowing and lending.

I'll attempt to unite economic theory and the futures market:

Generally speaking, a commercial bank generates most of its revenue through loans and consumer lending.  You could think of it as essentially selling / producing money.  They are inherently long money just like a gold miner is inherently long gold.  So their "product" becomes cheaper when interest rates are cut.  Since the price of gold behaves similarly to currencies, I suppose a bank could short gold futures in order to hedge their position.

The Fed's chairman Jerome Powell spoke recently. Many interpreted his economic outlook as a dovish signal which could imply lower interest rates.  If that happens, banks' revenue would decrease and the value of the dollar would be expected to decrease and the value of gold would be expected to decrease as well.  But nothing is guaranteed :)

Regarding irrational markets

A former coworker would say to me, "the market can remain irrational longer than you can remain solvent".  If you are able to predict irrationality then it would no longer be irrational. I recommend you read the book Fooled By Randomness by Nassim Taleb.


Why is the 10-Year Treasury Constant Maturity Minus 3-Month Treasury Constant Maturity Curve significant, but not the 5-year minus 1-year? I am new to investing and am trying to learn about economic indicators.

When the yield curve inverted this year on March 27th, the media published articles saying that this might indicate a recession. The Federal Reserve Bank of St. Louis site tracks the 10-Year Treasury Constant Maturity Minus 3-Month Treasury Constant Maturity curve, with the correlation with past recessions. It tracks a few other curves, correlating them with past recessions, perhaps because they are supposed to be significant with respect to recessions.

Thanks to Bob Baerker's answer on the Money site, I was able to get raw fed rate data. With this, I learned that the 5-year Treasury Constant Maturity Minus 1-year Treasury Maturity Curve was already inverted on 24th December, 2018, and has been almost constantly inverted since then!

So, why is it that nobody cares that this 5-year minus 1-year curve has been inverted since late last year, but everybody cares that the 10-year minus 3-month curve inverted this year? Why is it that the former is considered irrelevant to recessions, but the latter is considered relevant?

As a first approximation, we can think of the 3-month bill as as being the “market forecast” of the (geometric) average of the overnight rate for the next three months, while the 1-year is the average for the next year.

In a rate-hike cycle, the 1-year rate ends up much higher than the 3-month rate. This means that it will get close the the 5-year rate much faster.

Furhermore, there is presumably a greater risk premium - term premium - in the 1-year versus the 3-month maturity. This will also tend to compress the 1-/5-year slope faster.

Once the yields on the 1-year and 5-year are close, small “technical factors” in yields are much more likely to lead to an inversion. Therefore, it would be more likely to generate false positives.

The reality is that market commentators and economic researchers have searched through all the various slopes to find the “best” ones for forecasting. So it is probably not safe to say that the 1/5 slope is “irrelevant.”

In any event, yield curve slopes are hardly perfect. I discussed some of the issues in this question. Since slopes are not infallible guides to recession forecasting, one can argue that the choice of maturities (technically, tenors is a better term) is somewhat arbitrary.


Binary Relations for Cobb-Douglas I am reviewing old midterms to prepare for my upcoming midterm and ran across this question:

Let $\alpha , \beta \in (0,1)$. Now, let $f_{\alpha}$ and $f_{\beta}$ on $\mathbb{R^2}$ be defined as $f_{\alpha}(x)=x_1^{\alpha} x_2^{1 - \alpha}$ and $f_{\beta}(x)=x_1^{\beta} x_2^{1 - \beta}$

Now, let R be a binary relation on $\mathbb{R_x^2}$. Let ${x,y} \subset R_+^2$ We have that: $$xRy \leftrightarrow f_{\alpha}(x) \geq f_{\alpha}(y) \land  f_{\beta}(x) \geq f_{\beta}(y)$$

For which combinations of $\alpha$ and $\beta$ is this binary relation complete, for which combinations is it transitive and for which combinations is it continuous.

My thoughts

It seems this can only be complete if $\alpha=\beta$ but I can't quite finish the proof whenever I proceed WLOG with $\alpha < \beta$ Can anyone here offer an attempt at formally proving that this is complete iff $\alpha = \beta$ ?
I think that anytime we have xRy, yRz we will necessarily have xRz. That is. And so, I think this is transitive for all combinations of $\alpha,\beta$. My proof involves using the well-ordering of the reals and the definition given for this particular relation. If anyone thinks that this is not true for all $\alpha,\beta$ please let me know why/how.
I know what continuity is and how to prove it. However, I am not sure for which combinations of $\alpha,\beta$ this relation is continuous. I suspect it is continuous for all combinations of $\alpha,\beta$. Is this true? If so, can you prove it?

I will be using the following definition of continuity for binary relations.

Definition 1: A binary relation $\mathcal{R}$ on $\mathbb{R}^2_+$ is continuous if for every $x$, the following sets are closed.
$$
USC_x = \{y\in \mathbb{R}^2_+|y\mathcal{R}x\}
$$
$$
LSC_x = \{y\in \mathbb{R}^2_+|x\mathcal{R}y\}
$$

Definition 2: A set $Z$ is closed if $z_n$ is a sequence in $Z$ and $z_n\rightarrow z$, then $z\in Z$.

Now, let $\mathcal{R}$ be defined as in your question, i.e.
$$
x\mathcal{R} y\iff f_\alpha(x) \geq f_\alpha(y)\text{ and }f_\beta(x) \geq f_\beta(y)
$$
Let $x\in \mathbb{R}^2_+$. Let $x_n$ be a sequence in $USC_x$ converging to $x^\ast$. Then, for each $n$,
$$
f_\alpha(x_n) \geq f_\alpha(x)\text{ and }f_\beta(x_n) \geq f_\beta(x).
$$
Since $f_\alpha$ and $f_\beta$ are continuous, we have
$$
f_\alpha(x^\ast) \geq f_\alpha(x)\text{ and }f_\beta(x^\ast) \geq f_\beta(x).
$$
implying that $x^\ast\in USC_x$; hence, $USC_x$ is closed. We can show also that $LCS_x$ is closed by using identical arguments. This concludes that $\mathcal{R}$ is continuous.

Remark 1: The arguments above provide a general strategy of analyzing statements regarding $\mathcal{R}$. Transitivity of $\mathcal{R}$ can be proven in a couple of simple steps. Your statement regarding this property is a bit vague, and should be more rigorous imho.

Remark 2: Your explanation about completeness needs a clearly written argument as well. While it is true that $\alpha=\beta$ implies completeness of $\mathcal{R}$, the reasoning that makes it true is not exactly what you are proposing. It is also necessary to show that $\alpha\neq \beta$ implies that $\mathcal{R}$ wouldn't be complete (I believe that this should be the case). This would require a bit more work on your part. Let me know if you run into troubles in this.

Bottomline: In my sincerely humble opinion, you should exercise a lot with proving things. Maybe grab a book on introduction to abstract mathematics and such.


How to derive the Indirect Utility Function from the Marshallian Demand Function? I have been trying to derive the indirect utility function $(V(p,y))$, where $p$ is price and $w$ is wage, given the Marshallian demand functions $x(p,y)$ with the help of Roy’s identity (the utility function is not known. We only know the Marshallian Demand functions)

I would need to take the integral of the marshallian demand to obtain V. But this seems rather complicated to me.

If Roy’s Identity is:

$$ x(p,y) = - \frac{\partial V(p,y)/ \partial p}{\partial V(p,y)/ \partial y}$$

So if I know $x$ how can I derive $V$?

I have been thinking about this and trying some equations, but unfortunately I could not come up with a solution.

Thank you for your help!

Recovering the utility function given Marshallian demands only is called the 'Integrability problem'.

In general, it is quite difficult. However, there are some conditions under which it is possible. Kim Border has some notes on this topic on his website.


What happens to aggregate C, K, and Y when TFP increases permanently? I was wondering what would happen to aggregate capital, consumption and output (i.e. K, C, Y) in the Solow model with constant population growth (i.e. n > 0) and no technological growth (i.e. a = 0) if TFP suddenly increases permanently at time $t_{0}$ (i.e. $A_{0}$ --> $A_{1}$).  I am assuming that all three K, C, and Y will increase and converge to the new steady state level. But I wanted to know how it would adjust(i.e. would it be an instant increase or gradual increase from previous to new steady state level).

Take a look at the dynamics of the capital:
$k_{t+1}=sA_ty_t+(1-\delta-n)k_t$. A sudden positive shock to TFP in period $t$ increases the capital stock of the next period $k_{t+1}$. So, there is no contemporaneous effect on $k$, convergence to the new steady state will be gradual.

The other variables have contemporaneous relationship with TFP.

EDIT: A google search for a good explanation lead me to lecture notes from MIT which you can find here. Start reading slide # 62+. You will see the graphical explanation as well.


What are the alternative uses of unlimited wants and scarce resource? Actually I want to know what does it mean by alternative uses of this two terms of economy.

Scarce resource : is a (physical) limitation which forces us to make choices accordingly. It is what is available under current technology and cost of extaction. We could say its a supply side perspective and generally refers to material.

Unilimited desires: Is a demand side perspective. Individuals or organizations usually want more tomorrow than today. Even if you get satiated of one good you will want more. For instance if you have enough foood you can't eat more but maybe you would wish a special meal in a fancy restaurant. So even if cooking home was sufficient to narch your need, after an increase of income you will buy more services... bigger house... There are diminishing returns to consume more of the same good but imagination makes it possible to always find a new object of desire. Thus unlimited wants.

By combining these two phenomenons, a scarcity situation arises and humanity must make choices hopefully to fullfill the most pressing needs.


Do the efficiency savings of mergers indicate a type of waste or inefficiency in a market? In this BBC News article about the merger of Tata Steel and Thyssenkrupp, the following figure is reported:

  The merged group anticipates it will make costs savings of between £350m to £440m a year.

Presumably some or all of these savings would be achieved by eliminating redundant duplication of departments across the two organizations.

Are the cost savings mentioned in the article indicative of a fundamental inefficiency caused by a competitive market, that wouldn't be present in, say, a nationalized industry (or total monopoly)?

Are the cost savings mentioned in the article indicative of a
  fundamental inefficiency caused by a competitive market, that wouldn't
  be present in, say, a nationalized industry (or total monopoly)?

That "causation" is mischaracterized. It is not that a competitive market causes inefficiencies, but that it encourages their removal. Inefficiencies also exist in a state-controlled economy, but there the government pursues other policies because it does not need to be concerned about the risk of being left out of the [state-controlled] market.

The title of the article you shared serves to illustrate the point. The fact that the unions "welcomed" the merger reflects how they typically object to mergers (elsewhere, the article quotes one union officer in terms of having "made great sacrifices"). The historical friction from unions is antithetical to the optimization that eventually becomes indispensable in a market-based economy. Here, it appears from the article that the unions understood that Trump's tariffs on steels and the imminent consequences from Brexit are compelling reasons to reach an agreement and accept the merger.

A natural monopoly is the only monopoly that could thrive in a competitive market because, by definition of natural monopoly, the existence of competitors would not result in improvements in the market or economy.