What would be the income tax rate be if it were 'flattened'? In some recent conversations/speeches (It's voting season), I have noticed many people do not understand how a marginal income tax system works.

Not understanding how they are only taxed at the higher rate, on the income in the higher bracket is one thing.

However for today's question I am looking to address people feel sore that when they work harder (e.g. overtime) they are taxed at a higher rate, so they would like a flat tax rate.

This is true perhaps for those who are the very top income earners. But for everyone below them this is not true. Because they would have had to paid the same, but higher, tax rate on the lower brackets of their income.

So my question is:

Assuming the same dollar amount of income tax for the government* stays the same, what would be the income tax rate be if the marginal tax rates were flatten to a single rate?

Bonus: At what income amount would be the tipping point be, where you would be better or worse off under these different rates.

*I am most interested in what this would be in New Zealand. However I am happy to take answers for any OECD country.

A flat tax rate would almost certainly have some secondary effects. Most likely they would have a negative effect on the total tax taking, and would also likely cause an increased demand on government services; requiring raising of taxes. What and the extent of those secondary effects are warrants a separate question (thesis probably!) So for the sake of simplicity, let's keep them out of scope, for this question.

Having worked on these issues myself for quite some time, I am not aware of any study on this for New Zealand. For a back-of-the-envelope calculation of the revenue-neutral flat tax rate, you'd need the following:

The tax base $Y$, i.e. the amount of income subject to income tax. Most probably, the New Zealand Treasury has published statistics on this. Note that total taxable income is different to total earnings which are reported in national accounts.
The number of taxpayers $N$.
You might want to maintain the current exemption $E$ which remains untaxed for each individual.

With current income tax revenue $R$, the revenue neutral flat tax rate $\tau$ can be obtained from:

$ R = \tau * (Y-N*E)$

Note that is the minimal thing to do which abstracts, among other things, from behavioral effects of such a reform.


Co-integration in stationary series I am analysing a time series and all the variables are stationary using augmented Dickey–Fuller test (ADF). Does it make sense to test for co-integration in stationary series?

No, cointegration occurs when two series have the same stochastic trend. In order to have a stochastic trend, they should be nonstationary. Stationary variables do not have a trend. You can perform standard inference.


What Taylor approximation is used in this equation? In Wickens' Macroeconomic Theory book, in page 48(1st edition), the author states that by doing a taylor approximation we get the following result.

Why is that? What approximation did he use?
I've tried several to linearize the fraction $\frac{(1+\eta)^{\sigma}}{\beta}$ around those values, but I don't get the same...

Even though your question does not allow a definite answer, I am pretty sure the author used a Taylor expansion around the logarithm of both sides of the equation. This process is called log-linearization, and is fairly common.

We can approximate (logs of) growth rates as $x \approx log(1+x)$ when $x$ is small. (and by the rules of logarithm:  $\log((1+x)^\sigma ) \approx\sigma x$

Rewriting your equation
$1+(r_t-\delta)=(1+\eta)^{\sigma}(1+\theta)$

where
$r_t=\alpha (k^{\# *})^{\alpha -1}$

and applying this rule gives

$r_t-\delta=\theta+\sigma \eta$

which gives the desired result.


Is 'price hike' synonymous with 'price rise'? Since my childhood I have a belief that in economics price rise and price hike synonymous with each other.
Moreover, the Collin dictionary strengthens by belief:
Hike
But what you experts have to say--- are they absolutely same?

Yes there are used interchangeably in the literature e.g. see the occurrences printed in Mankiw Principles of Economics. For example, on page 509 its used completely interchangeably:

If a Pennsylvania gun manufacturer raises the price
of rifles it sells to the U.S. Army, its price hikes will
increase...

Price hike is also not special economic jargon, it is used pretty much consistently with dictionary definition.

A hike is a sudden or large increase in prices...


Is population growth irrelevant with respect to per capita GDP growth In Solow's growth model the growth rate of the output or GDP of a country is denoted by $g$. In the model this can be decomposed to
$$
g = g_l + g_k,
$$
where $g_l$ is the growth rate of the effective labor force and $g_k$ the growth rate of capital. If you calculate the growth rate of per capita GDP population growth will not play a role. (Per capita growth is 'kind of' like $g_k$, but not quite, as technological advancements  are factored into the growth rate of effective labor.)

Does historical data support the statement that the effect of population growth on per capita GDP growth is zero?

I did some limited searching and it seems that while US growth is sometimes set as an example to other western countries, the real difference is in population growth, not per capita GDP growth.

Source

Source

Am I being too superficial in my examination? Are there more subtle effects, such as a lagged effect due to the pension and elderly care systems?

Indeed, there is branch of literature about semi-endogenous models (Jones, 1995, Segerstrom 1999 etc.). They were basically arguing that there was a scale effect in endogenous growth models, which means that when population increases, by default, growth increases (it is due to the fact that there would be more researcher in society, this is the scale effect.) and this branch of literature shows that growth rate at the long run is equal to the growth rate of population, which is an exogenous term. It is why they called it as "semi-endogenous".

This was challenging endogenous models but the empirical literature states that that the semi-endogenous model does not fit to data.

Some empirical references are :

Ha and Howitt (2007)

http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4616.2007.00045.x/full

and

Madsen (2008)

http://link.springer.com/article/10.1007/s10887-007-9024-0


Does a strong dollar achieve the same tightening effect on the economy as rising interest rates? Rising interest rates means the cost of borrowing USD goes up. A stronger USD means USD becomes more expensive. Wouldn't that naturally follows that the cost of borrowing USD goes up since each dollar becomes more expensive?

Does strong USD achieve the same effect as rising interest rates? If yes, is it logical to conclude that the Fed would put off raising interest rates if the dollar rises too much?

ceteris paribus, you are absolutely right. The price for international borrowing and lending is determined by both the interest and exchange rate.

Three remarks:

Above; I wrote ceteris paribus, meaning nothing else changes. In reality, however, both (long-term) interest rates and exchange rates are heavily impacted by expectations on how the economy is going to evolve.
Note that the exchange rate only impacts international transactions, on both financial and goods markets, whereas the interest rate impacts all borrowing and lending. The impact of a change in the exchange rate is therefore mainly a quantitative question. Without going into too much detail, the effect is likely going to be a lot bigger for a small open economy, compared to the US.
Usually, causation is assumed to go the other way. That is, the Federal reserve sets interest rates (arguably on the backdrop of domestic economic conditions), and then the exchange rate reacts on changes in interest rates. However, this is conventional wisdom, not an economic fact.


Name for the intentional reduction in quality in a non-software, price discrimination setting Is there a general term in economics for the intentional reduction in quality to reduce deviation to the worst alternative in price discrimination? Like "crippleware," but applicable in non-software settings?

"Lemonization" I guess. I didn't exactly make up that term with that meaning, but I suspect you won't see it often.


What is the implicaiton of agent risk neutrality in moral hazard? I heard that risk-neutrality of agent in moral hazard imply that the action associated with first-best and the one associated with second-best will be the same. Is it true and why is it so?

Are there other implication of agent risk neutrality?

It is true that when both principal and agent are risk neutral, the first best can be obtained despite asymmetric information. You should refer to a textbook, such as MWG (ch.14), for the technical details of such models. I'll give an intuitive explanation here. The intuition of the result lies in optimal risk sharing between the principal and the agent.

With a risk neutral principal and risk averse agent, optimal risk sharing requires that the principal bear all the risk and the agent bear none. Hence, first best is generally not attainable in such a setting because, with asymmetric info, the principal cannot condition pay on effort but on outcome instead. As a result, the agent would have to bear some risk in equilibrium. To satisfy the agent's participation (or individual rationality) constraint, the principal needs to compensate the agent for his risk taking, thereby reducing the total gains from the contract.

When both parties are risk neutral, there is no cost for the agent to bear risk. Therefore, optimal risk sharing between the principal and the agent is attained even if pay is based on outcome, not effort. This results in the same outcome as the first best.

Let's view the problem of contracting with moral hazard from a slightly different perspective. Suppose, instead of trying to monitor the agent's effort, the principal simply sells the shop to the agent for a fixed fee, and let the agent retain whatever profit it can make from the business. As the de facto owner, the agent would thus have incentive to exert the optimal level of effort. [This is the quote from Bolton and Dewatripont mentioned in @Hal_Incandenza's answer.] But how much of the fixed fee can the principal charge for transferring ownership?

Well, to respect the participation constraint, the fee can be at most the certainty equivalent of the agent. If the agent is risk averse, his certainty equivalent is less than the expected value of the business, hence the efficiency loss in the second best outcome. If the agent is risk neutral, his certainty equivalent is the same as the expected value of the business; thus there is no efficiency loss in the second best outcome.


A world only with two contries (net exporter) We assume that we have two and only two contries: Albania and Bulgaria. There is complete free trade between the two countries.
The aggregate investments in Albania are given by:
$$I^A=A-ar$$
where $A, a >0$ and r real interest rates.
The aggregate investments in Bulgaria are given by:
$$I^B=B-br$$
where $B, b >0$ and r real interest rates.
They have total savings $S^A$ and $S^B$ who are independent of the interest rate.
Now I have to derive the condition that Albania is a net exporter.
My though so far is that I have to use that BNP(Y): $$Y=C+I+G+NX$$ and $$S_A=publicsavings+privatesavnings=(T-G)+(Y-T-C)=Y-C-G$$ and that $NX>0$. But when I use these can only find an expression of the form $S_A>f(A,a,r)$. But I think I have to find an expression of the form $S_A>f(A,a,B,b,r)$. Can someone help me?

So we have
$$S^A = I^A + NX^A $$
$$S^B = I^B + NX^B $$
where $S^A$ and $S^B$ are exogenous constants. And since there are only two countries we have
$$NX^A = -NX^B $$
which leads to
$$S^A - I^A = -( S^B - I^B ) $$
Use that last equation to solve for r (after plugging in the I formulas). Then solve the first equation and require that $NX^A$ be positive.


indifference curve slope from utility function in the economics book that I'm reading right now it is written that this utility function:
$$u(x_1,x_2) = 2x_1 + x_2$$
yields indifference curves with a slope of $−2$.
Could someone please explain me how they found the $-2$?

Initially, I was thinking that they derivated the utility function in respect of $x_1$ and $x_2$ but this would give $2$ instead of $-2$. Thank you very much for your help

Hint: First find the total derivative of $u(x_1,x_2)$, set it to zero as utility does not change along an indifference curve, then solve for $dx_2/dx_1$


How wealthy are modern day humans compared to preindustrial times? I would like to see a quantitative wealth comparison between the average human in a hunter gather or agrarian society to average human in the today's world.

I'm mostly interested in how the discovery of natural energy resources combined with Newtonian physics influence on technology has changed the world in terms of relative worth of a human.

The kind of answer I'm looking for would be something like: We are 10, 100 or 1000 times more wealthy based upon x. X being what ever you use as a basis to create that comparison.

There is significant debate about whether such x exists.

For example Louis XIV had things in his estate that are not in mine (I do not have two palaces). But there are also things in my estate that were not in his. I have access to 21st century healthcare, dental care, the internet, I can flush after going to the toilet...whose lifestyle is 'worth' more?

The comparison gets more difficult the farther you go back. So hunter gatherers, with tribal ownership, without any currency and frequently without any sort of industry are probably uncomparable to modern humans via any 'wealth' based standard.


Consumer behavior with constrained demand Suppose there is a linear demand function $D(p)$ describing the demand of an individual consumer. This is derived from a utility function or is just observed, but let us assume it is correct. Now suppose that the product is available at price $p$, but the store insists that each consumer buys a minimum amount that is in fact larger than $D(p)$, but only by very little.
 Say it is $D(p) + \epsilon$, where $\epsilon < D(p)/100$.

Can I say without additional assumptions that given the options of buying a quantity $q$ where $q \in \left\{0\right\} \bigcup \left[D(p) + \epsilon,\infty\right)$, the consumer will choose to buy $D(p) + \epsilon$?

My argument is that this will maximize her consumer surplus given the constraint on $q$. As I specified that this is a linear demand function and $\epsilon < D(p)/100$ you can do the math, but it is easy to see that the surplus will be positive for any continuous demand function given a small enough $\epsilon$.

Is this an accepted line of argumentation?

In most models it is accepted that consumers seek to maximize their utility. I am not sure however if one can argue absent a utility function that surplus maximization is the goal.
 A workaround would be specifying a quasi-linear utility function supporting $D(p)$ but I would like to avoid this if possible.

In a two-good space, initially the consumer maximizes $U(x,z)\;\; s.t. \;\;p_xx+p_zz =I$ and we assume it obtains the solution $(x^*, z^*)$ as a function of prices and income.

In the constrained case, the consumer will either choose $(0, \tilde z)$ or $(x^*+\epsilon, z'$), for some $\epsilon >0 $ always exhausting its budget, so in particular, $\tilde z = I/p_z$.
In order for the consumer to still choose to buy a strictly positive quantity of $x$, it must be the case that

$$U(x^*+\epsilon, z') > U(0, \tilde z)$$

Apply a first order approximation around $(x^*, z^*)$ without ignoring the remainders, we want

\begin{align}
 U(x^*, z^*) + U_x(x^*)\cdot \epsilon + U_z(z^*)(z'-z^*) + R_{\epsilon} &\\> U(x^*, z^*) + U_x(x^*)(-x^*) + U_z(z^*)(\tilde z-z^*) + R_0
\end{align}

Simplify and re-arrange, we want

$$U_x(x^*)(x^*+\epsilon) + R_{\epsilon} > U_z(z^*)(\tilde z-z') + R_0 $$

We know that from the unconstrained optimization, $U_x(x^*)/U_z(z^*) = p_x/p_z$  so

$$\frac {p_x}{p_z}(x^*+\epsilon) + \frac {R_{\epsilon}}{U_z(z^*)} > \left(\frac{I}{p_z}-z'\right) + \frac {R_0}{U_z(z^*)} $$

Multiply throughout by $p_z$,

$$p_x(x^*+\epsilon) + p_z\frac {R_{\epsilon}}{U_z(z^*)} > I - p_zz'  + p_z\frac {R_0}{U_z(z^*)} $$

but $p_x(x^*+\epsilon) + p_zz' = I \implies p_x(x^*+\epsilon) = I-p_zz'$ so we are left with the requirement that (ignoring positive terms)

$$R_{\epsilon} >  R_0 $$

in order for the consumer to choose $x^*+ \epsilon$ and not $0$ for $x$.

Note that the above take into account also the signs of the remainders, it is not just about their absolute magnitudes.

Now let's go back to our first-order expansions. We know that both candidate bundles yield utilities lower than $U(x^*, z^*)$, because they were feasible in the unconstrained case, and they weren't chosen.

Looking at the expansion of $U(0, \tilde z)$ we then conclude that we have

$$U_x(x^*)(-x^*) + U_z(z^*)(\tilde z-z^*) + R_0 < 0 $$

$$\implies U_z(z^*)\cdot \Big[(U_x(x^*)/U_z(z^*))\cdot(-x^*) + \tilde z-z^*\Big] + R_0 < 0$$

$$\implies \frac {U_z(z^*)}{p_z}\cdot \Big[-p_xx^* + p_z\tilde z-p_zz^*\Big] + R_0 < 0$$

But $-p_xx^* -p_zz^* = -I$ and $p_z\tilde z =I$ so the term in brackets is zero. Therefore we conclude that

$$R_0 <0$$

Looking now at the expansion of $U(x^*+\epsilon, z')$, we know we have

$$U_x(x^*)\cdot \epsilon + U_z(z^*)(z'-z^*) + R_{\epsilon} < 0$$

Performing the same manipuations as before we obtain here too that

$$R_{\epsilon} < 0$$

So the condition to buy $x^*+\epsilon$ can be re-written as

$$|R_{\epsilon}| < |R_0|$$

This formalizes somewhat the notion that if $\epsilon$ is "sufficiently small", $R_{\epsilon}$ will be smaller in absolute terms than  $R_0$, since the approximation to the same function will be "better", and so we will observe $x^*+\epsilon$ and not $0$. But it also tells us what the graphs in the other answer told us too, that there is not a single general answer to the matter.


How does what companies produce and sell factor in GDP? The usual GDP formula is

$$GDP = C + I + G + (X-M)$$

But suppose I am a company and I produce some goods $q$ which I sell at a price $p$. Suppose also I don't know how much of the units actually get sold.

How do I include this information into the GDP equation?

This formula of GDP is an expenditure approach, which classify the country's output by category of final consumers. Therefore, you should determine who demands your product (ie who spends money to purchase your production): If $q_C$ is consumed by households, $q_I$ by firms, $q_G$ by the Government and $q_X$ is exported, then your new GDP is:

$$ GDP' = C \times p\cdot q_C + I\times p\cdot q_I + G\times p\cdot q_G + ( X\times p\cdot q_X - M) $$


Does trade lead to economic growth in the most basic models of trade? In the standard models of trade, such as Ricardo or Hecksher-Ohlin, I know that openness to trade will lead to increased consumption as (roughly) the consumption possibility frontier expands beyond the PPF. However, does this mean that the countries will grow?

Technically, consumption expands because the relative price of the goods in which you won't specialize will decrease. Therefore, I don't see how I could infer from this increased consumption that there has been economic growth.

I am asking because I have seen many lectures jump from the classic diagrams of international trade to the idea that the baseline theory suggests that trade is benefitial to economic growth.

It depends on how you define "growth". Trade models have multiple goods in them, so there's no unique way to define "growth" - you are just moving along a fixed production possibility frontier. You can calculate nominal GDP, but then you have to come up with a measure of inflation so that you can deflate the nominal figure into something real.

One of the results here is that if your economy which produces $ n $ goods has a production possibility frontier given by the zero set of a $ C^2 $ function $ Q : \mathbb R^n \to \mathbb R $ (with the usual properties, i.e increasing in each coordinate and with positive definite Hessian at every point), then a simple application of the chain rule gives (here the $ dx $ notation denotes derivatives with respect to time, so we're assuming that the economy shifts continuously along the ppf instead of a unit step jump from one point to another - this assumption is important, otherwise we can't lose the higher order terms in the Taylor expansion of $ Q $...)

$$ 0 = dQ = \sum_{k=1}^{n} \frac{\partial Q}{\partial x_k} dx_k $$

if you're moving along the ppf, so that the value of $ Q $ is conserved. However, we also know from the first order conditions of producers in a competitive market that

$$ \frac{\partial Q/\partial x_i}{\partial Q / \partial x_j} = \frac{p_i}{p_j} $$

where $ p_i, p_j $ are the nominal prices of good $ i $ and good $ j $ respectively. Substituting this into the above identity gives

$$ 0 = \sum_{k=1}^n p_k dx_k $$

This is an important result: it says that if you calculate growth by looking at changes in production and hold the prices fixed, then you will detect no growth if the economy moves along a fixed production possibility frontier. Furthermore, this identity combined with the identity

$$ NGDP = \sum_{k=1}^{n} p_k x_k $$

gives, using the product rule, that

$$ d(\log(NGDP)) = \frac{1}{NGDP} \sum_{k=1}^n x_k d p_k = \textrm{GDP deflator} $$

In other words, if we deflate GDP by using the GDP deflator which is defined as the percent change in the price of a basket of goods weighted by the share of total production they represented in a given time period, we will measure zero RGDP growth so long as the economy remains along the same production possibility frontier $ Q(x_1, x_2, \ldots, x_n) = 0 $. The results hold true in autarky as well as in an environment of free trade, so in this sense free trade does not lead to "more growth", at least not due to the effects present in Heckscher-Ohlin.

We can get away from this result if we choose to deflate nominal GDP by an alternative measure, but I think this should be enough illustration that you should be thinking about the welfare effects of trade and not about the "growth" effects. If you do come up with an appropriate notion of CPI inflation in a model, it will most likely be a "cost of living index" of the kind you find in Dixit-Stiglitz type models, so you will still indirectly be measuring welfare. The basic proof of the first welfare theorem carries over to the case of international free trade vs autarky, so under the usual assumptions (locally nonsatiated preferences and such) free trade outcomes are Pareto optimal, whereas autarky outcomes are in general not Pareto optimal.


How does the US have gross national savings while running a trade deficit? If a country has a positive savings rate, that means that more money had to come into the country from somewhere outside of the country. However, we run a trade deficit, so we're actually sending more money out than we are bringing in. How is this possible?

Premises of your Q are simply false:

If a country has a positive savings rate, that means that more money had to come into the country from somewhere outside of the country.

This is completely incorrect. Total savings of a country is sum of private and public saving. For an open economy output is given by $Y=C+I+G+X-M$ (where $Y$ is output $C$ consumption $I$ investment $G$ gov spending, $X$ exports and $M$ imports, the private saving is $S_p=Y-C-T$ and public saving is $S_g=T-G$ (see Blanchard et al Macroeconomics a European Perspective). Thus we can clearly see that $S_p+S_g=I+X-M$. In another words in open economy public and private saving must be equal to investment plus exports minus imports.
Let us suppose investment is 1000 exports are 0 and imports are 500 thus trivially country runs trade deficit yet has positive saving of $S_p+S_g = 1000+0-500 = 500$. Trivially saving is possible.
In addition, country having trade deficit is not equivalent to country sending out money. Generally you can only use home currency in your home country. Generally speaking one cannot use Japanese yens in the UK. If Japan wants to import cars from UK it has to sell its yens and buy pounds. Yens will be purchased by people who want to buy something in Japan because yens can be generally used to buy stuff etc only in Japan. So the total number of yens in Japanese economy will not change just because of trade deficit vis-a-vis UK, the same way as money supply of pounds in UK will not increase just because UK is running trade surplus vis-a-vis Japan.


Why are things usually cheaper in absolute terms the poorer a country is? I think something like this can be seen with something like the big mac index: http://www.economist.com/content/big-mac-index, there you can see that at the cost of one big mac in switzerland you could buy 10 in Venezuela if price is taken in dollars.

In a globalized economy like the one we have right now, I think it would make more sense for any consuming good to have aproximately the same price everywhere, (if they have the resources for making the consuming good in their own country it would be then cheaper), then depending on how rich is the country the salaries would be according (salaries would be as much higher for one country to the other as how much richer is that country).

I don't know about economy, but I'd like to know why that happens. so I'd like in explanation in layman terms if possible.

Thanks for your attention.

It does seem kind of puzzling. However, there is one simple explanation. It´s a theory of why this happens, called the Balassa-Samuelson theory.

It takes about three steps to see it:

The idea is, first, that the productivity in the case of tradable goods is different in the two countries. It takes 100 hours of work in Switzerland to produce a computer. It takes 1000 hours of work in Venezuela to produce a computer. (This is easy to believe, you could think this is the result of Switzerland having more capital, infrastructure, etc.)  Because these computers are tradable, they should have the same price everywhere, once expressed in dollars. So suppose the computer is worth 1000.
The second step is to realize what this means for wages. It means that in Switzerland, people that make computers are paid 1000/100=10 dollars an hour. (Assume the workers get paid the whole price of the computer...), and in Venezuela they get paid 1000/1000 = 1 dollar per hour (!).

The third step is to realize a) that there are many goods that are non-tradable, like restaurant meals. They are usually services. These goods don't have to have the same price everywhere; and b) that there is not such as big a difference in the productivity of these goods across countries.  So it takes one hour of work to make a nice meal in Switzerland and the same in Venezuela. (One way to rationalize this is to see that if you want to invest a lot, you want to invest in producing something that can be sold worldwide, a tradable good. Therefore, rich countries have invested in increasing the productivity of tradable goods.) But now you have the result, because the price of a meal is 10 in Switzerland (1 hour of work) and 1 in Venezuela (1 hour of work) (!!).

In sum, what the Big Mac index reflects is that the price of non-tradeables is different in a way that reflects the productivity differences in tradable goods.

Magic!


Whether the demand in the panels satisfies the weak axiom The Walrasian demand function $x(p,w)$ satisfies the weak axiom of revealed preference if the following property holds for any two price wealth situations $(p,w)$ and $(p',w')$:
  If $p•x(p',w')\le w$ and $x(p',w')\ne x(p,w)$, then $p'•x(p,w)>w'$.
  Where $x$ is the amount of commodity, $p$ is price and $w$ is wealth.

The book(MWG's Microeconomics Theory, Page 29-30) says that the graph below satisfies the weak axiom. I have difficulty in understanding the graph. To be specific, I don't know why there is a dot in each of the budget set and I can't understand why it satisfies the weak axiom.

So WARP says that if bundle x' you choose under budget B' is affordable at budget B'' (and you don't choose x' - i.e x'$\not=$x''), then x'' cannot be affordable under budget B'.

The picture you showed gives the 2 bundles that the person chooses. Those are given in the picture. As you can see, x' is not affordable at budget B'' and bundle x'' is not affordable at budget B', so WARP is satisfied.

If you are reading MWG and you don't understand what those dots represent in the consumption space, then I would recommend reading more from the beginning of chapter 2.


FOC for King–Plosser–Rebelo preferences I am reading Dynamic scoring: A back-of-the-envelope guide by Mankiv and Weinzierl (here) and on page 1420, I don't get the FOC in equation $(10)$, which says $r=...$.
I do get the FOC with $v'(n)=...$ by using Lagrange.

I found the same FOC in a paper from Ferede (Dynamic Scoring in the Ramsey Growth Model, here) and he says, that it

  is obtained by combining the first order conditions of the utility
  maximization with respect to capital and consumption (page 5).

But I only observe $\lambda=-c^{-\gamma}e^{gt(1-\gamma)}e^{(1-\gamma)v(n)}$ from the FOC w.r.t. consumption and $-\lambda[(1-\tau_k)r-g]=0$ from the FOC w.r.t. capital.

How am I supposed to get $\dot{n}$ and $\dot{c}$ there?

Well let me show you, what I have got: The Lagrange-function is given by:

$$L=\frac{1}{1-\gamma}[c^{1-\gamma}e^{gt(1-\gamma}e^{(1-\gamma)v(n)}-1]-\lambda [(1-\tau_n)wn + (1-\tau_k)rk - c - gk +T - \dot{k}]$$

So the FOC w.r.t. consumption is given by $\frac{\partial L}{\partial c}=c^{-\gamma}e^{gt(1-\gamma)} e^{(1-\gamma)v(n)}+\lambda=0$, while the FOC w.r.t. to capital is $-\lambda[(1-\tau_k)r-g]=0$.

So the equation for $\dot{\lambda}$ is based on the equation $\frac{\partial \lambda}{\partial t}=\frac{\partial \lambda}{\partial c} \frac{\partial c}{\partial t}$. And you are fully differentiating it.

I hope someone can help me.

NEW:
So again: $\lambda=e^{-pt}u'(c)$. So you are indeed right with your equation after your words "Then substitute back in the FOC for consumption", but then you substitute it to the FOC wrt to k: $\dot{\lambda}=\lambda[g-(1-\tau)r]$, so we get $\gamma \dot{c}/c - (1-\gamma)(g+v'(n)\dot{n})+p=g-(1-\tau)r$, so that the signs don't fit anymore and this unfortunately leads to something else than equation $(10)$.

So Lets use a present value Hamiltonian here:

$H=e^{-pt}u(c)+\lambda(\dot k)$

FOC:
wrt c: $0=e^{-pt}u'(c)-\lambda$

wrt k: $-\dot\lambda=\lambda[(1-\tau)r -g]$

Take the FOC from consumption and differentiate wrt to time:

$\dot\lambda =-\gamma c^{-\gamma-1}\dot c e^{-pt+gt(1-\gamma)}e^{(1-\gamma)v(n)}+c^{-\gamma}e^{-pt+ gt(1-\gamma)}e^{(1-\gamma)v(n)}[(1-\gamma)(g+v'(n)\dot n)-p]$

Then substitute back in the FOC for consumption:

$\dot\lambda =-\gamma c^{-1}\dot c\lambda +\lambda[(1-\gamma)(g+v'(n)\dot n)-p]$

Then substitute this guy into the Foc for capital:

$g-(1-\tau )r=-\dot c/c\gamma+(1-\gamma)[g+v'(n)\dot n]-p$

leading to:

$r(1-\tau)=p+(\dot c/c +g)\gamma+(1-\gamma)[-v'(n)\dot n] $


Theory about supply of money, prices, and output? "In theory, we should have enough money in an economy so at current prices we can buy all of the goods and services the economy is producing. What economic theory does this remind you of?"

On a basic level this reminds me of a simple supply/demand equilibrium. In addition, it brings to mind the importance of reserve ratios in banking. As a side note, I also thought banking's use of debt would assert we could not buy every good and service in the economy at this time.

My professor enjoys trick questions. Any thoughts on what I have proposed?

The first thing that comes to mind is classical economics' Say's Law

  In a market equilibrium, aggregate production will match aggregate quantity demanded.

In this case, this law on markets could be applied to your money market. Of course, Say's law has its weaknesses and doesn't always uniformly hold, given that markets aren't always in equilibrium. It is probably still a good guiding principle for the money market though. For example, debt and fractional reserve banking seem to indicate, as you note, that money supply doesn't match money demand, but people are consumption smoothing creatures. Their behavior may be matching their demand over multiple periods with supply (their time-path of income) over multiple periods.

A simpler explanation: money supply is also more than just the money base of course. Modern measures of the money supply are meant to capture the reserve rate.


Negative Inflation, AS/AD framework, What Graph to use? My macroeconomic homework contains the question below, and I'm not sure what graphs we're suppose to use to solve it. I believe I can answer the whole question using the IS-MP Diagram, but do I need another? Is the AS/AD question just referring to the changes in demand for funds when the new interest rate is applied in the IS-MP Diagram?

In the late 1990s and early 2000s, inflation was actually negative in Japan. I want you to consider a policy to achieve a higher inflation rate. Consider an economy that beings with output at potential and an inflation rate of ̅, so that the economy begins in steady state. A new chair of the central bank decides to raise the long-run inflation target to ̅2 (greater than the original ̅). Show how the economy responds over time using the AD/AS framework. Comment on your results.

It seems that your teacher wants you to analyze the effects a higher inflation rate might have on the level of aggregate output based on whatever policy you might choose, i.e. drawing an AD/AS graph in long run equilibrium and demonstrating some shift as a result of the inflation-increasing policy.


What would happen in Venezuela if the currency exchange control is removed overnight? What would happen in Venezuela if the government all of a sudden starts offering currency exchange by the prices of the free market?

To my knowledge, the main reason for the government in Venezuela to have currency exchange controls is that they don't want everybody to start buying less volatile currency in order to protect their savings from inflation. What would lead in turn to the government losing all of its reserve currency.

Would that hypothesis hold true in such situation?

You could probably think about the policy trilemma. It's the idea that a country can only have up to two of the following: free capital flow, a fixed exchange rate, and independent monetary policy. Right now it seems that Venezuela wants a stable currency exchange (so they control it) and they want reserve currency available to stabilize the economy if need be and have independent monetary policy.

So if you got rid of currency exchange controls so people could buy foreign currency more readily, in the short run, you'd lose control of the exchange rate without gaining anything. Long term, since the money market is clearing, and assuming Walras' Law holds, then capital will be able to flow more freely and contribute to economic growth. It might force Venezuela to be serious about not causing hyperinflation for that to happen that.


Software for field work: collecting survey data (multi-platform, on-line and off-line) As part of an RCT, I am looking for Software to record digitally the answers some survey questionnaires. The questionnaire is somewhat long,  ~100 questions  divided into 10 blocks.
We will collect  3 rounds (baseline, follow-up 1 and 2) of 600 surveys. Surveyors have access to a windows laptop and perhaps an Android or iPhone.

Desired features:

Must function online and offline (as in some places there won´t be internet access).
Must have a functionality to skip questions. Ex: if q1=no, then skip to question 7
Preferably multi-platform (Android, OS and Windows)
Fast to set-up infrastructure and create the questionnaire
Free or reasonably cheap service
Ability to record GPS coordinates (in case of phone survey)
Ability to add Pictures (in case of phone survey)

What do most working on RCTs use?
Do JPAL, IPA and similar outfits have any recommendations on this front?

I've worked in 2015 on a survey collecting ~300 answers from 130 different countries. We had similar requirements to what you described, with multilanguage functionality on top. it was not a RCT (Randomized Controlled Trial), we were surveying on conditions of work.

We ended up using SurveyMonkey which costed 900€ and had only the online functionality, which is a mobile optimized web page survey (compatible with any system), very fast to set up and with the ability to skip questions and add pictures. We could not capture GPS data (never heard of surveys doing that), but we could get the IP address of respondents, which can be a proxy for their location. Pictures were also possible to add, but we used it only to brand the survey.
We used Word-files via email for "offline answers", which we then manually inserted back on the website. We didn't have much field work, but I know it would have worked great to fill the survey in a phone or tablet easily, as long as there was internet access.

The main thing that made us take SurveyMonkey vs using self-hosted open-source software like LimeSurvey was:

The ability to set up quickly (your survey is up as soon as you insert the questions, no IT configuration time needed),
Speed of connection for respondents: our server in Europe would mean long loading times for the respondents in other continents, and SurveyMonkey has powerful servers everywhere
Text mining features for open-answers and pre-made dashboards to share quick and high-level results

If you want to look at other providers, most of the surveys I've seen recently used Qualtrics, Typeform, SurveyMonkey or GoogleDocs.


In a hyper-inflated economy, how do vendors know how much to raise their prices? You regularly see stories about hyper-inflated economies. The common feature is that as prices spiral out of control, stores continually raise their prices to match the level of inflation, leading to insane costs for basic items and with note-values being increased to match prices.

Let's say that I'm running a cake stall. How do I know that I need to be charging 100 trillion fakedollars per cake rather than 200 trillion? Where do normal vendors get that kind of in-depth market info?

It's anecdote, but in this fantastic Planet Money piece on breaking Brazil's hyperinflation, there's a pretty good description of how in Brazil, shopkeepers would raise their prices multiple times a day. The strategies described (starting around the 10:00 mark, after the description of people running ahead of the guys with the price guns to buy things before they could raise the prices) include:

Assuming that inflation will run at some constant rate
Running around checking competitors' prices
Using the exchange rate against the US Dollar as a benchmark
Pooling information and colluding with competitors, agreeing to all raise prices by the same fixed amount each day.


Real world evidence that voluntary exchange is mutually beneficial? The other day I was having a debate with a supporter of high taxes.  I decided to argue against this by explaining the concept of the deadweight loss of taxation.  In order to do so, I started with the following example, to explain the deadweight gain of trade:

Bob and Sam live next door. Bob can mow his lawn in 4 hours, and clean his gutters in 2 hours.  Sam is the other way around:  He can mow his lawn in 2 hours and clean his gutters in 4.  If Bob cleans Sams gutters in exchange for Sam mowing his lawn, they both save 2 hours.

My friend replied: "I understand the mathematics, and don't dispute that in your example both people would be better off.  But is there any evidence that this works in the real world?  Perhaps there is some unforeseen factor that causes voluntary exchange to not be mutually beneficial."

This question left me momentarily stumped, because I had always found the concept self evident and did not have any obvious examples at hand.

Improvising, I tried using the example of China and the USA both benefiting from trading with each other (my thinking was that this was a more contemporary form of Ricardo's original wheat example).  However this caused my friend to object on grounds of geopolitical issues.  So I am hoping to find a better example, that does not raise other issues.

Therefore I wanted to ask:  Can anyone suggest some unambiguous, real world (ie non-hypothetical) evidence of the mutual benefits of voluntary exchange?  If this could relate to exchange between individuals rather than countries I believe this would make the case more clearly.

First of all, there is no need to believe any economic dogma. The real world is usually more complicated than these stories. If anyone can convince me of something with a two minute anecdote, that was probably not an important aspect of my world view, and I should probably not engage in setting such policy. (E.g. via voting for the person who tells the same anecdote.)

The statement that voluntary exchange is mutually beneficial relies on the assumption that both parties are rational and well-informed. If the exchange was not mutually beneficial, the one who is losing via the exchange would just say "no, thank you". Hence literally all voluntary exchange is mutually beneficial (so long as the parties are rational and well-informed). This does not mean that the situation voluntary exchange leads to is optimal, just that it is better than having no market at all.

Some further remarks on taxation:

Deadweight loss is indeed bad. (By the way what you are describing is comparative advantage, not deadweight gain, as you yourself noted correctly in the tags.) However taxation is not the only thing that can cause  market failure, which is when the free market leads to a suboptimal outcome. For example market power (monopoly, oligopoly, monopsony, etc.) may also result in deadweight loss.

Unregulated externalities (e.g. pollution) may cause harm, and in this case taxation (or a proper market for the externalities) can actually improve everyone's situation.

Underfinanced public goods (e.g. roads) may also mean market failure. Voluntary financing usually leads to underfinancing, hence taxes (or some revenue mechanism) are needed.

So taxation, while it does have downsides, is not the devil. It may do more harm than good and it may do more good than harm, it all boils down to the details.


What determines rent prices of houses? Does it depend only on interest rates? My hypothesis: the renting is determined by the opportunity cost of selling the house and gaining interests in a bank or some investment company. That is, instead of renting, sell it, put the money in a bank, and gain interest on them.

In other words, the renting prices of real state are determined by only two factors: The price of the house + the interest rates.

However, it has been my observation here where I live, in very few houses (thus lacking some statistical weight), that house renting for commercial entities is around the same as selling the house and gaining interest, but, house renting for a physical person is around half than selling house and gaining interest.

Questions:

The hypothesis of renting determined by interest rate is a good one in the context of theoretical microeconomics, or merely simplistic understanding?
In the real world, is renting primarily determined by interest rate and house price? In other words, is the relationship causal? Or just a correlation? Is there a correlation anyway?
Are there more mechanisms for determination of the prices of renting a house?
Why sometimes the renting price can be lower than if gaining on interest? Why would anyone prefer to keep the property of the house, if they could gain more by selling it and gaining interest?

What you're referring to is called the "rental yield", i.e. income generated from rentals as a portion of the amount you have invested in the house.

The interest rate is definitely one of the factors determining rental prices. Most other factors would be included in the house price (e.g. how big and nice the house is, how many bedrooms, are there many workplaces around, crime rate, etc.)

Other things that might be left out apart from the interest rate and house price is how competitive the house rental market is. You could imagine a neighborhood where there's only a few houses that are for rent. If there's demand, there's no reason the rental yield should be lower than another neighborhood with more competitive rental market.

If a person buys a house as an investment, then he/she would have taken into account the return he/she would get if this money was invested elsewhere. Say the average stock market return is about 7%, then it makes no sense for a person buying a house as an investment to seek for rental yield lower than that.

Having said that, of course, you need to take into account property price increase as well. You might be ok getting lower rental yield than your next best option if you foresee that the house price in your neighborhood would rise in the future.

Lastly, if you have a house and need to move away for a few years knowing that you'll eventually move back, it might be a good choice to rent it out in the meantime. For this, your primary reason of owning that house is not for investment, so you might be ok with getting lower rental yield (perhaps in exchange for being able to select suitable renters).


Solving for profit function $\pi (w,p)$ given the output of production function $f(z) = \sqrt{2z_1 + 3z_2}$ Solving for profit function $\pi (w,p)$ given the output production function $f(z) = \sqrt{2z_1 + 3z_2}$.
I approached this problem by trying to solve the $p\nabla f(z) = w$. This is derived from setting up the Lagrangian for the Profit Maximization Problem,
\begin{align*}
\text{maximize } &pf(z)-w^Tz\\\
\Rightarrow \mathcal{L}(z) &= pf(z) -w^Tz
\end{align*}
Then taking the partial of the Lagrange to zero,
\begin{align*}
\frac{\partial \mathcal{L}}{\partial z} = 0 = p\nabla f(z) - w\\
\Rightarrow p\nabla f(z) = w.
\end{align*}
The issue is, I thought that I could solve for an optimal $z^*$, but that does not seem possible, but I know that a solution exists.
To showing this issue simply, let $q=f(z)$, then the gradient is:
\begin{align}
\nabla f(z) = \begin{bmatrix}
1/q\\
3/2q
\end{bmatrix}
\end{align}
So solving our equation $p\nabla f(z) = w$, should let us solve for $z_1,z_2$, but as you can see,
\begin{align*}
\begin{bmatrix}
1/q\\
3/2q
\end{bmatrix} = \begin{bmatrix}
w_1/p\\
w_2/p
\end{bmatrix}\\
\Rightarrow \begin{bmatrix}
q\\
q
\end{bmatrix} = \begin{bmatrix}
p/w_1\\
3p/2w_2
\end{bmatrix}\\
\Rightarrow \begin{bmatrix}
\sqrt{2z_1 + 3z_2}\\
\sqrt{2z_1 + 3z_2}
\end{bmatrix} = \begin{bmatrix}
p/w_1\\
3p/2w_2
\end{bmatrix}
\end{align*}
This shows I cannot isolate $z_1$ or $z_2$. Without an optimal $z^*=<z_1^*,z_2^*>$, I cannot find my profit function $\pi(w,p) = pf(z^*) - w^Tz^*$.
EDIT
My guess is that actually, for some output $q$, my profit function is what I already solved for, $\pi(w,p)=\max{\{pw_1, 3p/2w_2\}}$
Can anyone confirm this?

The production function has a particular feature: the inputs are perfectly substitutable. One unit of input 1 can be substituted by 2/3 of input 2 to produce the same quantity of output.
Intuitively, a producer would optimally use only one output to produce.
Suppose the production plan is $(z_1,z_2)$. By choosing $(z_1-1,z_2+2/3)$, the firm produces the same quantity but profits are increased by $w_1-2/3w_2$. We can conclude: the producer would buy only input 1 ($z_2=0$) if $w_1<2w_2/3$, and they would buy only input 2 ($z_1=0$) if $w_1>2w_2/3$. From that point, you can solve the maximisation problem by distinguishing these two cases.
The question can also be solved as a constrained optimisation problem if you add the constraints $z_1\geq 0$ and $z_2\geq 0$ to the Lagrangian. If $\lambda_1$ and $\lambda_2$ denote the Lagrangian parameters of these two constraints, you obtain the two cases aforementioned when i) $\lambda_1=0$ and ii) $\lambda_2=0$.


Multiproduct firms and horizontal product differentiation I am having difficulty modelling the effect of horizontal product differentiation between multiproduct firms. I've been looking at models specifically by Hotelling and d'Aspremont. Hotelling concluded that in duopolistic competition, an equilibrium was found through firms differentiating minimally, (i.e. designing products of similar attributes) whilst d’Aspremont shows the opposite with the equilibria resting at maximal product differentiation.

However, both of these principles do not take into account multiproduct firms, where firms could produce different varieties of the same product (take shoes for example) where some are highly differentiated and others may be similar to a competitor. Is there a model that explains this situation?

Here is a link to Schmalansee's classic paper.  Use SSRI to look forward in time from this paper.  Useful search terms in Econlit or Google Scholar would be "crowding the product space" or "product space congestion."


Utility Maximisation Subject to Income and Time Constraints The consumption of economic goods often takes time. Consider, for example:

Transport services, eg flights, rail journeys;
Leisure goods, eg watching a film, visiting a park.

I would like to explore models of consumer or household behaviour in which utility in a period is maximised subject to both income and time constraints.

From a Google search, two important (but rather old) papers on this topic appear to be:

Becker, G S (1965) A Theory of the Allocation of Time
De Serpa, A C (1971) A Theory of the Economics of Time

What are other (and more recent) key papers on this topic?

Addendum 31 May 2018

To give a simple example, suppose there are just two goods $X_1,X_2$ and utility $U$ is given by:

$$U = X_1^{0.5}X_2^{0.5}$$

Suppose further that the respective prices and time requirements are for $X_1 (1,2)$ and for $X_2 (2,1)$.  Thus the income and time constraints are:

$$X_1 + 2X_2 \leq I$$

$$2X_1 + X_2 \leq T$$

where $I$ is income and $T$ is available time. If $T$ is much larger than $I$ (low-income person), then the income constraint will be binding, and the time constraint will be slack, and vice versa if $I$ is much larger than $T$ (high-income person). Over an intermediate range, including $T = I$, both constraints will be binding. These different scenarios have different implications for the effect of a marginal change in price.  Perhaps time preference is relevant here but I can't immediately see how.

Addendum 23 July 2018

This book by Ian Steedman, reviewed here by Diane Coyle, looks relevant.

Despite its funny title and although it is quite old you may find this paper interesting:

The economics of the afterlife by Scott Gordon in the JPE. His argument is basically that in the presence of an infinite amount of time there would still be a rate of time preference.

A follow-up paper disproving Gordon's claim was written by Amegashie, but I haven't checked that one in detail. You can find that  here.

Nb credit where credit is due: I would probably never have read the first paper without Yoram Bauman's presentation "Hyperinflation in hell"


Macroeconomics Homework Question I am curious how I solve this question, I will include an image below. I am not looking to be spoon-fed just informed. If you could answer and provide an expiation for the answer that would be awesome!

The graphs below depict the perfectly competitive market for apples on the left and Farmer Johns perception of the market for apples as an individual farmer on the right. Assume farmer Johns costs are represented by SRATC-1. In the long run will farmer John choose a high, medium, or low level capital for his farm. Indicate the SRATC curve associated with Johns decision. Explain what is going on short term for Johns apple farm. (Drawing a typical MC curve might be helpful)

Is the equilibrium price depicted here a long run equilibrium ? How do you know? If not what will happen to move the market towards the long run? Show the change the move the market towards the long run equilibrium and label the long run equilibrium price, market quantity and johns long run produced quantity?

It's been a while since I've look at perfect competition and cost curves.

First off, it's helpful if you draw the standard diagram for a perfectly competitive firm, one with supernormal profits and the other with normal profits (and compare it to the 3 types of situations in Johns diagram)

From what I do remember, Long run equilibrium under perfect competition consists of:

1) P = MC = MR (profit maximisation)
2) P = Min ATC

Remembering that the market is the price maker, and the individual firm (johns farm) is the price taker.

In the long run, market price (indicated by demand and supply intersection) must be level with the lowest point on the LRATC curve (also lowest point on SRATC-2). This doesn't appear to be the case in these diagrams, thus it must be a short run equilibrium.

So in order to adjust to this long run equilibrium two things need to happen

1) Either demand for apples falls, or supply of apples rises in the market for apples. To bring about a price consistent with the long run equilibrium

2) John needs his ATC to move from SRATC-1 to SRATC-2. (Because any perfectly competitive firm not at its minimum LRATC will, in the LR, change its input combination to take advantage of lower average costs).

According to Johns apple farm, the firm is earning abnormal/supernormal profits because of the position of price on SRATC-1 i.e it is not the case that P=min ATC=AR. There is a distance between ATC (higher than minimum ATC on SRATC-1) and AR. This distance is abnormal profits.

If firms are able to make positive profits by moving outward on the LRATC curve, those profits will attract entrants into the industry in the usual fashion (shifting the supply cure outward). Profits will eventually dissipate to zero.

In the long run, a perfectly competitive firm is allocatively and productively efficient: P=MC & ATC=MC i.e lowest point on SRATC-2 and LRATC.

In regards to the high medium or low level of capital, because there are 3 options and 3 SRATC curves, I believe it is medium (greater than the quantity associated with SRATC-1, and lower that then quantity associated with SRATC-3).


Investment = Saving relation in an open economy I am reading the book Macroeconomics by Olivier Blanchard.

It states that an alternative way of looking at an goods market equilibrium is investment = saving.  In an open economy it states the equilibrium condition is Net Exports = Saving (both private and public) - Investment.

I am struggling a little bit with the intuition of understanding this condition.  Would it be because the difference between saving and investment would contribute to the capital account aspect of the balance of payments in some way?

I would be very grateful if someone could help me to gain an understanding of this equilibrium condition.

Thankyou.

First it should be clear that this is an (ex post) national account equality:

$Y=C+I+G+NX$, the private saving is $S_p=Y-C-T$ and public saving is $S_g=T-G$
thus you have $S_p+S_g-I=NX$.

Later you see in this book that the net exports, which depend on the exchange rate, are exactly equal to the Net Capital Outflow. Why? because an export is like a capital import (and vice versa).


Are the goods in additively separable utility functions normal goods? Inspired by this answer.

To make it a bit more precise, by normal good I mean demand is (not necessarily strictly) increasing in income, and by additively separable utility function I mean that a monotone transformation exists for which
$$
U(x_1,x_2,\dots) = f_1(x_1) + f_2(x_2) + \dots
$$
(Also assume $U$ is increasing in all variables.)
Given a linear budget constraint and a utility maximizing consumer, do these goods $x_i$ exhibit normal behavior for all income levels?

Yes if you assume that the sub-utility functions are concave. Notice that this is a standard assumption as otherwise, the utility function $u = \sum_i f_i$ is not guaranteed to be concave (nor quasi-concave).
Let denote by $u_i = \dfrac{\partial u}{\partial x_i}$ and by $u_{i,j} = \dfrac{\partial^2 u}{\partial x_i \partial x_j}$. By additivity $u_{i,j} = 0$ if $i \ne j$.
The first order conditions for the utility maximisation problem give:
$$
\begin{align*}
u_i = \lambda p_i, \tag{1}\\
\sum_i p_i x_i = m \tag{2}
\end{align*}
$$
Differentiating both with respect to income $m$ (and using $u_{i,j} = 0$) gives:
$$
\begin{align*}
&u_{ii} \frac{\partial x_i}{\partial m} = p_i \frac{\partial \lambda}{\partial m} \tag{3}\\
&\sum_i p_i \frac{\partial x_i}{\partial m} = 1 \tag{4}
\end{align*}
$$
Substitute $(3$) into $(4)$:
$$
\begin{align*}
&\sum_i (p_i)^2 \frac{\partial \lambda}{\partial m} \frac{1}{u_{ii}} = 1,\\
\to &\frac{\partial \lambda}{\partial m} = \frac{1}{\sum_i \frac{(p_i)^2}{u_{ii}}} \tag{5}
\end{align*}
$$
Notice that $u_{ii} < 0$ by concavity of the sub-utility functions. As such, $\frac{\partial \lambda}{\partial m} < 0$ and also, by $(3)$:
$$
\frac{\partial x_i}{\partial m} = p_i \frac{1}{u_{ii}} \frac{\partial \lambda}{\partial m} > 0
$$
as the right hand side is the product of two negative numbers.
This shows that $x_i$ is a normal good. By symmetry, this holds for all goods.
An alternative quicker way to notice this is to see that

by $(3)$ the sign of $\dfrac{\partial x_i}{\partial m}$ will be the reverse of the sign of $\dfrac{\partial \lambda}{\partial m}$.
This has to be true for all goods, which means that either all goods are normal, or all goods are inferior.
From $(4)$, it follows that at least one good should be normal (as otherwise the sum cannot be equal to 1 which is greater than zero).
Conclude that all goods have to be normal.


Why is it that the "right" inflation is positive? I have read in several places that inflation should be positive, at about 2%-3%. The most recent example was in this answer from another stack exchange site.

How is this value obtained and under what assumptions?

In addition to the reasons provided by EnergyNumbers, there are possibly a few more, such as:

Deflation (even if small) is broadly considered worse that moderate inflation. This is because deflation is very difficult to fight. If consumers expect prices to fall (because of deflation) they will wait before consuming and push consumption into the future. This fall in current demand reduces prices again, which increases deflation. The cycle then keeps going on, which is a phenomenon known as the deflationary spiral. One reason deflation is bad is for the same reasons inflation is bad (e.g. menu costs). On top of that, deflation is an issue because it increases real wages, which increases costs of firms, which can have negative effects on employment. Japan has tried to fight deflation unsuccessfully for some time for example, leading to what is called "Japan's lost decade". So once you get a little deflation it may persist for a long time. Policymakers are potentially scared, that if they are always at 0 inflation that a small shock could push them into deflation, which is very bad. So having small, positive inflation is a buffer against deflation.
Many countries have estimated or continue to estimate inflation using a Laspeyres index. It is well known, that such an index has an upward bias, i.e. overestimates inflation. Let's say we want to have 0 inflation. If the Laspeyres index says we have 0 inflation, we probably have negative inflation, which is also not optimal. So measurement error provides a case for positive inflation numbers.
Inflation provides government revenue through what is called "inflation tax". Further, most governments are in debt and holders of debt profit from inflation.


Does Preference have a Hierarchy? A Silly Question I have what is probably a very silly question, but I have gone down the rabbit hole and can’t get back out.....

Is there is a hierarchy of preference, and within each level of choice do we reset the rationality clock? i.e. suppose I choose a property investment (my investment preference) as I believe it will maximise my utility over investments X and Y. I am a utility maximising rational econ. However, a layer down, I choose to invest in property B instead of property A, despite property A being a better investment on every financial indicator. I do so, because in this round of choice, property B meets my preference, which is based upon having a new build property, which is closer to home.

I am maximising utility and acting rationally for my new preference, but not in relation to my first preference. In choosing investment B, am I therefor acting rationally or irrationally? Or have I got this all wrong?

*A little disclaimer, this is more  me ruminating than providing a rigorously proofed response.

I have never thought of preferences being related that way before, especially through the use of hierarchies.

$\textbf{Main response}$

The way I think about the scenario above is through preference weightings, were the values of the goods that can be chosen are weighted according to the good-specific preferences of the agent. This allows the agent to still be a rational econ and maximise their utility, but make sub-optimal financial choices. In a simple scenario similar to your example,  there would be two goods, $X$ and $Y$. $Y$ provides greater returns and  from what I understand above, the agents utility would take an additive form (to ensure that the goods are substitutes)  i.e.
$$
U_1 = 2Q_Y+Q_X
$$
Thus, a utility maximising agent would choose to spend his budget on $Y$ as it provides greater returns.

$\textbf{However}$, we can incorporate the agents preferences for

  a new build property, which is closer to home.

which we can call $\beta_{nbp}$. Thus, as $X$ has characteristics which match the above, the agents utility would now take the form;

$$
\hat {U}_1 = 2Q_Y+\beta_{nbp}\cdot Q_X
$$

Thus, the agents utility now incorporates the financial superiority of good $Y$, as it outperforms good $X$ by a factor of 2, and it incorporates the agents non-financial preferences through $\beta_{nbp}$. For a utility maximising agent to choose $X$ over $Y$, $\beta_{nbp}$ must be greater than 2, which implies that the agents non-monetary preferences are more important than his financial preferences. Thus, by adding preference weighting,it is one way to show that a rational utility maximising agent will choose a financially worse product over another product, as there are other non-financial elements which the agent desires more. However, if the agent had been a profit maximiser the choice of $X$ over $Y$ would not be rational, and in the problem above we would not include $\beta_{nbp}$ in the analysis.

$\textbf{Real life example}$

A real-life example I suppose which is slightly related, would be choosing between an ultra cheap  but crappy mobile(cell) phone and an expensive but good quality phone. On a strictly monetary basis, the ultra cheap one is preferable. However, as soon as you start incorporating quality, the utility-values of the phones change. The change isn't financially, but based on the utility (eg. combined preferences for monetary and non-monetary benefits) derived by whoever is buying the phone, and hence they may choose the better quality phone at the expense of spending more money.

$\textbf{meta-discussion}$

On a more meta-level, I think your question has some really interesting points. It appears to be that there is a misinterpretation between utility and profit maximisation. Considering this definition of utility;

  utility is the want satisfying power of any commodity or capacity of a commodity to give satisfaction.$^1$

It can be seen that utility is not solely reliant on money, but rather is only partially reliant on financial benefits. However, as money is such a large part of our society and can be (relatively)easily measured and compared,  it is used a lot to quantify the non-monetary preferences (through monetary trade-offs, which is a really interesting field of research by itself!). Thus, this quantification seems to lead to a bit of confusion between profit maximisation (which is solely focused on money) and utility maximisation (which is focused on utils and want satisfaction), which I wouldn't be surprised is from the way economics is taught and very rarely explicitly mentions this difference. Hence, economics is not necessarily not just solely focused on money, but it does use money to help compare the costs and benefits of tangibles and intangibles.  This is probably, a reason why economics is rather practical  and often relied upon during policy development, as it provides easily comparable estimates to values which would otherwise be illusive.

$^1$ https://en.wikibooks.org/wiki/Principles_of_Economics/Utility


Showing that a preference relation admits a utility function representation Setting: We have two choices of goods $(x_1,y_1)$ and $(x_2,y_2)$ from the set of choices $[-1,1]^2$. Moreover, we have the following preference relation $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff |x_1|\geq|x_2|\>\>\text{or}\>\> |y_1|\geq|y_2|$$

Question: We have to check if there exists a utility function reprensation of this preference relation.

My attempt: So from what I have learned, we know that a preference relation admits a utility function representation if it is rational (reflexive, complete, transitive) and continuous. I have found that this preference relation is not transitive, but this does not mean that there does not exist a utility function representation, because the aforementioned statement is not an if and only if statement.

Moreover, I thought we could try to derive a contradiction from the fact that if there exists a utility function $u$ representation of the preference relation, then we have $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff u(x_1,y_1)\geq u(x_2,y_2)$$
I tried to use the fact that the relation is not transitive to derive a contradiction by using the statement above, but was unsuccessful.

Sadly, these are the two main theorems/propositions that I've learned to solve these problems.

Any help is appreciated!

You just need to use the violation of transitivity and proceed by contradiction.

Suppose you have  that $(x_1,y_1)R(x_2,y_2)$ and $(x_2,y_2)R(x_3,y_3)$ and a utility function, $u:[-1,1]^2\rightarrow \mathbb{R}$, exists, then $u(x_1,y_1)\geq u(x_2,y_2)$ (these are two reals) and $u(x_2,y_2)\geq u(x_3,y_3)$. (another two reals). Since the reals are transitive, we conclude  $u(x_1,y_1)\geq u(x_3,y_3)$ which in turn implies that $(x_1,y_1)R(x_3,y_3)$. However this is a contradiction (if you choose carefully your three bunddles).


If petrol/gas prices were locked down, how would normal consumers and the producers be affected? Hey economics stack exchange! Congrats on getting to beta! I wanted to ask a question that was running through my head on a road trip earlier today.

Let's say a magic fairy grants a person his wish, and gas prices would instantly be solidified (locked) to their current state for the next five years. (I understand logistically how complicated this would be). It's currently about $1.63/gallon where I live.

So now gas prices is more like milk, and we can go into the future planning road trips, and commutes with more accurate budgeting for how much we spend on fuel.

But what would life really look like for consumers with fuel prices locked down? in 6 months? In a year? And the same for fuel producers - how would locked fuel prices affect their future operations and business?

Would it be possible for gas to exist as a fixed-price commodity?

If the price is higher than the market price it will lead to less people buying gasoline. If the price is lower, more people will buy gasoline. The inverse is true of sellers.

In the first case, there will be over supply of gasoline, leading to a growing inventory.

In the second case, there will be more buyers than sellers, leading to a shortage.


Why don't shipping businesses own their own shipping containers? About two or three years ago I attended a talk by a consulting statistician, one of whose clients was a company in the business of leasing out intermodal shipping containers.  He said those who are in the business of using those containers to transport goods typically do not own the containers, but pay a company such as his client for their use.  They pay rent periodically forever and don't normally ever return the containers to the permanent owner.

My question is: Why is it done that way?  Why not buy the containers if you're going to use them for as long as you're in business?

(The occasion for the speaker's experience of this phenomenon was that Congress passed a bill granting tax deductions to companies whose containers are used in U.S. commerce rather than being used only, for example, to carry things back and forth between South Africa and Australia, etc.  Companies could not claim the tax deduction unless they had records indicating how many of their containers were used in U.S. commerce, and they had no records at all of where their containers had been because they hadn't expected Congress to pass such a measure.  Trying to get the information about where each container had been was far more expensive than what they'd save in taxes, and in many, maybe most, cases, the shipping companies didn't have the information at all.  So the consulting statistician and a colleague came up with a theory: For tax purposes, intermodal shipping containers are fungible.  They didn't need to know which containers had been where, but only how many with the company's logo had entered and left the U.S.  It turned out that information could be acquired inexpensively from port authorities. The company argued that that would underestimate the number of the company's containers used in U.S. commerce, since, for example, ships that transport wool from Australia to China to be made into sweaters to be sold in the U.S. were engaged in U.S. commerce when the retailer in the U.S. paid for the transportation.  The IRS accepted the fungibility theory and allowed the deduction.)

First, it appears there are historical reasons: it was the initiative of the producers to standardize the way their goods were transported, already from the factory. And it involved transportation by rail initially, rather than ship. See interesting information here.

Second, I see an economic rationale: overseas commerce is rather volatile, especially at individual-shipping-company level. In such a situation, it would be difficult for each individual shipping company to optimize the number of containers owned. But if there are companies that lease out containers to all the shipping industry, fluctuations dampen and overall capacity is more easily optimized.

Another approach can be found here, where on the subject the authors write

  “Own or lease?” The question has long lain at the heart of container-shipping strategy. From our analysis, the industry typically
  relies too much on leasing. While leasing may be the only option for
  many cash-strapped liners that already have substantial debt, other
  lines should take advantage of this by owning more of their fleet.
  Leasing does provide a little more flexibility to change vessel
  deployment. But that breathing room often comes at too high a price.

The "substantial debt" usually comes from building/buying new ships.


How does the Federal Reserve remove money from circulation? I was watching a video about what gives money its value, and they say it's the total number of bills in circulation.

The Federal Reserve can print or remove money from circulation. But if somebody owns that money, they can't just take that money away right?  So how do they take money out of circulation?  Is there a limit on how much they can take out?

One of the Federal Reserve's (the Fed) primary policy tools is the Federal Open Market Committee (FOMC). Through open market operations the Fed can buy or sell securities on a secondary market. By buying securities they bring new money into circulation, by selling securities they take money out of circulation.
Thus the Fed has a direct influence on the so called monetary base (M0, consisting of currency in circulation and reserves held by banks at the Fed).

It is true that the Fed cannot take the $-bills out of your pocket, but they don't have to. The Fed trades in securities, and every security has a price. Hence, if the Fed wants to take money out of circulation they "buy" dollars, by selling securities. At the market price there will by definition be people who are willing to give their money to the Fed in return for securities.

The value of money is determined by numerous factors beyond the monetary base (e.g. the money supply M1,M2,M3..., exchange rates) and is a concept harder to grasp, because value can be defined in various ways (as opposed to the "price" of money). But I think that goes beyond your question.


Can an F-test be used in a regression that is quadratic, or can it only be used in a linear regression model? My regression I'm testing is quadratic but everything I've read about using F-tests state that it is used in a linear regression model.

Since your model is like
$$
Y = \alpha + \beta_1 X_1 + \gamma_1 X_1^2 + \beta_2 X_2 + \gamma_2 X_2^2 + \epsilon,
$$
it is still a linear model -- because it is linear in the terms. ("Linear" refers to the terms like $X_1$ and $X_1^2$ being linearly combined.)
You can use an $F$-test for your model.


In what sense are "new-Keynesian" models "new" and in what sense are they "Keynesian"? Hopefully, the title of this question is quite descriptive. Whilst I have a broad understanding of the research agenda of macroeconomics, I don't have a very good picture of how it is divided into various schools and traditions. Is there a way to briefly summarise what exactly New Keynesian macro is and how it relates to the rest of what is going on in macroeconomics?

In essence New-Keynesians adapt micro to macro theory. This is in contrast to new classicals which adapt macro theory to orthodox neoclassical market-clearing microfoundations. New-Keynesians adapt the rational expectations hypothesis but accept that market may fails due to wage and price stickiness and Friedman's natural rate hypothesis. The New-Keynesians, the RBC school and New Classicals focus on issues relating to aggregate supply and have been the dominating schools since the 1970's, especially the new-Keynesians have dominated the last one to two decades. On the other hand "old"-Keynesians and the orthodox monetarists mainly focused on issues relating to aggregate demand and these dominated economic thinking pre-1970's.

As an example of the differences between New-Keynesian New Classicals and the RBC school consider an increase in money: This increase will have real effect in a New-Keynesian model due to these market imperfections. In a new classical model on the other hand money will only have real effects if they are unanticipated (Lucas' Island model) while in a RBC model the increase will only feed into higher prices due to perfect clearing markets and rational expectations.

Note that it has been argued by N. Gregory Mankiw that the New-Keynesian school could just as well have been called New-Monetarist.

For an excellent reference on the different schools, what they represent and their differences see Snowdon and Vane: "Modern Macroeconomics: It's Origins, Development and Current State"


What are the most popular technical models used for forecasting exchange rates in international economics? Are there any de facto standards when publishing, or is there substantial latitude in deriving one's own methodology?

I understand in practice, even the St. Louis Fed is gently skeptical of the validity of most technical methods, but I was wondering how academia viewed them.

While Dooley and Shafer (1976, 1984) were largely dismissed, Neely and Weller (1999) seemed to fare fairly well using genetic algorithms, and Markov and ARIMA methods are reviewed more or less favorably in terms of predictive value.

Is accuracy of prediction (and consequently profitability) even necessarily a factor in modelling for academia, or is the simplicity and explanatory value more heavily favored?$^1$
$^1$*Note: Not sure if this merits a separate question, or can be answered as an elaboration of the primary*

Writing as an academic modeller who would use the outputs of such models, what's required (and what I look for as a reviewer) is:

reproducibility: the algorithm is described with sufficient detail to enable someone else to reimplement it;
validation, using data that is completely distinct from the calibration dataset; and
that the output is a distribution of forecasts, not just point values.

Such a distribution can then be fed into ensemble modelling. So instead of using a single forecast of the future value of a currency pair, I could feed in the distribution to a monte carlo simulator or similar.

It doesn't need to have the right expected value, nor a correct value for volatility (or any other moment).

All that makes it essentially useless for trading. And that's a good thing, because no one of sound mind would give away a profitable forex forecaster: such a forecaster would immediately render itself obsolete as it entered common use.


If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference? Problem: According to Wulf Gaertner’s (2009, p. 13) A Primer in Social Choice Theory, any strictly increasing transformation of an individual’s ordinal utility function is informationally equivalent. He says that:

  “The only thing which matters in terms of available information is
  whether, say, commodity bundle $a$ is preferred to or indifferent to or
  dispreferred to commodity bundle $b$ or, expressed in terms of utility
  indices, whether $a$ has a higher or equally high or lower utility index
  than $b$.”

This makes sense, however, when I looked up the definition of a `strictly increasing function/transformation’ I became confused regarding how this would allow one to represent cases of indifference as well as cases of strict preference.

Ken Binmore’s (1983, p. 109) Mathematical Analysis: A Straightforward Approach formally defines an increasing and strictly increasing function as:

Increasing function: $\forall x,y \in X: (x > y) \Longrightarrow ( \ f(x) \geq f(y) \ )$

Strictly increasing function: $\forall x,y \in X: (x > y) \Longrightarrow ( \ f(x) > f(y) \ )$

So a strictly increasing transformation in utility terms–––for individual $i$–––would (I think) be defined formally as:

Strictly increasing transformation: $\forall x,y \in X: ( \ u_i(x) > u_i(y) \ ) \Longrightarrow ( \ f(u_i(x)) > f(u_i(y)) \ )$

But, since this is defined solely in terms of strict inequality ($ \ u_i(x) > u_i(y) \ $) I’m confused as to how this can allow for cases where an individual is indifferent between two alternatives: $xI_iy = ( \ u_i(x) = u_i(y) \ )$. Or cases of three or more alternatives where $i$ strictly prefers some and is indifference regarding others: e.g. $ ( \ u_i(x) = u_i(y) \ ) > u_i(z) $. Wouldn’t these be ordering cases, where the orderings are not characterised by strict inequality of utilities?

Duplication information: I am aware that a question very similar to this has been asked before by Eric '3ToedSloth' (Ordinal utility and monotonic transformations). Eric '3ToedSloth'’s question was focused on the definitions of both ordinal-scaled utility functions and monotone transformations. He also mentioned the difficulty of representing indifference. The reason that I have asked this question is that the accepted answer (by 201p) was focused on answering the question by showing that increasing (/weakly monotone) transformations destroy ordering information, rather than the issue which I am most confused about: how ordinal utility functions (defined in terms of strictly increasing transformations) can represent indifference. (There is a chance that 201p’s answer did cover this, but I am too stupid to be able to see it). Ideally I would have posed this as a clarificatory comment, but I lack the reputation level to post one. I am happy for my question to be closed if the community thinks it is too similar :).

I think you are most confused about what is meant by “defined in terms of strictly increasing transformations” or being “informationally equivalent.

You should think it in the following way, a utility function represents someone’s preferences if the function gives a higher/lower/equal value from bundle a than from bundle b if that person prefers more/less/the same bundle a than bundle b. Suppose that such function is $u(x)$, then you can ask, is there a unique function with such properties (I.e. that represents the person’s preferences) and the answer is NO. Any strictly increasing monotonic transformation of $u(x)$, say $f(u(x))$ is also a function describing the preferences of the person. Hence we say that these two are valid representations, and are equivalent (or informationally equivalent).

Note that whenever you are comparing two bundles you can use any one of the possible representations, and the “strictly increasing monotonic transformation” part is just to check if two functions are equivalent representations of preferences.


Isn't recession is when there's an actual decrease and not just a less rapid growth? I heard that for 2020, the global economic forecast is recession. The growth will be less than 2.5%. But isn't recession is when there's a decrease in GDP (for two consecutive quarters, as I recall), not just a lower growth? Why is the term applied so unusually (unusually, right?) in this case?

NOTE: the question has been modified to refer to a global recession (or I missed the global qualifier). This answer is for a national recession. The answer by @Fizz discusses the global case. I will leave my answer unchanged.

There is no international standard for a recession definition. Definitions are country-specific. For example, in the United States, the National Bureau of Economic Research (NBER) has a committee that makes recession date determination decisions, based on a number of criteria.

The NBER has a FAQ, which probably covers everything you want to know: link.

(Other countries have similar committees.)

Otherwise, people use two consecutive quarters of declining real GDP as the definition of recession. The advantage is that this is uniform across countries. Some people call this a “technical recession” in countries that have a recession-dating body (like the NBER).

Note that we need to look at quarterly GDP, annual GDP could still rise (as in the question), yet there is a recession.

For countries that grow very rapidly in real terms, some people will call a reduction in the growth rate a “a growth recession”. The developed countries no longer grow that fast (in recent decades, only some Asian economies like China grew that fast on a sustained basis), and so it does not come up very often. As such, the term is not very well defined, since it is not used much.


Why not just print money to combat deflation? If interest rates are zero and inflation is under 2% per year then why not have the fed print money without borrowing until inflation is back at 2% per year? The money could be used to pay off the national debt. Businesses would have a predictable floor of a 2% inflation rate.  The slippery slope argument against that sort of policy could be prevented by having the policy written into law. It's a fix where everyone wins, right?

That's essentially what Quantitative Easing was supposed to be.

However, we've known for about 80 years that it doesn't work in times like these, and like the 1930s, when demand is flat because of a massive debt overhang. The demand for money just isn't there.

In these times, trying to simply expand the money supply is like pushing on a piece of string.

Japan's been battling with non-responsive flat demand for many years now (though driven largely by demographics). Monetary stimulus has failed. Fiscal stimulus has at least steadied the ship.


Is it fair to compare 1950 US economy to 2016 US economy? In the last 2 days, bond market has declined a bit. All major news outlets published articles like these: Can We Ignore the Alarm Bells the Bond Market Is Ringing?

Such an event in bond market occurred back in ~1950 (according to the graph on that article). The stockmarket had a major dip around ~1932 due to the great depression but it has looked good since then till 2007.
Overall things also bounced back in 1950, 1960, slow down in 1970 due to energy crisis and then it recovered after 1982.

I am not an economist but trying to understand how will the economy will behave when it will face a similar situation. Is it fair to compare 1950 US economy to 2016 US economy?

Yes. It is a fair comparison.

Human nature, market behavior and principles of finance and economics have not changed much in the recorded history of mankind. For example, the principles set forth by Adam Smith in his opus The Wealth of Nations are just as relevant today as they were in 1776 when the book was published.


Any databases with CEO letters and shareholder letters? I am doing a research with content analysis, verifying certain disclosures on CEO letters and Shareholder letters present in annual reports of listed companies in the London Stock Exchange.

Can someone recommend a database where these letters would be available in plain text? Or at least where all the PDFs could be downloaded as a whole package? All I've found until now was the website AnnualReports but I believe someone must have done already this work :)

Perhaps you could try something like the Bloomberg Terminal; I hear they have a lot of information.

If you were looking for annual reports from American companies, I'd tell you to go to the SEC website. However, I've noticed that http://www.luse.co.zm/ has some annual reports from companies on the London Stock Exchange, such as British American Tobacco, here.


When to use the market and when to use central planning? I have a basic question: my understanding is that in a market economy, economic decisions are governed by prices, i.e prices signal what should be produced & how much. This is opposed to central planning, where a committee decided what should be produced & how much.

Now, in companies or households, such economic decisions are made by "central planning": i.e. - the CEO/board, or parents. Why shouldn't prices be used at these levels too? For example, why don't companies create a "currency" and tell employees to work on things that people with more "money" (senior management) will buy? Or, in a family, for parents to create a "currency" and tell family members to work on things that others will pay for? (done in small ways in some families, but not with everyone participating).

Bottom line of the question: When is it better to use a "market economy" (with prices) as compared to central planning? Is it a function of size? I don't think so...

There is a school of thought that says that people unconsciously use cost-benefit analyses in their relationships with other people. In this idea, people show kindness only because they anticipate getting rewarded for those acts, so it is in their own self-interest to do so.

Monetizing small tasks takes time, and then collecting money for tasks done takes more time. So people do this mentally instead, moreso by feelings than rational calculation. At the level of an interpersonal relationship, words and feelings matter whereas in a business relationship, only tasks and services or goods rendered matter. Thus, monetizing the countless miniscule interactions that take place in a personal relationship would be impossible and there needs to be some degree of trust to replace that.

At the level of a firm, an employment contract stipulates generally what somebody is being paid for. It is more efficient for the company to let individuals decide what to do in a day, or to instruct them to undertake certain tasks (depending on the organizational structure of the firm) than to spend time haggling for a price at which they should be paid in order to carry out various parts of their jobs. As other users have commented, when a firm gets too large, there are diseconomies of scale as it becomes too difficult to control a large number of workers. Then work tends to be contracted out to other firms and the use of money comes in.

However, token economies work well in situations such as mental asylums, to encourage those people to undertake tasks and follow rules.


Good textbook in applied microeconomics I noticed many textbooks in undergraduate microeconomics cover the impacts of taxation but hardly any go in depth about the types of tax (unit tax vs proportionate tax). My question is, is there any microeconomic texts cover a broad range and in depth topics in applied microeconomics?

A classic on public choice and taxation theory is

"The Power to Tax: Analytic Foundations of Fiscal Constitution" by Brennan and Buchanan

Really interesting book and relatively easy read.


Can stock exchange workers go on strike? Today, trade in the stock exchange of my country Israel (TASE) was cancelled due to a union dispute. So clearly, in Israel the answer to the question in the title is "yes". I can't say this comes as a surprise, as our country was founded on the bedrock of socialism, and those roots last until this day. But this is unfortunate as such disruptions surely concern foreign investors (and justly so).

However, I cannot imagine the same happening in the US, and indeed I couldn't find such an occurrence. Did I miss anything? Reading in Wikipedia, it looks like both NYSE and TASE are public (non-government) companies. So how come we see stock exchange strikes in Israel (this is not the first) and not in the US?

Is it because in the US there are multiple stock exchanges as opposed to Israel where TASE is a monopoly? Is it because unions in Israel are more powerful than in the US (and if so, how and why)? Perhaps US stock exchange workers are somehow classified as essential workers who aren't permitted to strike (e.g. by force of the Taylor Law)?

The Stock Exchange workers in US could strike if they wanted. The right to strike in US is enshrined in the US National Labor Relations Act of 1935. See also explanation of the law by the National Labor Relations Board  to see conditions under which strike can occur. None of the conditions seem to exclude stock exchange workers.

However, as @BrianRomanchuk points in his +1 comment, strikes are normally called by unions. According to the statistics published by U.S. Bureau of Labor Statistics in 2019 by occupation only $4.2\%$ workers were members of union and only $5.1\%$ represented by unions in the "Business and financial operations occupations" and if we look more narrowly only at finance as industry (which is arguably more appropriate for this question) the figures become $1.4\%$ and $2\%$. This being said I could not find any statistics specifically for only stock exchanges, but I would expect that unionization rates there would be lower than the aggregate for whole industry.

At the same time statistics show that people in the US working in finance and insurance industry were in 2018 ranked 4th in terms of average salary (see here).

So to sum up, people in US working in financial industry are not generally members of unions or even represented by unions. This would presumably make organizing any meaningful strike difficult.  At the same time people working in finance industry in US are already in one of the highest paying professions meaning that there is most likely not much incentive to strike.


Limits to Quantitative Easing Programmes I have been reading recently on the quantitative easing programmes by the ECB and the BOJ, see http://www.cnbc.com/2016/04/07/what-the-bank-of-japan-boj-will-do-now-that-negative-rates-have-disappointed.html, and, http://www.bloomberg.com/news/articles/2016-04-21/ecb-to-start-buying-corporate-bonds-in-june-as-part-of-stimulus.

The ECB will be expanding its current programme to include corporate bonds and  it is being suggested that the BOJ may give up on negative interest rates and possibly could buy japanese equities instead. It seems that these central banks are just working their way up the risk asset spectrum. My question is where do these asset buying programmes stop (penny stocks/distressed debt?)? Also what happens to these assets, surely if they sit on the central banks books it could go bankrupt like a commercial bank? Moreover, what could cause these asset buying programmes to be abandoned/fail?

1) In principle, there is nothing material to stop the central banks. Apparently, during the great recession in the 1930's in the US, the fed bought even stranger stuff. They could go domestic bonds, equities, houses, etc, and then they could go to foreign assets.

2) No, they cannot literally go bankrupt because they can always print money. Some banks have in fact begun to consider printing money as a way to forcefully lower the value of their currencies.

3) My guess is that the issue is really the opposite one. Banks are doing too well: they buy assets, and those assets do well, then the bank is actually backing up each unit of currency with more value than before. It's hard to create inflation like that.

4) The practical limits are twofold: it might be politically unsustainable. A) Sooner or later the public thinks this is useless and they elect a new central banker or ask the president to appoint a new one. B) It might create all kinds of strange incentives. For example, you might want to bribe the central bank reserve's managers to buy your company's assets.


When building a social accounting matrix, do you input domestic intermediate demand or total intermediate demand? I have been trying to build a social accounting matrix (SAM) after building an input-output table (IOT). In the IOT, I had to distinguish between total intermediate demand (which includes import of intermediate products) and domestic intermediate demand (which excludes imports). Therefore, I had to look at trade data to perform a breakdown of imports per intermediate and final products.

I was wondering if SAMs also used this breakdown of imports information. Since IOTs are used as a source of information to build a SAM, I figured it would. I know SAMs include intermediate demand information (see the following image, it's called intermediate inputs), but I don't know if it refers to total demand or domestic demand. Does anyone know?

Thanks in advance!

It depends on the structure of the particular SAM, although in the case of the diagram you've provided, intermediate inputs should include any imports (as should final demand and exports - in other words, you should be using the Combined Use table to populate this SAM, not the Domestic Use table).

You can work this out by looking at the commodity balance identity.  Rows of the SAM must sum to the same total as the corresponding column of the SAM.  For commodities, the SAM structure requires:

Domestic sales + Tariffs + Imports = Intermediate inputs + Final Demand + Exports

i.e. total supply of commodities = total use of commodities (note that this is also the row balancing condition for the Supply-Use tables).  Since imports are included on the left hand side, they need to be included on the right hand side as well.


Why are German bonds used as the reference for the calculation of Eurozone bond spreads? I can't find the source, either on the the ECB homepage or any other internet source to verify why German bonds are used as a reference point in the eurozone when talking about risk spreads for other European bonds.

German bonds placed as a reference in the eurozone is a form of tacit understanding and i don't think you will find official conventions about this. This practice comes from market Finance pricing technics, as the CAPM, which use a risk (-free-rate) referential to price different kind of assets. Given the higly positive trade balance of Germany, the stability of its revenue base, etc... the country is seen by financing markets as higly creditworthy, i.e. viewed as the "most risk-free" of the eurozone.


Is "normal distribution" a good choice for modeling future inflation rates? I have a financial model that generates future values for a present sum of money based on its growth by investment minus inflation adjusted expenditure. Rather than use fixed rates for growth and inflation (say over the next 20 years), I'd like to use a range with a probability distribution. e.g. inflation "normally" distributed between 1 to 5 percent (90% confidence). Question is, is a normal distribution a good choice for modeling future inflation rates? Or does the history of inflation point towards some other distribution?

With many financial variables you can deduce the distribution from the options market , but there isn’t a sufficiently developed inflation options market (at least in the US).  However, experience shows that market participants are unwilling to sell options with strikes either very low (say 0%) or very high (say 5%) at anywhere near theoretical prices, suggesting that the right distribution might be more fat tailed than a normal distribution.  This wouldn’t be shocking , since many financial variables have similar characteristics.
It also matters what measurement period you are working with. The inflation rate for a given 12month period in the future could have a wider distribution than the average inflation over a 20year period, which might be better behaved.
In the US , the center of the distribution can be estimated from the inflation bond and derivatives markets , and is in the area of 2% for long term forecasts, in line with the target of the Federal Reserve.


Terminology: _______ financing (meaning financed through the private sector) I have encountered several similar terms on this notion, including:

private sector financing (very clear, but a bit wordy)
market financing (somewhat clear, usage seems infrequent)
alternative financing (not quite as clear, but seems fairly standard
in the literature)

Question

Are these terms interchangeable? And is there not a more succinct/elegant way to express the idea?

“Private sector” financing or “non-government” financing will certainly be most clear. “Market” financing is succinct but it can be confused with “capital market” financing, that is, borrowing by issuing tradable debt instruments. “Alternative” financing is generally used to refer to non-bank, non-capital-market financing, such as borrowing from private equity or hedge funds.