Ec 10 is still number one

But just barely.

Who predicted the sluggish economy?

Robert P. Murphy looks back.

Wynne Godley On Front Business Page Of New York Times

The New York Times, even outside of their editorial pages, seems to think their readership should know about the non-mainstream economists I generally like:

• 11 September 2013 profile of Wynne Godley.
• 18 July 2013 article on Steve Keen and how his work builds on Hyman Minsky.
• 5 July 2013 profile of Warren Mosler.
• 4 March 2009 article on the difficulties heterodox economists face in academia.
• 23 April 2008 profile of George Soros.
• 11 July 2007 article on heterodox economics.

I predict that this profile of Godley will get a more positive response from Post Keynesians and advocates of endogenous money than their profile of Warren Mosler did. One caveat: I think Godley was more about using his stock-flow consistent modeling to identify unsustainable trends, than to quantitatively predict the course of, say, Gross Domestic Product (GDP) over the next n quarters. (He also accepted the conclusions of the Cambridge Capital Controversy.)

Update: I should have noticed that the Jonathan Schlefer is the author of the article on Godley. L. Randall Wray comments.

Utility Maximization For A Numeric Example Of International Trade

Overlapping Generations

1.0 Introduction

The theory of comparative advantage does not justify free trade in consumer goods. The mainstream textbook presentation is just logically mistaken. I have proven these claims in a paper building on work staring from a third of a century ago. My paper provides a numeric example. I have previously presented the production side of another numeric example here. My paper concludes with an utility-maximizing closure, but I have decided that this part of my paper could be improved. Accordingly, this post provides a simple overlapping generations example to combine with my previous numeric example in the blog post.

2.0 Overlapping Generations

Accordingly, consider an Overlapping Generations (OLG) model in which each agent lives for two years. Each agent works in the first year of their life and is retired in the second year. They are paid their wages at the end of the year in which they work. They can choose to save some of their wages for consumption at the end of the second year of their life.

Suppose each agent has the following utility function:

U(x₂₀, x₂₁, x₄₀, x₄₁) = (x₂₀ x₄₀)^γ(x₂₁ x₄₁)^{1/2 - γ}, 0 < γ < 1/2

where:

• x₂₀ is the quantity of wine consumed at the end of the first year of the agent's life.
• x₂₁ is the quantity of wine consumed at the end of the second year of the agent's life.
• x₄₀ is the quantity of silk consumed at the end of the first year of the agent's life.
• x₄₁ is the quantity of silk consumed at the end of the second year of the agent's life.

In the numeric example, 4,158 agents are born each year in country A, and 3,969 agents are born each year in country B. Since wine and silk enter the utility function symmetrically, equal amounts of wine and silk are consumed each year in each country in a stationary state, given an (international) price of silk of unity. Although all agents are assumed identical in a given country, agents may vary across countries. In particular, difference in the parameter γ in the utility function between countries can rationalize the difference in income distribution between the two countries in the example.

It remains to outline in more detail a demonstration of these claims. The agent is faced with the following mathematical programming problem:

Given p, w, and r
Choose x₂₀, x₂₁, x₄₀, x₄₁
To maximize U(x₂₀, x₂₁, x₄₀, x₄₁)
Subject to:

(x₂₀ + px₄₀)(1 + r) + (x₂₁ + px₄₁) = w(1 + r)
x₂₀ ≥ 0, x₂₁ ≥ 0, x₄₀ ≥ 0, x₄₁ ≥ 0

Three independent marginal conditions arise in solving this optimization problem:

(∂U/∂x₂₀)/(∂U/∂x₂₁) = 1 + r

(∂U/∂x₂₀)/(∂U/∂x₄₀) = 1/p

(∂U/∂x₂₁)/(∂U/∂x₄₁) = 1/p

These three marginal conditions, along with the budget constraint, constitute a system of four equations in four variables. Its solution is:

x₂₀ = γ w

x₂₁ = (1 - 2 γ) w (1 + r)/2

x₄₀ = γ w/p

x₄₁ = (1 - 2 γ) (w/p) (1 + r)/2

The total demand for, say, wine to consume at the end of each year is summed over workers and retirees in that year:

X₂ = l_Total(x₂₀ + x₂₁)

where:

• X₂ is the quantity of wine demanded in a given country each year.
• l_Total is the annual endowment of labor in the given country.

A similar equation arises for the demand, X₄, for silk:

X₄ = l_Total(x₄₀ + x₄₁)

One can use the above equations to close the with-trade case in my numeric example, at least in cases where the interest rate is not too big. In the latter sort of cases, I might want to consider models in which agents either work or retire for more than one year. At any rate, agents, in this extension, will live for more than two years, and more than two generations will be alive in any given year.

3.0 Autarky

An autarky for my model of production is closed with this model of utility-maximization. A degree of freedom does not exist. The condition that both wine and silk both be produced leads to the determination of the wage and the price of silk as a function of the interest rate.

The equality of savings and investment is an equilibrium condition. In the above model, savings, S, is:

S = l_Total(w - x₂₀ - p x₄₀)

Using the aforementioned price equations, one can express savings as:

S = l_Total(1 - 2 γ)/(l₁R + l₂),

where:

R = 1 + r

Investment, I, is a numeraire quantity of capital, found from an indirect demand from consumer goods:

I = (l₁ X₂ + l₃ X₄)w

Once again, using the price equations, one can express investment as a function of model parameters and the interest rate:

I = l_Total[2 γ + (1 - 2 γ)R](2l₁l₃R + d)/[2 (l₁R + l₂)² (l₃R + l₄)]

where:

d = l₁ l₄ + l₂ l₃

The equilibrium interest rate and, hence, the (domestic) price of silk and wage are found by equating savings and investment. I am hoping that this solution is sufficient to guarantee the quantities demanded of wine and silk lie on the Production Possibilities Frontier (PPF).

4.0 Numeric Values

In the numeric example, prices are specified. Wine is taken as the numeraire. The price of silk on the international market is unity. The wage is (1/200) units wine per person-year in country A and (1/194) units wine per person-year in country B. The interest rate is 20% in country A and 5% in country B. Let the parameter of the utility function be as follows in the two countries:

γ_A = 47/99

γ_B = 89/378

Then the quantities of wine and silk demanded for consumption are as in Table 1. But the entries in Table 1 are taken from my numeric example. So this utility-maximization model does, in fact, close the model of production and international trade used in the numeric example, at least in the with-trade case. When I worked out the autarky case, though, I ended up with a negative interest rate in the two countries.

Table 1: Selected Results for the Numeric Example

		With-Trade Specialization
Endowments	Country A	lTotal,A = 4,158 person-years
	Country B	lTotal,B = 3,969 person-years
International Price of Silk		p = 1 Unit wine per Unit silk
Wine Consumption	Country A	10 1/2 Units wine
	Country B	10 1/2 Units wine
	Total	22 Units wine
Silk Consumption	Country A	10 1/2 Units silk
	Country B	10 1/2 Units silk
	Total	22 Units silk

5.0 Conclusion

I have constructed a numeric example in which trade in consumer goods unambiguously leaves the Production Possibilities Frontier (PPF) rotated inward, as compared with autarky, for country A. And I have rationalized, in a way consistent with neoclassical theory, why a positive interest rate exists and varies between countries in the with-trade equilibrium. But I have not found an example in which the corresponding autarkic equilibrium is consistent with positive interest rates in the two countries in the example.

Appendix: Definition of Parameters and Variables

• γ: A parameter of the agent's utility function.
• γ_A: A parameter of the agent's utility function for country A.
• γ_B: A parameter of the agent's utility function for country B.
• I: National investment.
• R: 1 + r.
• S: National savings.
• U(x₂₀, x₂₁, x₄₀, x₄₁): The agent's utility function.
• X₂: The quantity of wine demanded yearly in a given country, summed across all agents.
• X₄: The quantity of silk demanded yearly in a given country, summed across all agents.
• d: A parameter relating to the relative labor intensity of wine and silk production.
• l_Total: The total endowment of labor in a given country; that is, the number of agents born each year.
• x₂₀: The quantity of wine the agent consumes at the end of the first year of his life.
• x₂₁: The quantity of wine the agent consumes at the end of the second year of his life.
• x₄₀: The quantity of silk the agent consumes at the end of the first year of his life.
• x₄₁: The quantity of silk the agent consumes at the end of the second year of his life.
• p: The price of silk (in unit's wine per unit silk).
• r: The interest rate.
• w: The wage (in unit's wine per person-year).

What To Think Of This Alex Rosenberg Piece?

Alex Rosenberg writes on Free Markets and the Myth of Earned Inequalities.

What should we think of this essay? Philosophers of science, as I understand it, tend, these days, to take the consensus viewpoint in the sciences they examine as a given. They do not, in their professional role, advocate some overarching, context-free, scientific rationality and attempt to dictate to each specific science. Rather, they are engaged in trying to understand how scholars reason in specific disciplines. Furthermore, if one wants to be effective in practical policy advice, one might want, as a rhetorical strategy, to show how your policy conclusions follow from consensus views, no matter how mucked up that consensus may be. So I can understand how, sometimes, Rosenberg might be inclined to take neoclassical economics as given.

Furthermore, I accept some of the points of this essay. I can see how one might describe increased inequality in income distribution as part of a process of cumulative causation. Winners in competitive markets will tend to use their gains as a source of political power. And with that power, they will try to rewrite the rules of the game to gain even more. So competitive markets will lead, endogenously, to non-competitive markets. Is Rosenberg influenced by Dean Baker or Chris Hayes here?

In what sense do people born with better endowments deserve more because they earn more with those endowments? I think Rosenberg is correct to raise this question. (In agreement with Adam Smith, I question whether inborn talents have much to do with the distribution of income.)

I also agree with the general conclusion that government is violating no ethical norm when it institutes redistributive taxation. I would argue for the current need for such policy in the United States on the basis of the lack of sustainability of trends for the last third of a century.

But I think the following observations undermine much of the economics that Rosenberg draws on in his essay: Arrow and Debreu's proof of the Pareto efficiency of a static "competitive" General Equilibrium does not have much to do with the magnificent dynamics that Adam Smith and the classical economists were arguing about. Furthermore, price-taking in General Equilibrium Theory is a model of central planning (by the so-called auctioneer), not of competition. In actually existing capitalist economies, prices are formed in a range of institutions. Even when price-taking occurs, that occurrence depends on existence of certain algorithms for matching bids and offers, say, on the Chicago Mercantile Exchange. Marginal productivity, correctly understood, is not a theory of distribution; it is a theory of the choice of technique. Thus, marginal productivity cannot be correctly cited in an argument that, under competitive capitalism, agents earn what they get. Does Rosenberg know about reswitching examples, in which the same relative quantity flows in production are compatible with vastly different (functional) distributions of income? Besides, as Joan Robinson asked, in what sense is the ownership of capital productive?

A Striking Labor Market Fact

John Lott points out the following: "So far this year there have been 848,000 new jobs. Of those, 813,000 are part time jobs.... To put it differently, an incredible 96% of the jobs added this year were part-time jobs."

Update: Here is the CEA take on this general topic.  And this is from the San Francisco Fed.  I found the following chart of interest.

 Part-time employment as a share of total employment for selected groups

This shows that part-time work is notably higher than it has been historically for prime-age workers with little education (no more than a high school degree).  Whether this is just due to a weak labor market or other more structural changes is an open question.

How Canadians are Different from Americans, but similar to Germans

I don't always keep track of goings-on in the Old Country but this article tells us, if nothing else, that the Canadian Finance Minister, Jim Flaherty, is rather confused. Flaherty says he doesn't like QE (quantitative easing), which would be OK, as long as he could come up with some semi-coherent reasons. But, Flaherty says:

The Americans tend to emphasize creating more jobs and less concern about the accumulation of public debt and printing more money, with which I’ve never agreed. The Germans tend to be more prudent and frugal like Canadians tend to be.

First, Flaherty doesn't seem to understand that managing the size of the public debt is actually his job, and not the job of the central bank. Central banks may indeed be venturing into the traditional territory of the fiscal authority by engaging in QE, as QE looks more like debt management (altering the maturity structure of the outstanding government debt) than traditional monetary intervention. But QE cannot change the total quantity of consolidated government debt outstanding, only the composition of the debt, except perhaps indirectly. Further, in present circumstances in the U.S., QE is not "printing money." QE consists (in the QE3 operation currently underway) of swaps of interest-bearing reserves for long-maturity government debt and mortgage-backed securities. The reserves in question currently look more like short-maturity government debt than they look like anything we might want to call "money."

The really funny part of the quote above involves Flaherty's unflattering view of profligate Americans. Apparently he hasn't been talking to the Americans who think of their government as ridiculously austere. Somehow Flaherty thinks that Canadians are more like Germans. I just don't see it. This reminds me of a joke, which goes something like this: Canada could have had American technology, British government, and French culture. Instead it got French government, British technology, and American culture.