Friday, February 27, 2009
The Poverty of Economic Philosophy
Steve Keen brings to our attention a couple of attacks, based on the ongoing global economic crisis, on mainstream academic economics:
Tuesday, February 24, 2009
Davidson Writes A Letter
This is from last Sunday's (22 February) New York Times:
Paul D. Ryan repeats the tired idea that when the Federal Reserve prints money for the government to spend on economic recovery, the result will be inflation because "it is a situation in which too few goods are being chased by too much money." This is based on a false assumption that the output of the country will not increase when government lets contracts to business to produce more goods and services that will improve the productivity and health of our country.
If there is significant unemployment and idle capacity in the private sector (and who can deny there is?), then this deficit spending will not cause inflation. Rather, the "printed" money spent on a recovery plan creates profit opportunities that induce private enterprise to hire and produce more goods. Then there will be many more goods for this money to chase and no inflation need occur.
Paul Davidson
Boynton Beach, Fla, Feb 14, 2009
The writer is editor of The Journal of Post Keynesian Economics
Sunday, February 22, 2009
Another Reswitching Example
1.0 Introduction
I have previously presented examples of reswitching and capital reversing. These phenomena were discovered as part of the Cambridge Capital Controversy, and you will occasionally see commentators bring up the CCC on various blogs. This post presents another example. This example has a different structure than my favorite models. In this example, not all commodities are produced with the aid of commodities. Some capital goods not explicitly shown are produced directly with unassisted labor.
2.0 Some Theory And An Example
Consider a firm choosing among a set of techniques for producing a given commodity. Each technique, as in Table 1, exhibits Constant Returns to Scale (CRS) and can be represented as a series of dated labor inputs. The first element in this series is the amount of labor that must be applied in the technique during the current production cycle to produce one unit of the commodity. The second element is the amount of labor that must be applied one cycle ago to produce the capital goods required for use by the first labor input in the series. And so on. This representation of a technique is known as a flow-input, point-output model.
Consider the the cost of producing a unit of output with a given technique, where the calculation of the cost is performed at the end of the year in which the output becomes available. The cost is the sum of the cost of the labor inputs over previous years, with the cost of each labor input including an interest charge:
The best rate of profits (also known as the interest rate) available to the firm should be used in finding the cost of producing a unit of output with each technique. Since the only use of financial capital available to the firm here is to produce with one or another of the techniques of production, the best rate of profits is the rate of profits obtainable with cost-minimizing techniques. The following algorithm traverses the techniques to find the rate of profits associated with cost-minimizing techniques:
Figures 1, 2, and 3 illustrate the application of the algorithm to the example. Figure 1 shows the wage-rate of profits curves associated with each technique. In flow-input, point-output models, these curves never cross the axis for the rate of profits. Instead, the curves approach it asymptotically. Points at which such curves intersect are called switch points. The "perverse" or "paradoxical" switch point is at a wage of 1/78 units of output per person year and a rate of profits of 50%. The higher-wage switch point is at a wage of 5/286 units of output per person-year and a rate of profits of 10%. A switch point is called "paradoxical" merely because it illustrates behavior contradicting mistaken and outdated neoclassical beliefs. The algorithm can be considerably simplified:
The theorem is easily applied to the example. By the theorem, the alpha technique is cost-minimizing for wages between the switch points. The beta technique is cost-minimizing for wages below 1/78 units of output per person-year and between wages of 5/286 and the maximum wage of 1/52 units of output per person-year.
Now to show that the algorithm yields the same answers. Suppose one starts by choosing the alpha technique at Step 1. The rate of profits sought in Step 2 is read off the wage-rate of profits curve for the alpha technique in Figure 1, given the wage. The costs found in Step 3 are shown in Figure 2. Figure 1 shows that the alpha technique is, indeed, cost minimizing for intermediate wages, that is, between the switch points. If the wage is either too low or too high, the beta technique is selected in Step 4, as shown in Figure 2. According to Step 6, the flow of control in the algorithm then goes to Step 2 with the beta technique selected. Figure 3 shows the costs of the techniques using the rate of profits for the beta technique. Here too, the algorithm concludes with the same answer as suggested by the theorem.
3.0 Conclusion
Once the cost-minimizing technique has been determined, one can consider how much labor firms will want to hire per unit output at any given wage. Figure 4, which is based on the assumption of a stationary-state output, illustrates this calculation for the example. If a firm is operating the alpha technique, for example, to produce an unchanged output over the next three years, workers producing consumption goods available at the end of the current year, producing capital goods to be used to produce consumption goods available at the end of the next year, and producing capital goods to be used to produce capital goods available at the end of the next year will all be working side-by-side. That is, 53 workers will be employed per unit output under the alpha technique for a stationary state. As the graph shows, around the switch point at the lower wage, a higher wage is associated with a cost-minimizing technique in which firms want to employ more workers for a given stationary-state output.
So much for the theory that wages and employment are determined by the intersection of well-behaved supply and demand curves in the labor market.
I have previously presented examples of reswitching and capital reversing. These phenomena were discovered as part of the Cambridge Capital Controversy, and you will occasionally see commentators bring up the CCC on various blogs. This post presents another example. This example has a different structure than my favorite models. In this example, not all commodities are produced with the aid of commodities. Some capital goods not explicitly shown are produced directly with unassisted labor.
2.0 Some Theory And An Example
Consider a firm choosing among a set of techniques for producing a given commodity. Each technique, as in Table 1, exhibits Constant Returns to Scale (CRS) and can be represented as a series of dated labor inputs. The first element in this series is the amount of labor that must be applied in the technique during the current production cycle to produce one unit of the commodity. The second element is the amount of labor that must be applied one cycle ago to produce the capital goods required for use by the first labor input in the series. And so on. This representation of a technique is known as a flow-input, point-output model.
| Year Before Output | Labor Hired for Each Technique | |
| Alpha | Beta | |
| 0 | 33 Person-Years | 0 Person-Years |
| 1 | 0 Person-Years | 52 Person-Years |
| 2 | 20 Person-Years | 0 Person-Years |
Consider the the cost of producing a unit of output with a given technique, where the calculation of the cost is performed at the end of the year in which the output becomes available. The cost is the sum of the cost of the labor inputs over previous years, with the cost of each labor input including an interest charge:
L0 w + L1 w (1 + r) + L2 w (1 + r)2 + ... + Ln w (1 + r)n + ...where w is the wage for a unit of labor, r is the rate of profits, and (L0, L1, L2, ...) is the series of dated labor inputs representing the technique. The wage is paid at the end of the year for the labor expended during that year.
The best rate of profits (also known as the interest rate) available to the firm should be used in finding the cost of producing a unit of output with each technique. Since the only use of financial capital available to the firm here is to produce with one or another of the techniques of production, the best rate of profits is the rate of profits obtainable with cost-minimizing techniques. The following algorithm traverses the techniques to find the rate of profits associated with cost-minimizing techniques:
- Choose a technique.
- For the given wage w, find the rate of profits r that, when used to cost up the labor inputs, equates that cost to the price of a unit of the produced commodity.
- Cost up the labor inuts for all techniques with this wage and rate of profits.
- Choose a technique with the minimum of the costs found in Step 3.
- If the technique for which the rate of profits was obtained in Step 2 can be selected in Step 4, stop. You have found a cost-minimizing technique and the rate of profits.
- Else, go to Step 2 and repeat with the newly selected technique.
Figures 1, 2, and 3 illustrate the application of the algorithm to the example. Figure 1 shows the wage-rate of profits curves associated with each technique. In flow-input, point-output models, these curves never cross the axis for the rate of profits. Instead, the curves approach it asymptotically. Points at which such curves intersect are called switch points. The "perverse" or "paradoxical" switch point is at a wage of 1/78 units of output per person year and a rate of profits of 50%. The higher-wage switch point is at a wage of 5/286 units of output per person-year and a rate of profits of 10%. A switch point is called "paradoxical" merely because it illustrates behavior contradicting mistaken and outdated neoclassical beliefs. The algorithm can be considerably simplified:
Theorem: Consider a technology specified as a choice among techniques, where each technique is represented by a flow-input, point-output model. Let the outer envelope of the wage-rate of profits curves for each technique be constructed by finding the maximum rate of profits for each wage over all wage-rate of profits curves. For each point on the outer envelope, a technique in which the technique’s corresponding wage-rate of profits curve contains that point is selected by the above algorithm as a cost-minimizing technique at that wage.
 |
| Figure 1: Rate of Profits by Technique |
The theorem is easily applied to the example. By the theorem, the alpha technique is cost-minimizing for wages between the switch points. The beta technique is cost-minimizing for wages below 1/78 units of output per person-year and between wages of 5/286 and the maximum wage of 1/52 units of output per person-year.
Now to show that the algorithm yields the same answers. Suppose one starts by choosing the alpha technique at Step 1. The rate of profits sought in Step 2 is read off the wage-rate of profits curve for the alpha technique in Figure 1, given the wage. The costs found in Step 3 are shown in Figure 2. Figure 1 shows that the alpha technique is, indeed, cost minimizing for intermediate wages, that is, between the switch points. If the wage is either too low or too high, the beta technique is selected in Step 4, as shown in Figure 2. According to Step 6, the flow of control in the algorithm then goes to Step 2 with the beta technique selected. Figure 3 shows the costs of the techniques using the rate of profits for the beta technique. Here too, the algorithm concludes with the same answer as suggested by the theorem.
 |
| Figure 2: Cost of Techniques at Alpha Rate of Profits |
 |
| Figure 3: Cost of Techniques at Beta Rate of Profit |
3.0 Conclusion
Once the cost-minimizing technique has been determined, one can consider how much labor firms will want to hire per unit output at any given wage. Figure 4, which is based on the assumption of a stationary-state output, illustrates this calculation for the example. If a firm is operating the alpha technique, for example, to produce an unchanged output over the next three years, workers producing consumption goods available at the end of the current year, producing capital goods to be used to produce consumption goods available at the end of the next year, and producing capital goods to be used to produce capital goods available at the end of the next year will all be working side-by-side. That is, 53 workers will be employed per unit output under the alpha technique for a stationary state. As the graph shows, around the switch point at the lower wage, a higher wage is associated with a cost-minimizing technique in which firms want to employ more workers for a given stationary-state output.
 |
| Figure 4: Labor Intensity of Cheapest Technique |
So much for the theory that wages and employment are determined by the intersection of well-behaved supply and demand curves in the labor market.
Friday, February 20, 2009
The Undermining Social Democratic Downhill Slide...
"[Michael] Harrington was a 'democratic socialist', not a social democrat. Whereas social democracy endorsed the welfare state, democratic socialism expanded proletarian decision-making into every corner of society, including the workplace, thereby reversing capitalist priorites. In America, democratic socialism meant taking the New Deal beyond its first two stages [1930s and 1960s?]. By empowering workers, a 'Third New Deal' would complete the process begun in 1929, when control of key economic investments was passed from unfettered boardrooms to a capitalist-controlled welfare state." -- Robert A. Gorman, Michael Harrington: Speaking American, Routledge (1995)
Tuesday, February 17, 2009
Two Crises Of Economic Theory
The American Economic Association held their annual meeting in New Orleans in 1971. At the invitation of John Kenneth Galbraith, the AEA president that year, Joan Robinson delivered the keynote Ely address. She identified "The Second Crisis of Economic Theory".
The first crisis occurred in the 1930s. Economists had no theory, at the time, to guide policy for addressing the dramatic drop in the volume of output and the increase in unemployment. John Maynard Keynes, as well as Michal Kalecki, developed the theory to address this crisis.
As I recall, the second crisis of economic theory relates to the mix of goods being produced, even when the volume is such that more-or-less full employment is being achieved. Many of her time did not think the balance correct. Conspicuous consumption, positional goods, and the means of destruction are produced in abundance. But as for the production of amenities useful for modern life typically provided by government (e.g., public transportation) - not so much. Mainstream economic theory does not provide a perspective for a thorough-going improvement on what comes out of more-or-less capitalist markets.
Consider the context of Robinson's Ely lecture. Although she had already developed a theory of stagflation, she couldn't have known how poor western economies would perform over the next decades. So at the time of her lecture, the second crisis of economic theory might have been more readily apparent than the first.
It seems to me that both crises are evident today. The world's economic problems are not only how to get people back to work during this worldwide global downturn. We also need to reorient the world's economy to operate with more sustainable and renewable energy resources, encourage the production of more public goods in many economies, decrease the workweek, etc.
Reference
The first crisis occurred in the 1930s. Economists had no theory, at the time, to guide policy for addressing the dramatic drop in the volume of output and the increase in unemployment. John Maynard Keynes, as well as Michal Kalecki, developed the theory to address this crisis.
As I recall, the second crisis of economic theory relates to the mix of goods being produced, even when the volume is such that more-or-less full employment is being achieved. Many of her time did not think the balance correct. Conspicuous consumption, positional goods, and the means of destruction are produced in abundance. But as for the production of amenities useful for modern life typically provided by government (e.g., public transportation) - not so much. Mainstream economic theory does not provide a perspective for a thorough-going improvement on what comes out of more-or-less capitalist markets.
Consider the context of Robinson's Ely lecture. Although she had already developed a theory of stagflation, she couldn't have known how poor western economies would perform over the next decades. So at the time of her lecture, the second crisis of economic theory might have been more readily apparent than the first.
It seems to me that both crises are evident today. The world's economic problems are not only how to get people back to work during this worldwide global downturn. We also need to reorient the world's economy to operate with more sustainable and renewable energy resources, encourage the production of more public goods in many economies, decrease the workweek, etc.
Reference
- Joan Robinson (1972) "The Second Crisis of Economic Theory", American Economic Review, Papers and Proceedings, V. 62 (May): 1-10
Sunday, February 15, 2009
Empirical Evidence On Minimum Wages
A theme of this blog is that it is illogical to explain wages and employment by the interaction of well-behaved demand and supply curves in the labor market, even under assumptions of perfect competition, no information asymmetries, etc. Since orthodox teaching on the subject is simply incorrect, David Card's empirical results on minimum wages did not astonish me.
For those interested in these results, I notice that researchers at Berkeley have extended them. So this paper goes on my long list of ones to read some day:
For those interested in these results, I notice that researchers at Berkeley have extended them. So this paper goes on my long list of ones to read some day:
"We use policy discontinuities at state borders to identify the effects of minimum wages on earnings and employment in restaurants and other low-wage sectors. Our approach generalizes the case study method by considering all local differences in minimum wage policies between 1990 and 2006. We compare all contiguous county pairs in the U.S. that straddle a state border and find no adverse employment effects. We show that traditional approaches that do not account for local economic conditions tend to produce spurious negative effects due to spatial heterogeneities in employment trends that are unrelated to minimum wage policies. Our findings are robust to allowing for long term effects of minimum wage changes." -- Amdrajit Dube, T. Wiliam Lester, and Michael Reich "Minimum Wage Effects Across State Borders: Estimates Using Contiguous Counties", working paper (2008)
Thursday, February 12, 2009
In Honor Of The Day
Today is the bicentennial of Darwin's birth.
I think of evolutionary economics as equivalent to (old) institutional economics.
Clarence Ayres was one prominent institutionalist economist, maybe the most prominent of his generation. He ended up at the University of Texas at Austin and helped develop the Texas school of institutional economics. (James Galbraith is currently at UT.) Ayres most well known book is probably The Theory of Economic Progress, which I have not read. I have read The Divine Right of Capital, in which I found some echoes of Joan Robinson's capital critique, even though it precedes the relevant portions of her work.
But I want to point out that Ayres also wrote Huxley, a 1932 biography of Thomas Huxley, also known as "Darwin's bulldog". In 1860 Huxley debated Bishop Samuel Wilberforce:
I think of evolutionary economics as equivalent to (old) institutional economics.
Clarence Ayres was one prominent institutionalist economist, maybe the most prominent of his generation. He ended up at the University of Texas at Austin and helped develop the Texas school of institutional economics. (James Galbraith is currently at UT.) Ayres most well known book is probably The Theory of Economic Progress, which I have not read. I have read The Divine Right of Capital, in which I found some echoes of Joan Robinson's capital critique, even though it precedes the relevant portions of her work.
But I want to point out that Ayres also wrote Huxley, a 1932 biography of Thomas Huxley, also known as "Darwin's bulldog". In 1860 Huxley debated Bishop Samuel Wilberforce:
"Turning to Huxley he inquired with a charming show of solicitude whether the scientist supposed himself to be descended from an ape on the side of his grandmother or his grandfather... And then [Huxley] delivered his famous counterstroke, the upshot of which is that ancestor apes are preferable to bishops."
Sunday, February 08, 2009
Infinite Are The Arguments Of Mages
The following letter comes after five interchanges of letters between Keynes and Hayek and a summary letter by Keynes. Keynes was trying to get at what definitions of saving and investment Hayek was using, what Hayek meant by "forced saving", and why Hayek thought a constant proportion of the money in circulation must be saved to keep the capital stock at the same level. The date of this letter is 29 March 1932, and it is reprinted in The Collected Works of F. A. Hayek: Volume 9: Contra Keynes and Cambridge: Essays, Correspondence (edited by Bruce Caldwell, Chicago University Press, 1995):
Dear Hayek,
I will certainly reserve you space in this June [Economic] Journal for a reply to Sraffa. But let it be no longer than it need be. It is the trouble of controversy - from an editor's point of view - that it is without end. Your MS should reach me not later than May 1.
Having been much occupied in other directions, I have not yet studied your Economica article as closely as I shall. But, unless it be dealt with in isolation from the main issue, I doubt if I shall return to the charge in Economica. I am trying to re-shape and improve my central position, and that is probably a better way to spend one's time than in controversy.
Yours sincerely
J. M. Keynes
Wednesday, February 04, 2009
Economists As Creationists Who Have Never Heard Of Evolution
I found this quote amusing:
"One of Brad DeLong’s commentators compares what’s going on to the discovery that some eminent biologists are creationists, but it’s actually worse than that: it’s like discovering that some eminent biologists have never heard of the theory of evolution and the concept of natural selection." -- Paul KrugmanI am in agreement with, for instance, Krugman and DeLong that the U.S.A. government currently needs to spend a lot on a stimulus package. But I wondered if such more-or-less liberal economists acknowledge other controversies in economics. Have they heard factor prices (like wages) cannot necessarily be explained by the interaction of well-behaved supply and demand curves in factor markets, even under ideal assumptions of perfect competition, flexible prices, perfect information, etc? I don't know whether I want to put much emphasis on Brad DeLong's failure to note such in this post about immigration.
Tuesday, February 03, 2009
Simple And Expanded Reproduction
1.0 Introduction
This is a repost. I've switched templates, and the new one interferes with the layout of the mathematics in the previous version. I've made a few minor changes here and there.
This post presents a model in which a capitalist economy smoothly reproduces itself. The purpose of such a model is not to predict that capitalist economies will converge to some such path as illustrated in the model. Rather, the model provides a basis for the analysis of where things can go wrong.
This sort of model has a long history. My exposition is close to Marx (1956), with the difference that Marx sets out the conditions of simple and expanded production in terms of labor values, not in terms of prices of production. Rosa Luxemburg (1951) and Michal Kalecki (1969) used Marx's department break-down to develop a Keynes-like model of the long run and the short run. Shigeto Tsuru (1942) apparently exposed this model to english-speaking academics when few were looking at Marx's analysis. Paul Samuelson (1957) thought this model of interest. Joan Robinson (1962) drew on these ideas, among others, in her models of metallic ages. Goodwin's generalization (1949) of Keynes to a multisectorial model and Pasinetti's (1981, 1993) analyses of vertically integrated sectors also seem to me to bear family resemblances to this model. Doubtless, my references could be extended in many directions.
2.0 Two Departments
This model considers a capitalist economy with no government and no foreign trade. The outputs of this economy are grouped into two great departments. In the first department, capitalists direct workers to produce means of production (also known as capital goods) with the means of production in that department. In the second department, the workers are directed to produce means of consumption (also known as consumption goods) with the means of production in that department.
For ease of exposition, I make certain additional simplifying assumptions. The workers consume all of their wages. Only the capitalists save, and they save only in the case of expanded reproduction. All capital is circulating capital. That is, there is no fixed capital, such as long-lived machinery. In other words, all capital goods are totally used up each year in producing the yearly output. No technological innovations are introduced.
I think introducing technological innovations and fixed capital makes the possibility of smooth reproduction more incredible. A government can be introduced as a third department, or perhaps by dividing government output among the two departments shown. Foreign trade introduces the possibility of correcting imbalances in domestic demand from outside the domestic economy. But then one could recast the model as of the world economy.
3.0 Prices
A necessary condition for smooth reproduction of a competitive capitalist economy is that the same rate of profit be made in all departments. Otherwise, some capitalists are finding that the expectations on which investments were made are being unfulfilled. They would want to have contracted some departments and expanded others. I also impose the condition that spot prices remain stationary. The following equations express these conditions:
4.0 In Balance
4.1 Simple Reproduction
The economy is in simple reproduction when it is replicated on the same scale year after year. A necessary condition for an economy in simple reproduction is that the production of capital goods each year be equal to the capital goods used up each year. In the model shown here, the value of the capital goods used up each year must equal the value of the output of the first department:
An alternate method of deriving the last equation is available. Start from the equation of the value of total demand for consumption goods and the value of the output of the department producing consumption goods. This condition, when simplified, yields the same equation.
4.2 Expanded Reproduction
The economy experiences expanded reproduction when it consistently expands each year. In this case, the demand for capital goods from the second department includes the savings of the capitalists receiving profits from that department. Likewise, the demand for consumption goods from the first department excludes the savings of the capitalists in that department. Observing these qualifications, it is easy to mathematically express the condition that the demand for capital goods from the second department match the demand for consumption goods from the first department:
5.0 Conclusion
In the model, capitalists independently decide on what department to enter, and how much to produce in that department. A collective result of those decisions is the total output of each department. For those decisions to be validated, the value of consumer goods demanded by workers and capitalists in the department producing capital goods must match the value of capital goods demanded by the capitalists in the department producing consumption goods.
The model is silent on how such an equality can come about. Supply and demand seems like an inadequate answer to me.
References
This is a repost. I've switched templates, and the new one interferes with the layout of the mathematics in the previous version. I've made a few minor changes here and there.
This post presents a model in which a capitalist economy smoothly reproduces itself. The purpose of such a model is not to predict that capitalist economies will converge to some such path as illustrated in the model. Rather, the model provides a basis for the analysis of where things can go wrong.
This sort of model has a long history. My exposition is close to Marx (1956), with the difference that Marx sets out the conditions of simple and expanded production in terms of labor values, not in terms of prices of production. Rosa Luxemburg (1951) and Michal Kalecki (1969) used Marx's department break-down to develop a Keynes-like model of the long run and the short run. Shigeto Tsuru (1942) apparently exposed this model to english-speaking academics when few were looking at Marx's analysis. Paul Samuelson (1957) thought this model of interest. Joan Robinson (1962) drew on these ideas, among others, in her models of metallic ages. Goodwin's generalization (1949) of Keynes to a multisectorial model and Pasinetti's (1981, 1993) analyses of vertically integrated sectors also seem to me to bear family resemblances to this model. Doubtless, my references could be extended in many directions.
| Variable | Definition |
|---|---|
| a01 | The person-years of labor hired per unit output (e.g., ton steel) in the first sector. |
| a02 | The person-years of labor hired per unit output (e.g., bushel corn) in the second sector. |
| a11 | The capital goods (measured in tons) used up per unit output in the first (steel-producing) sector. |
| a01 | The capital goods (measured in tons) used up per unit output in the second (corn-producing) sector. |
| p1 | The price of a unit output in the first sector. |
| p2 | The price of a unit output in the second sector. |
| r | The rate of profits. |
| s | The savings rate out of profits. |
| w | The wage, that is, the price of hiring a person-year. |
| X1 | The number of units (ton steel) produced in the first sector. |
| X2 | The number of units produced (bushels corn) in the second sector. |
| g | The rate of growth. |
2.0 Two Departments
This model considers a capitalist economy with no government and no foreign trade. The outputs of this economy are grouped into two great departments. In the first department, capitalists direct workers to produce means of production (also known as capital goods) with the means of production in that department. In the second department, the workers are directed to produce means of consumption (also known as consumption goods) with the means of production in that department.
For ease of exposition, I make certain additional simplifying assumptions. The workers consume all of their wages. Only the capitalists save, and they save only in the case of expanded reproduction. All capital is circulating capital. That is, there is no fixed capital, such as long-lived machinery. In other words, all capital goods are totally used up each year in producing the yearly output. No technological innovations are introduced.
I think introducing technological innovations and fixed capital makes the possibility of smooth reproduction more incredible. A government can be introduced as a third department, or perhaps by dividing government output among the two departments shown. Foreign trade introduces the possibility of correcting imbalances in domestic demand from outside the domestic economy. But then one could recast the model as of the world economy.
3.0 Prices
A necessary condition for smooth reproduction of a competitive capitalist economy is that the same rate of profit be made in all departments. Otherwise, some capitalists are finding that the expectations on which investments were made are being unfulfilled. They would want to have contracted some departments and expanded others. I also impose the condition that spot prices remain stationary. The following equations express these conditions:
(a11 p1)(1 + r) + a01 w = p1
(a12 p1)(1 + r) + a02 w = p2I suppose one could put time indices on the prices in the above equations, thereby defining a dynamic system for prices. Suppose distribution and the ratios of physical quantity flows remain unchanged year after year. Then the steady-state prices expressed in the above equations (without time indices) would be a limit point of the dynamic process so defined. It is this caveat, I think, that allows me to ignore that constant prices are, perhaps, not a necessary condition for smooth reproduction.
| Department | Capital | Wages | Profits |
| Capital Goods | a11 X1 p1 | a01 X1 w | a11 X1 p1 r |
| Consumption Commodities | a12 X2 p1 | a02 X2 w | a12 X2 p1 r |
4.0 In Balance
4.1 Simple Reproduction
The economy is in simple reproduction when it is replicated on the same scale year after year. A necessary condition for an economy in simple reproduction is that the production of capital goods each year be equal to the capital goods used up each year. In the model shown here, the value of the capital goods used up each year must equal the value of the output of the first department:
a11 X1 p1 + a12 X2 p1 = (a11 X1 p1)(1 + r) + a01 X1 wThe above equation can be simplified:
a12 X2 p1 = a01 X1 w + a11 X1 p1 rThe above is easily summarized in words. It states that the value of capital goods demanded from the second department matches the demand for consumption goods from the first department. In a sense, this equation is a generalization of Keynes' idea of effective demand. The condition that all workers looking for a job are able to find one at the going wage is a separate condition, not stated here. This model generalizes Keynes' theory, in some sense, to the long-run.
An alternate method of deriving the last equation is available. Start from the equation of the value of total demand for consumption goods and the value of the output of the department producing consumption goods. This condition, when simplified, yields the same equation.
4.2 Expanded Reproduction
The economy experiences expanded reproduction when it consistently expands each year. In this case, the demand for capital goods from the second department includes the savings of the capitalists receiving profits from that department. Likewise, the demand for consumption goods from the first department excludes the savings of the capitalists in that department. Observing these qualifications, it is easy to mathematically express the condition that the demand for capital goods from the second department match the demand for consumption goods from the first department:
a12 X2 p1 + s a12 X2 p1 r = a01 X1 w + (1 - s) a11 X1 p1 rOr:
a12 X2 p1(1 + s r) = a01 X1 w + (1 - s) a11 X1 p1 rFocus on the left-hand side of the above equation. Is it apparent that the rate of growth of the value of the capital goods in the second department is the product of the capitalists' saving propensity and the rate of profit? In expanded reproduction, under these simplifying assumptions, both departments and their components all grow at the same rate. In other words, the rate of profit along a warranted growth path is the quotient of the rate of growth and the saving propensity of the capitalists.
r = g/sThis is the famous Cambridge equation typically arising in a Post Keynesian theory of distribution, especially in, say, Luigi Pasinetti's version.
5.0 Conclusion
In the model, capitalists independently decide on what department to enter, and how much to produce in that department. A collective result of those decisions is the total output of each department. For those decisions to be validated, the value of consumer goods demanded by workers and capitalists in the department producing capital goods must match the value of capital goods demanded by the capitalists in the department producing consumption goods.
The model is silent on how such an equality can come about. Supply and demand seems like an inadequate answer to me.
References
- Richard M. Goodwin (1949). "The Multiplier as Matrix", Economic Journal, V. 59, N. 236 (Dec.): 537-555
- M. Kalecki (1969). Theory of Economic Dynamics: An Essay on Cyclical and Long-Run Changes in Capitalist Economy, Second Edition, Augustus M. Kelly
- Rosa Luxemburg (1951). The Accumulation of Capital (Trans. by Agnes Schwarzschild), Yale University Press
- Karl Marx (1956). Capital, Volume 2, Progress Publishers
- Luigi L. Pasinetti (1981). Structural Change and Economic Growth: A Theoretical Essay on the Dynamics of the Wealth of Nations, Cambridge University Press
- Luigi L. Pasinetti (1993). Structural Economic Dynamics: A Theory of the Economic Consequences of Human Learning, Cambridge University Press
- Joan Robinson (1962). Essays in the Theory of Economic Growth, Macmillan
- Paul A. Samuelson (1957). "Wages and Interest: A Modern Dissection of Marxian Economic Models", American Economic Review, V. 47 (Dec.): 884-912
- Shigeto Tsuru (1942). "On Reproduction Schemes", Appendix A in Paul Sweezy's The Theory of Capitalist Development, Monthly Review Press [This reference I haven't read]
Sunday, February 01, 2009
Leijonhufvud's Corridor
The ideas of a number of economists have been cited in popular accounts of the current economic crisis.
Some have been calling this a "Minsky moment" and have been exploring the Post Keynesian economist Hyman Minsky. In building on this trend, Michael Perelman sees connections to Marx's views on fictious capital. I have pointed out Hugh Townshend basically describing (in 1937) the housing crisis as part of his account of
Another popular interpretation points to erroneous Austrian Business Cycle Theory. For some reason - probably political, although I'm willing to accept ignorance also - very few who go on about the ABCT bring up the Austrian concept of the "secondary depression". Yet this epicycle would seem to be precisely relevant as the crisis becomes a general downturn, instead of being more restricted to financial institutions.
Another interesting idea, although one I am not sure I agree with, is Axel Leijonhufvud's corridor. Leijonhufvud became famous for arguing "Keynesians" had misinterpretated Keynes. As I understand it, his interpretation is closely related to that offered by Robert Clower in his 1965 paper, "The Keynesian Counter-Revolution: A Theoretical Appraisal". Clower argues that households, in making consumption and savings decisions, are constrained by realized income, not by the income they would receive at a point of full-employment equilibrium. Clower and Leijonhufvud end up with thinking of Keynes as describing a disequilibrium. I think Keynes claimed to have described an equilibrium that could be consistent with the presence of involuntary unemployment.
I think Leijonhufvud developed his notion of the corridor later. The corridor constitutes time paths near enough to full employment. If the economy falls outside the corridor, agents no longer have well-developed norms and expectations about what happens that are mutually consistent and likely to quickly lead the economy back to full employment.
Some have been calling this a "Minsky moment" and have been exploring the Post Keynesian economist Hyman Minsky. In building on this trend, Michael Perelman sees connections to Marx's views on fictious capital. I have pointed out Hugh Townshend basically describing (in 1937) the housing crisis as part of his account of
Another popular interpretation points to erroneous Austrian Business Cycle Theory. For some reason - probably political, although I'm willing to accept ignorance also - very few who go on about the ABCT bring up the Austrian concept of the "secondary depression". Yet this epicycle would seem to be precisely relevant as the crisis becomes a general downturn, instead of being more restricted to financial institutions.
Another interesting idea, although one I am not sure I agree with, is Axel Leijonhufvud's corridor. Leijonhufvud became famous for arguing "Keynesians" had misinterpretated Keynes. As I understand it, his interpretation is closely related to that offered by Robert Clower in his 1965 paper, "The Keynesian Counter-Revolution: A Theoretical Appraisal". Clower argues that households, in making consumption and savings decisions, are constrained by realized income, not by the income they would receive at a point of full-employment equilibrium. Clower and Leijonhufvud end up with thinking of Keynes as describing a disequilibrium. I think Keynes claimed to have described an equilibrium that could be consistent with the presence of involuntary unemployment.
I think Leijonhufvud developed his notion of the corridor later. The corridor constitutes time paths near enough to full employment. If the economy falls outside the corridor, agents no longer have well-developed norms and expectations about what happens that are mutually consistent and likely to quickly lead the economy back to full employment.