Reswitching

In economics , reswitching is understood to mean that under certain circumstances companies first switch to a different production technology when wages rise, and then "paradoxically" again when wages rise further original technology "switch back". The discussion about this phenomenon was also part of the so-called capital controversy .

The theoretical possibility of reswitching was discovered by Piero Sraffa and used as a serious criticism of the basic assumptions of neoclassical theory . Based on a neoclassical production function, such as a Cobb-Douglas function , also known as a one-good parabolais criticized, reswitching cannot be represented. There, rising wages mean that work is always being replaced by capital in one direction, i.e. that other production techniques are chosen that are less and less labor-intensive, but more and more "capital" -intensive. The fact that a reswitching can theoretically occur is accordingly seen by critics as a refutation of the neoclassical theory.

The growth model

The national economy should consist of two departments I and II, with I producing capital goods and II producing consumer goods for workers. The production coefficients indicate how much of the various inputs is necessary to produce a unit of a certain output. In this simple case there are only two outputs , the amount of capital goods and , the amount of consumer goods. ${\ displaystyle x_ {1}}$ ${\ displaystyle x_ {2}}$

The production coefficients:

${\ displaystyle a_ {11}}$ : Number of capital goods to manufacture one capital good.
${\ displaystyle a_ {21}}$ : Number of hours worked to produce an investment good.
${\ displaystyle a_ {12}}$ : Number of capital goods to manufacture a consumer good.
${\ displaystyle a_ {22}}$ : Number of hours worked to manufacture a consumer good.

The workers receive a certain wage at the wage rate 1 per unit of work, which is expressed in consumer goods.

${\ displaystyle l \ cdot a_ {21}}$ : Number of consumer goods that are necessary to produce an investment good.
${\ displaystyle l \ cdot a_ {22}}$ : Number of consumer goods that are necessary to produce a consumer good.

Schematically, the economy can be represented as follows:

	Input ${\ displaystyle x_ {1}}$	Input ${\ displaystyle x_ {2}}$	output
Department I.	${\ displaystyle a_ {11} \ cdot x_ {1}}$	${\ displaystyle a_ {21} \ cdot l \ cdot x_ {1}}$	${\ displaystyle x_ {1}}$
Department II	${\ displaystyle a_ {12} \ cdot x_ {2}}$	${\ displaystyle a_ {22} \ cdot l \ cdot x_ {2}}$	${\ displaystyle x_ {2}}$

The output quantities must not be smaller than the input quantities. If the economy as a whole and the two departments I and II are to grow equally at the same rate r, then the following equations can be set up between input quantities and output quantities for the two goods of the economy and : ${\ displaystyle x_ {1}}$ ${\ displaystyle x_ {2}}$

${\ displaystyle (a_ {11} \ cdot x_ {1} + a_ {12} \ cdot x_ {2}) \ cdot (1 + r) = x_ {1}}$
${\ displaystyle (a_ {21} \ cdot l \ cdot x_ {1} + a_ {22} \ cdot l \ cdot x_ {2}) \ cdot (1 + r) = x_ {2}}$

So you have two equations with and . Both equations can be expressed as the product of and one expression each that depends on r and l. If both equations are to apply, there is first the trivial solution: ${\ displaystyle x_ {1}}$ ${\ displaystyle x_ {2}}$ ${\ displaystyle x_ {1}}$ ${\ displaystyle x_ {2}}$

${\ displaystyle x_ {1} = x_ {2} = 0}$ .

In order to get (infinitely) more solutions for and not just this trivial solution, the two expressions in r and l must be equated with each other. One then obtains an equation which is quadratic in (1 + r). For given production coefficients, one then obtains a relationship between r and l, where r is greater the smaller l is. ${\ displaystyle x_ {1}}$ ${\ displaystyle x_ {2}}$

The "reswitching"

In the neoclassical theory , rising wages lead companies to switch to technologies that use less work and more capital, they switch to more capital-intensive technologies. This process is only one-way. In the neoclassical world, there is no reason why, if wages continue to rise, a technology should be chosen that was abandoned because wages were too high.

In the Sraffa model, on the other hand, the case is conceivable that when wages rise, production technology is abandoned first, and then suddenly selected again when wages continue to rise. In the case of very high wages, there is a switch back to a technology ("reswitching") that was previously abandoned when wages rose when they were, however, lower. This is explained in detail as follows:

At Sraffa, one technique is defined by the size of the production coefficient. For example, a technique # 1 is given with:

${\ displaystyle a_ {11} = 0 {,} 3}$ : Number of capital goods to manufacture one capital good.
${\ displaystyle a_ {21} = 0 {,} 2}$ : Number of hours worked to produce an investment good.
${\ displaystyle a_ {12} = 0 {,} 1}$ : Number of capital goods to manufacture a consumer good.
${\ displaystyle a_ {22} = 0 {,} 3}$ : Number of hours worked to manufacture a consumer good.

A technique No. 2 is given with:

${\ displaystyle a_ {11} = 0 {,} 2}$ : Number of capital goods to manufacture one capital good.
${\ displaystyle a_ {21} = 0 {,} 2}$ : Number of hours worked to produce an investment good.
${\ displaystyle a_ {12} = 0 {,} 4}$ : Number of capital goods to manufacture a consumer good.
${\ displaystyle a_ {22} = 0 {,} 2}$ : Number of hours worked to manufacture a consumer good.

Illustration of the profit rate-wage rate curves of two different techniques defined by Sraffa

For the two techniques one obtains two curves of the rate of profit r as a function of the wage rate l, which are shown in the figure . For very low wage rates 1, the economy will opt for technology No. 2 because it yields the higher rate of profit. When the wage rate rises, however, a point is finally reached where technology no. 1 is "switched", that is, because 1 now yields a higher profit rate than 2. If the wage rate continues to rise, it is finally "switched back" and technology No. 2 is selected again.

This reswitching, which means that when the wage rate rises, a technology suddenly becomes profitable that has already been abandoned because of the rising wage rate, is unthinkable in a neoclassical model with an aggregated (e.g. Cobb-Douglas) production function.

Reswitching as an aggregation problem

Reswitching can be viewed as a special case of the so-called aggregation problem. According to this, microeconomic properties are not necessarily retained at the macro level after aggregation (see also Sonnenschein-Mantel-Debreu theorem ). From this point of view, the critical assumption of the neoclassical growth model is that there is only one homogeneous capital good. Analogous aggregation problems can arise with the factor labor, which is also assumed to be homogeneous.

literature

Sraffa, Piero: Goods production by means of goods. Afterwords by Bertram Schefold (1976 [first published in 1960]), Suhrkamp-Verlag Frankfurt / Main

Web links

Bertram Schefold : Reswitching as a Cause of Instability of Intertemporal Equilibrium. (PDF; 504 kB) Metroeconomica, (2005) 56: 4, pp. 438-476.

Individual evidence

^ Andreu Mas-Colell, "Capital Theory Paradoxes: Anything Goes", in "Joan Robinson and Modern Economic Theory" (ed. By GR Feiwel), New York University Press, 1989.

[1] Andreu Mas-Colell, "Capital Theory Paradoxes: Anything Goes", in "Joan Robinson and Modern Economic Theory" (ed. By GR Feiwel), New York University Press, 1989.