Technical progress function

The technical progress function was developed by the economist Nicholas Kaldor. Technical progress is measured by the growth rate of labor productivity. This growth rate is determined as a function of the growth rate of capital intensity. This technological progress is no longer exogenously given, as in the neoclassical growth models keynesiansichen or up into the 70s, but is determined endogenously as a function of the rate of change in capital intensity. So it is with the technical progress function is a precursor of the later endogenous growth theories.

The model can be described as a case of A -Good - parabola, as it is assumed that a produced good, which is used either in a certain amount per job ( capital intensity ) or used for the equipment of additional jobs or just as a consumer. Qualitative changes, it's that new and different types are used by means of production or that new and other consumer industries, must be represented by a quantity increase of one good by just more products are produced per worker, more goods per worker employed is ( capital intensity ) or be consumed.

Thus, some simple relationships can be represented. From the individual company's perspective is not any increase in labor productivity profitable, it must be paid for with an increase in capital intensity yes. For simplicity (neglecting the wage costs) can be found that an increase in capital intensity by a certain percentage is profitable if and when they. To an increase in labor productivity by a higher percentage, thus leads to a higher- proportional increase If both percentages are equal, then pays for the introduction of technical progress or not just as one wants to take it. The assumption that labor productivity, capital intensity grow at the same rate, is a common equilibrium assumption of growth models.

Kaldor made ​​about the form of technical progress function of assumptions ( see figure). Low growth rates of capital intensity lead to disproportionately higher rates of growth of labor productivity, higher growth rates of capital intensity but only to a disproportionately higher rates of growth of labor productivity. In between, ie a growth rate of capital productivity must occur ( in the figure 1% growth), which leads to exactly the same high growth rate of labor productivity.

Stability

This point is stable according to Kaldor, because as long as the growth rate of capital productivity leads to an even higher growth rate in labor productivity, the company will try in the next period, even more to increase the capital intensity. Performs a growth rate of capital intensity only to a below-average growth rate of labor productivity, this is not profitable and the company will not expand in the next period capital intensity so strong.

Thus, once the technical progress function alleged by Kaldor course, is then the equilibrium state that capital intensity and labor productivity grow with the same growth rate, as is the case also in the Harrod - Domar model or in the Solow model. Since these technical progress function includes a balance, it is called a " well-behaved ", it behaves well.

After all, however, the adjustment process would be represented mathematically in an imbalance model, in order to decide, above the equilibrium point is actually stable. This would be no easy task, however.

Would arbitrarily large rate of increase in capital intensity lead to even greater growth rates of labor productivity, would be an incentive for companies to permanently the entire corporate profit not result in additional jobs, but in the expansion of the capital stock per job to invest. If, however predominates such intense growth, it will ever work invested more and more, not in new jobs ( extensive growth ), then it comes to contradictions at the macroeconomic level, what the background on physical or material level to the law of the tendency of the rate of profit by Karl Marx forms.

Mathematical properties

The technical progress function is not integrable in general, that is, it can not specify to their " appropriate" production function. An exception is the Cobb -Douglas production function with Harrod - neutral, ie labor-saving technical progress or arbeitsvermehrendem with constant returns to scale.

• Y: production volume
• K: Use of capital
• A: Use of tools
• C: constant
• T: time
• A: parameter between zero and one.
• M: rate of technical progress

The Cobb -Douglas production function with labor-saving technological progress, which is growing at the rate m:

. By A by dividing the formulation results in per capita variables. Labour productivity is a function of capital intensity:

So if Y / A = y (labor productivity ) and K / A = k ( capital intensity )

The transition to a function, which is formulated in the growth rates of labor productivity and capital intensity is, by the logarithmic derivative with respect to time t:

Logarithms:

After the time t are derived:

On the left is as dependent variable the growth rate of labor productivity, the right of the equal sign appears as an explanatory variable the growth rate of capital intensity. Here are

And the derivatives with respect to time, also the growth rate is defined as: and Thus, there is the growth rate of labor productivity as a linear function of the growth rate of capital intensity with the intercept m ( 1-a) and the slope a, since a under the assumption of constant returns to scale Cobb - Douglas function has a value between zero and one assumes this curve intersects the 45 ° line, so that there is an equilibrium value, which is that the growth rate of labor productivity is equal to the growth rate of capital intensity:

References