Extensions of Arrow’s “Learning by Doing”
D. Levhari
Chapter 12 in Readings in the Theory of Growth, 1971, pp 150-164 from Palgrave Macmillan
Abstract:
Abstract In a recent paper1 Arrow discusses the behavior of an economic model in which technological change is related to cumulated gross investment, or to the serial number of the machines used in production. Arrow uses a model of fixed proportions, and for a machine of specified vintage and serial number there is a fixed labor requirement for production. In the following paper we shall show that most of Arrow’s results can be extended to any homogeneous production function of the first degree with the type of technological change discussed by him. The production function shows ordinary convexity. Here we shall distinguish two types of production function according to the properties of the marginal product of labor with zero labor input. In type I the marginal product of labor with zero input is. finite and it is impossible to produce without labor (as an example we have the CES production function with elasticity of substitution smaller than 1). In type II the marginal product of labor with zero labor input is infinite, or it is possible to produce without labor input (as an example we have CES with elasticity of substitution greater than or equal to 1; if it is 1, we have of course the known Cobb-Douglas case). As we shall see, in type I, as in the fixed proportion case, there is discarding of capital. Capital is used up to the time when it is scrapped. We shall ignore physical wear and tear and assume that the economic life of machinery is shorter than its physical life. There is no difficulty, and none of the results would change, if we include an exponential force of mortality. In type II, where marginal productivity is infinite with zero labor input, there is of course no complete discarding.
Keywords: Production Function; Technological Change; Wage Rate; Time Preference; Marginal Product (search for similar items in EconPapers)
Date: 1971
References: Add references at CitEc
Citations:
There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-1-349-15430-2_12
Ordering information: This item can be ordered from
http://www.palgrave.com/9781349154302
DOI: 10.1007/978-1-349-15430-2_12
Access Statistics for this chapter
More chapters in Palgrave Macmillan Books from Palgrave Macmillan
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().