# Essays in the theory of endogenous technical change

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In his 1932 book, The Theory of Wages, J. R. Hicks introduced two concepts of endogenous technical change. The first of these is induced technical change which occurs as the firm's response to an increase in the relative price of a factor of production. The basic premise of this view is that the firm will direct its technical change efforts toward saving on the factor which has become relatively more expensive The second concept is what Hicks termed autonomous technical change. This refers to all endogenous technical change that is not in response to changes in relative factor prices This dissertation considers several theoretical models of endogenous technical change and the inducement properties possessed by each. These models build upon and extend the works of Kennedy, Samuelson, Ahmad, Binswager and Kamien and Schwartz which were reviewed in Chapter 2 Chapters 3, 4, and 5 present the theoretical models of endogenous technical change. These models possess two common features. The first is that the firm's production technology is represented by a neo-classical factor augmenting production function. The second common feature is that the augmentation parameters can be changed through directed research efforts applied according to technological production functions In Chapter 3 the firm is assumed to maximize the reduction in costs subject to the technology production functions and an R & D budget constraint. The equilibrium conditions are derived and it is shown that these conditions correspond to those in the Kennedy and Samuelson approaches. In addition it is shown that the Kennedy-Samuelson Innovation Possibilities Frontier (IPF) is derivable from this framework and exists solely because of the R & D budget constraint. The induced technical change hypothesis is found to hold as long as the elasticity of substitution between inputs is not equal to one. In addition the system will converge to a state of Hick's neutral technical change for all values of the elasticity of substitution less than two and for some values greater than two. This is in direct conflict with the usual results which require that the elasticity of substitution be less than one Chapter 4 considers the case of a profit maximizing firm whose current decisions with respect to capital and R & D expenditures affect profits one period in the future. The equilibrium conditions are derived and compared to the result of the previous model. The effects of changes in the discount rate, equipment costs, and the wage rate on the level of investment in capital and R & D and on the level of employment are determined The inducement properties of the model are found to be obscured by profit-maximizing effects so an alternative approach treating the firm as a cost minimizing entity is used. The results show that Hicksian induced technical change is only one possible response to a change in relative factor prices Chapter 5 considers a firm in a certain world with an infinite horizon. The firm is assumed to maximize the discounted present value of net revenues subject ot the technology production functions and a given initial level of technology. The equilibrium conditions require the equality of the discounted marginal revenues and marginal costs of technical change. The conditions for the non-trivial steady state solution are derived and found to be rather strong so an alternative steady state is defined in terms of the ratios of the purchased factor inputs and the augmentation parameters. This modified steady state requires Hick's neutral technical change and is stable under the assumptions of the model for all values of the elasticity of substitution less than or equal to two and possibly stable for some values greater than two. Finally the inducement properties of the model are considered and it is shown that the Hicksian induced technical change hypothesis can not be ruled out