Consider a by-now-standard production function for an individual firm: Y=BKL (5.1) In this equation, there are...

  

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Consider a by-now-standard production function for an individual firm: Y=BKL (5.1) In this equation, there are constant returns to capital and labour. Hence, if B is accumulated endogenously, production is characterized by increasing returns. Suppose that individual fi rms take the level of B as given. However, assume that in reality, the accumulation of capital generates new knowledge about production in the economy as a whole. In particular, suppose that B=AKI-a (5.2) where A is some constant. That is, an accidental by-product of the accumulation of capital by firms in the economy is the improvement of the technology that fi rms use to produce. An individual firm does not recognize this effect when it accumulates capital because it is small relative to the economy. This is the sense in which technological progress is external to the firm. Firms do not accumulate capital because they know it improves technology; they accumulate capital because it is a useful input into production. Capital is paid its private marginal product "Y/K. However, it just so happens that the accumulation of capital provides an extraordinarily useful and unexpected benefit to the rest of the economy: it results in new knowledge. Combining equations (5.1) and (5.2), we obtain YAKL¹- (5.3) Consider the above AK model in which we do not normalize the size of the labour force to one. (a) Using the production function in equation (5.3) and the standard capital accumulation equation, show that the growth rate of output depends on L. (b) What happens if L is growing at some constant rate n? (c) Specify the form of the externality in equation (5.2) differently to avoid this implication. (d) Does labour affect production? Consider a by-now-standard production function for an individual firm: Y=BKL (5.1) In this equation, there are constant returns to capital and labour. Hence, if B is accumulated endogenously, production is characterized by increasing returns. Suppose that individual fi rms take the level of B as given. However, assume that in reality, the accumulation of capital generates new knowledge about production in the economy as a whole. In particular, suppose that B=AKI-a (5.2) where A is some constant. That is, an accidental by-product of the accumulation of capital by firms in the economy is the improvement of the technology that fi rms use to produce. An individual firm does not recognize this effect when it accumulates capital because it is small relative to the economy. This is the sense in which technological progress is external to the firm. Firms do not accumulate capital because they know it improves technology; they accumulate capital because it is a useful input into production. Capital is paid its private marginal product "Y/K. However, it just so happens that the accumulation of capital provides an extraordinarily useful and unexpected benefit to the rest of the economy: it results in new knowledge. Combining equations (5.1) and (5.2), we obtain YAKL¹- (5.3) Consider the above AK model in which we do not normalize the size of the labour force to one. (a) Using the production function in equation (5.3) and the standard capital accumulation equation, show that the growth rate of output depends on L. (b) What happens if L is growing at some constant rate n? (c) Specify the form of the externality in equation (5.2) differently to avoid this implication. (d) Does labour affect production?

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aGrowth rate of output AKLY Since L is not normalized to one the growth rate of output will depend o... View the full answer