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Fisher's theory

# Fisher's theory - Irving Fisher's Theory of Investment...

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Irving Fisher's Theory of Investment Irving Fisher's theory of capital and investment was introduced in his Nature of Capital and Income (1906) and Rate of Interest (1907), although it has its clearest and most famous exposition in his Theory of Interest (1930). We shall be mostly concerned with what he called his "second approximation to the theory of interest" (Fisher, 1930: Chs.6- 8), which sets the investment decision of the firm as an intertemporal problem. In his theory, Fisher assumed (note carefully) that all capital was circulating capital. In other words, all capital is used up in the production process, thus a "stock" of capital K did not exist. Rather, all "capital" is, in fact, investment. Friedrich Hayek (1941) would later take him to task on this assumption - in particular, questioning how Fisher could reconcile his theory of investment with the Clarkian theory of production which underlies the factor market equilibrium. Given that Fisher's theory output is related not to capital but rather to investment, then we can posit a production function of the form Y = ƒ (N, I). Now, Fisher imposed the condition that investment in any time period yields output only in the next period. For simplicity, let us assume a world with only two time periods, t = 1, 2. In this case, investment in period 1 yields output in period 2 so that Y 2 = ƒ (N, I 1 ) where I 1 is period 1 investment and Y 2 is period 2 output. Holding labor N constant (and thus striking it out of the system), then the investment frontier can be drawn as the concave function where ƒ > 0 and ƒ < 0. The mirror image of this is shown in Figure 1 as the frontier Y 2 = ƒ (I 1 ). Everything below this frontier is technically feasible and everything above it is infeasible. Letting r be the rate of interest then total costs of investing an amount I 1 is (1+r)I 1 . Similarly, total revenues are derived from the sale of output pY 2 or, normalizing p = 1, simply Y 2 . Thus, profits from investment are defined as π = Y 2 - (1+r)I 1 and the firm faces the constraint Y 2 = ƒ (I 1 ) (we have omitted N now). Thus, the firm's profit- maximization problem can be written as: max π = ƒ (I 1 ) - (1+r)I 1 so that the optimal investment decision will be where: ƒ = (1+r) In Fisher's language, we can define ƒ -1 as the "

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