Irving Fisher's theory of capital
and investment was introduced in his In his theory, Fisher 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 = ¦
(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 Letting r be the rate of interest then total costs of investing an amount
I
so that the optimal investment decision will be where:
In Fisher's language, we can define ¦ ¢ -1 as the "
In Figure 1, we have drawn Fisher's investment frontier Y So far, we have said nothing about the ownership structure of the firm or how this theory can be grafted into a wider macroeconomic theory. There might be potential modifications in this regard. There are two main questions that arise here. Firstly, if we suppose that firms are owned by entrepreneurs, might not the investment decision of the firm be affected by the owner's desired consumption-savings decision? Secondly, what exactly is the relationship between the firm's investment decision, its financing decision and wider financial markets? As Jack Hirshleifer (1958,
1970) later noted, we can answer these questions by reworking Fisher's full theory of
investment into a "two-stage" budgeting process. Specifically, Hirshleifer noted
that If we consider an entrepreneurial firm, i.e. a firm owned by a person,
then we must endow the firm with a utility function U(.). Now, if we have the entrepreneur
maximize utility with respect solely to the intertemporal investment frontier, we achieve
a solution akin to point G* in Figure 2. In this case, then, it seems that the optimal
investment decision of the firm is affected by owner's preferences. However, by realizing
that firms have, in fact, a two-stage budgeting process by which firms
The two central results of this two-stage budgeting has become known as
the
We can see the first by noting that The second part of the separation theorem effectively claims that the
firm's financing needs are independent of the production decision. To see why more
clearly, we can restate this in terms of the Neoclassical
theory of
but by plugging in the details for these terms:
and rearranging:
Now, each agent invested E
i.e. total investment equals total savings. Note the condition that for total investment to be equal to total savings,
then the demand for loanable funds must equal the supply for loanable funds and this is [Note: our expression is slightly different from Fisher's original 1930 formulation as, instead of netting out as we have done, Fisher had the supply for loanable funds defined as savings plus disinvestment and demand for loanable funds defined as investment plus dissaving; nonetheless, the equilibrating interest rate is unchanged by whichever definition we choose.] |

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