4. The Fisher Diagram and the Neoclassical Theory of Interest and Capital

The Fisher Diagram and the Neoclassical Theory of Interest and Capital: After Fisher’s recovery from tuberculosis, he wrote developed the neoclassical theory of interest and capital in The Nature of Capital and Income (1906) and The Rate of Interest (1907) (later combined as The Theory of Interest, 1930), emphasizing the time pattern of expected income, the concept of present discounted value, and the role of the interest rate in equilibrating investment and saving, balancing impatience to spend with opportunity to earn interest, as shown in the “Fisher diagram” (the two-period consumption-smoothing diagram on Fisher [The Rate of Interest, Macmillan, New York, 1907, p. 409]). The Fisher diagram’s depiction of the terms of trade between consumption in two periods inspired fundamental diagrams in risk analysis (terms of trade between consumption in two states of the world) and international trade theory, while his identification of the present discounted value of expected lifetime income as the relevant budget constraint for consumption decisions (assuming perfect credit markets) led to the Friedman permanent-income and Modigliani-Ando-Brumberg life-cycle theories of consumption. Ironically, given the neoclassical emphasis of Fisher’s work on interest and capital, his 1907 demonstration of the possibility of multiple solutions for Boehm-Bawerk’s average period of production was a precursor of capital paradoxes that emerged fifty or sixty years later in the Cambridge capital theory controversies.