Chapter 55: Intertemporal Utility Maximization – the Fisher Diagram
Thomas M. Humphrey Francis Y. Edgeworth invented indifference curves in his 1881 Mathematical Psychics. Similarly, Vilfredo Pareto pioneered the use of transformation, or production possibility curves in his 1906 Manual of Political Economy. But Irving Fisher in his 1907 The Rate of Interest was the first to combine indifference curves and a production possibility curve together with a budget line in a single diagram and use it to illustrate an individual’s optimum intertemporal consumption choice, or optimum investment decision, as well as his utility gains from borrowing and lending in the credit market. Fisher’s demonstration, largely reproduced in his 1930 The Theory of Interest, is definitive: modern analysts have hardly improved upon it. Fisher’s two-period diagram first appears on page 409 of The Rate of Interest (see Figure 55.1). Two commodities, labeled present and future consumption, are measured on the horizontal and vertical axes respectively. The production possibility curve ZPW shows alternative combinations of the two goods that the individual can produce given his resources and investment technology. The curve depicts his opportunity, moving, say, from point W to point P, to transform units of present consumption into a larger number of units of future consumption by saving (that is, not consuming) today, and investing the proceeds into productive capital projects yielding positive net returns. The curve forms the efficient outer boundary or frontier of feasible investment possibilities. Inefficient ones are represented by the swarm of dots beneath the curve. The curve’s slope-minus-unity at any point measures investment’s marginal rate...
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