2)
Figure 1: The Indifference Diagram of Economics An individual consumes a quantity KD of good 1, and K) of good 2. The dotted indifference curves connect consumption bundles to which he is indifferent. By buying or selling, the consumer moves left or right along the solid budget line. Utility is maximized at the point where the two lines have equal slope, or in other words, at the point where MRS p = MRSz.
2 Application to time preference
Suppose that, in figure 1, good 1 refers to food that is consumed today, and good 2 to food that is consumed 7 time units later. With this interpretation, the figure describes preferences regarding different paths of consumption over time, or in other words, time preference. In a recent paper [15], I developed an evolutionary theory of time preference using the methods outlined above. That paper simplified the problem by assuming that changes in consumption affect fitness solely via their effect on survival. Here, I extend that analysis to incorporate effects on fertility as well.
The analysis proceeds by deriving an expression for the MRS in fitness, and setting this equal to well-known expressions for the MRS in preferences and in exchange. I begin with a series of definitions.
2.1 Definitions
The MRS in preferences between immediate and delayed consumption is defined by
di?)
U constant
where the derivative is taken along a line of constant utility U, i.e. an indifference curve. The MRS in preferences is often measured by 9, the marginal rate of time preference (MRTP), which defined
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