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16.2 A consumption theory based on intertemporal optimization Consumer preferences The starting point for a micro-based theory of consumption is a specication of consumer preferences. Consider a consumer who plans for a certain nite time horizon. We will divide this time interval into two periods, which may be thought of as \"the present' {the current period I) and 'the future' (period 2). The limitation to only Mo periods isjust a simplification; one can show that all our qualitative conclusions will continue to hold in a setting with many periods. In each period I (where t= l, 2), the consumer derives utility :40) from consumption. However, because the consumer is 'impatient', he or she prefers a unit of utility today to a unit of utility tomorrow. When evaluated at the beginning of period 1, the consumer's iierime utility U is therefore given by: \"(C2) U=H(C.)+ l+' u'>0, a'0. (2) The consumer's impatience is captured by the parameter dwhich is referred to as lite rate aftt'me preference. The positive rate of time preference means that if C I = C2, a given additional amount of consumption today is valued more highly than a similar extra amount of consumption tomorrow- On the other hand, as long as dis not infinitely high, the consumer is not indifferent about the lture, and he or she will then have to decide how to allocate his or her consumption optimally over time. The assumptions u' > 0 and u\" 0 as Well as a situation where S