Word Count : 987

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An increase in the interest rate in an overlapping generations (OLG) framework where individuals work when young (period t) and live off interest income when old (period t+1) changes the intertemporal trade–off facing each agent and thereby affects consumption in period t through two opposing channels: the substitution effect and the income effect. Which channel dominates depends on preferences (in particular the intertemporal elasticity of substitution), the initial position of the individual (net saver or borrower), and whether the analysis is partial–equilibrium (r exogenous) or general–equilibrium (r determined by capital market conditions that also change wages). To set up the standard individual problem, let a representative young agent in period t receive wage income $w_t$. She chooses consumption when young $c_t$ and saving $s$ to maximize lifetime utility $$ U = u(c_t) + \beta u(c_{t+1}), $$ subject to the budget constraints $$ c_t + s = w_t,\qquad c_{t+1} = (1+r)\,s, $$ where $r$ is the interest rate between t and t+1 and $\beta$ is the subjective discount factor. Eliminating $s$ yields $c_{t+1}=(1+r)(w_t - c_t)$. The first–order (Euler) condition for an interior optimum is $$ u'(c_t) = \beta(1+r)\,u'(c_{t+1}). $$ This Euler equation summarizes how a marginal change in the interest rate influences the marginal utilities of consumption in the two periods and therefore the chosen $c_t$. Partial equilibrium intuition (r exogenous). An increase in $r$ raises the return to saving. Two effects operate on current consumption $c_t$: 1. Substitution effect: Higher $r$ makes future consumption relatively cheaper ______ ________ ______ _______ ________ _____ _________ ___ ______ _________ _________ ___.
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