Word Count : 945

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In the overlapping generations (OLG) model, individuals live for two periods: the first period, $t$, when they work and earn wage income, and the second period, $t+1$, when they retire and live off their savings and interest income. Their intertemporal consumption decisions are guided by the trade-off between consuming today and saving for future consumption. The consumer chooses consumption in period $t$ ($C_t$) and in period $t+1$ ($C_{t+1}$) to maximize lifetime utility, which is typically represented by a utility function $U(C_t, C_{t+1})$, subject to a budget constraint that incorporates wages and returns on savings. The budget constraint can be expressed as: $$ C_t + \frac{C_{t+1}}{1+r} = w_t $$ where $w_t$ is the wage income in period $t$ and $r$ is the interest rate. Savings, $S_t$, are the portion of wage income not consumed in period $t$, given by: $$ S_t = w_t - C_t $$ These savings grow at the interest rate $r$ to finance consumption in the second period: $$ C_{t+1} = (1+r) S_t $$ An increase in the interest rate affects consumption in period $t$ through two main channels: the substitution effect and the income effect. The substitution effect arises because a higher interest rate increases the return to saving. Saving becomes relatively more attractive than current consumption because each unit of consumption foregone today allows for more consumption in the future. Mathematically, a higher $r$ raises the marginal benefit of saving, leading the ____ __________ ____ _____ __________ ______ _______.
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