Consider the two-period endowment economy we discussed in class. In this economy, a household lives for two periods and can save s. The return on saving is the real interest rate,r. Income is exogenous and given as y and y'. Households have utility overconsumption,c, in each period by U(c)=In(c)+B In(c') where future utility is discounted with rate B. Households choose consumption in both periods,c and c'. 1-Write down the current period and future period budget constraints. Derive the lifetime budget constraints. 2-What is the slope of the lifetime budget constraint? What are the intercepts? What is the significance of the endowment point? 3-Write down the expression for the consumer's optimization problem. What is the tangency condition? Provide an intuitive explanation for this condition. 4-Solve for c,c', and s. Given that B=1 and r=0, how would you modify the answers for c,c; and s? Explain.
Consider the two-period endowment economy we discussed in class. In this economy, a household lives for two periods and can save s. The return on saving is the real interest rate,r. Income is exogenous and given as y and y'. Households have utility overconsumption,c, in each period by U(c)=In(c)+B In(c') where future utility is discounted with rate B. Households choose consumption in both periods,c and c'.
1-Write down the current period and future period budget constraints. Derive the lifetime budget constraints.
2-What is the slope of the lifetime budget constraint? What are the intercepts? What is the significance of the endowment point?
3-Write down the expression for the consumer's optimization problem. What is the tangency condition? Provide an intuitive explanation for this condition.
4-Solve for c,c', and s. Given that B=1 and r=0, how would you modify the answers for c,c; and s? Explain.
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