p > Dis the rate of time preference. 0 0. (a) Write down the agent's maximization problem and solve for the optimal intertemporal consumption ratio (i.=e the consumption this period divided by consumption next period]. If R p? Then, consider the case where R = p and calculate the average consumption 6 (cbar) as a function of 3? (yr-bar), where )7 [ybar] is defined below. Permanent Shock: Suppose there's a new technology will yield a permanent income increase for all agents, starting in period n. 50, for the first n periods, your average income is "y. After period n, your average income increases permanently to y\" = [1 + A] 3? > 5!, A > 0. {b} Modify Equation {1} to fit this permanent shock scenario. Also, using your result in part [a], now calculate the new average consumption as a function of "y, l). and n. Is this new average consumption greater or less than the average consumption in part [a]? How does this new average consumption relate to n (increasing or decreasing with n]? Temporag Shock: Now, suppose that there's a temporary shock to the income at time t = 0 {ya} so that now your y0 = (1 + s] y, s > 0 a very small number. tter period 0, then your average income is still 5?. (cl Modify Equation (1] to fit this temporary shock scenario. Also, similar to [b], now calculate the new average consumption as a function of y and 5. Is this new average consumption greater or less than the average consumption in part (a)? How does this new average consumption relate to 5 (increasing or decreasing with s)