PreTerences on a typicai ayem are such that. U (Ci, ct+1) = In ct + In ct+1 where 2 (0; 1) is a discount factor. Anything that is not consumed in period t, is saved, st (loaned out to the government). One unit saved in government bonds in period t yields 1 + rt units in t + 1 where rt is the interest rate on government bonds (return on savings). For simplicity assume that the price of consumption goods is one in both periods. Finally, suppose the government plays the same role as in the model we covered in class. In particular, the government consumes in both periods (government spending (Gt; Gt+1)) and levies lump sum taxes in both periods as well (Tt; Tt+1). As in the model covered class, the government incurs a budget decit in period t, so it has to borrow, bt units at the market interest rate. A. Write down the individuals problem of lifetime utility maximization. Be sure to derive the intertemporal budget constraint for the problem. Briey, explain the intertemporal budget constraint. (3 points) B. Write down the consumers Lagrangian. Derive the rst order conditions for all choice variables and provide economic interpretation for the choice of ct and ct+1.(3 points) C. Solve for the amount of consumption over time. (4 points) D. Derive the governments intertemporal budget constraint and provide economic interpretation. (5 points) E. i. For a given interest rate, show how a change in the discount factor, afects, ct, ct+1, and st. Explain your result intuitively. (5 points) 1 ii. How does the interest rate on government bonds adjust to clear the credit market? Explain your answer. (5 points) iii. Solve for the marginal propensity to consume and save from a change in income in period t. How does a change in agect MP C and MP S? Explain intuitively.(5 points) Problem 2 (20 points): Does the degree of income inequality in the economy afect the e cacy of Oscal policy in combatting a recession? For example is the government more or less successful in promoting economic activity if income is highly unequally distributed? Explain your answer. Problem #1: Intertemporal Consumption Choice (30 points) Consider a two period model similar to the one we covered in class, where agents are born at the beginning of the rst period. The total population size is one. In addition, each agent receives an exogenous vector of endowments (et; et+1) during her lifetime. Agents value consumption in both periods of their life. Denote ct and ct+1 to be the amount of goods consumed in periods t and t + 1, respectively. The preferences of a typical agent are such that: U (ct; ct+1) = In ct + In ct+1 where 2 (0; 1) is a discount factor. Anything that is not consumed in period t, is saved, st (loaned out to the government). One unit saved in government bonds in period t yields 1 + rt units in t + 1 where rt is the interest rate on government bonds (return on savings). For simplicity assume that the price of consumption goods is one in both periods. Finally, suppose the government plays the same role as in the model we covered in class. In particular, the government consumes in both periods (government spending (Gt; Gt+1) and levies lump sum taxes in both periods as well (Tt; Tt+1). As in the model covered class, the government incurs a budget decit in period t, so it has to borrow, bt units at the market interest rate. A. Write down the individuals problem of lifetime utility maximization. Be sure to derive the intertemporal budget constraint for the problem. Briey, explain the intertemporal budget constraint. (3 points) B. Write down the consumeris Lagrangian. Derive the rst order conditions for all choice variables and provide economic interpretation for the choice of ct and ct+1.(3 points) C. Solve for the amount of consumption over time. (4 points) D. Derive the governments intertemporal budget constraint and provide economic interpretation. (5 points) E. i. For a given interest rate, show how a change in the discount factor, afects, ct, ct+1, and st. Explain your result intuitively. (5 points) 1 ii. How does the interest rate on government bonds adjust to clear the credit market? Explain your answer. (5 points) iii. Solve for the marginal propensity to PreTerences on a typicai ayem are such that. U (Ci, ct+1) = In ct + In ct+1 where 2 (0; 1) is a discount factor. Anything that is not consumed in period t, is saved, st (loaned out to the government). One unit saved in government bonds in period t yields 1 + rt units in t + 1 where rt is the interest rate on government bonds (return on savings). For simplicity assume that the price of consumption goods is one in both periods. Finally, suppose the government plays the same role as in the model we covered in class. In particular, the government consumes in both periods (government spending (Gt; Gt+1)) and levies lump sum taxes in both periods as well (Tt; Tt+1). As in the model covered class, the government incurs a budget decit in period t, so it has to borrow, bt units at the market interest rate. A. Write down the individuals problem of lifetime utility maximization. Be sure to derive the intertemporal budget constraint for the problem. Briey, explain the intertemporal budget constraint. (3 points) B. Write down the consumers Lagrangian. Derive the rst order conditions for all choice variables and provide economic interpretation for the choice of ct and ct+1.(3 points) C. Solve for the amount of consumption over time. (4 points) D. Derive the governments intertemporal budget constraint and provide economic interpretation. (5 points) E. i. For a given interest rate, show how a change in the discount factor, afects, ct, ct+1, and st. Explain your result intuitively. (5 points) 1 ii. How does the interest rate on government bonds adjust to clear the credit market? Explain your answer. (5 points) iii. Solve for the marginal propensity to consume and save from a change in income in period t. How does a change in agect MP C and MP S? Explain intuitively.(5 points) Problem 2 (20 points): Does the degree of income inequality in the economy afect the e cacy of Oscal policy in combatting a recession? For example is the government more or less successful in promoting economic activity if income is highly unequally distributed? Explain your answer. Problem #1: Intertemporal Consumption Choice (30 points) Consider a two period model similar to the one we covered in class, where agents are born at the beginning of the rst period. The total population size is one. In addition, each agent receives an exogenous vector of endowments (et; et+1) during her lifetime. Agents value consumption in both periods of their life. Denote ct and ct+1 to be the amount of goods consumed in periods t and t + 1, respectively. The preferences of a typical agent are such that: U (ct; ct+1) = In ct + In ct+1 where 2 (0; 1) is a discount factor. Anything that is not consumed in period t, is saved, st (loaned out to the government). One unit saved in government bonds in period t yields 1 + rt units in t + 1 where rt is the interest rate on government bonds (return on savings). For simplicity assume that the price of consumption goods is one in both periods. Finally, suppose the government plays the same role as in the model we covered in class. In particular, the government consumes in both periods (government spending (Gt; Gt+1) and levies lump sum taxes in both periods as well (Tt; Tt+1). As in the model covered class, the government incurs a budget decit in period t, so it has to borrow, bt units at the market interest rate. A. Write down the individuals problem of lifetime utility maximization. Be sure to derive the intertemporal budget constraint for the problem. Briey, explain the intertemporal budget constraint. (3 points) B. Write down the consumeris Lagrangian. Derive the rst order conditions for all choice variables and provide economic interpretation for the choice of ct and ct+1.(3 points) C. Solve for the amount of consumption over time. (4 points) D. Derive the governments intertemporal budget constraint and provide economic interpretation. (5 points) E. i. For a given interest rate, show how a change in the discount factor, afects, ct, ct+1, and st. Explain your result intuitively. (5 points) 1 ii. How does the interest rate on government bonds adjust to clear the credit market? Explain your answer. (5 points) iii. Solve for the marginal propensity to