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Consider the standard two-periods consumption model where consumers have the utility func- tion u(c)-S Furthermore, let...
A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(c1,c2) =...
A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(c1,c2) = ccm, where Ct = consumption in period t and a + b = 1. Her income in period one is I1 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now that...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2)...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2) = ccm, where Ct = consumption in period t and a + b = 1. Her income in period one is 1 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2)...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2) = ccm where ct = consumption in period t and a + b = 1. Her income in period one is 11 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now...
1. Consider the following two period consumption savings problem. A consumer cares about consumption (c and...
1. Consider the following two period consumption savings problem. A consumer cares about consumption (c and future consumption c according to Assume that U(c) is given by for some constant y. In the present the consumer chooses how much to consume and how much to save out of her income y>0 This decision is made in the knowledge that in the future she will be retired, have no income, and thus future consumption will be entirely out of savings: c)a,...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and...
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and the budget constraint: C - 1+r 1+r where y = 100, y 120, and the interest rate r = 0.05. a) What is the optimal value of current consumption c*? b) What is the optimal value of future consumption, c*? c) Suppose the interest rate r -0.10. What is the new value of optimal current consumption c*? Suppose the new interest rate r =...
Please give a detailed solution, thank you! 4. Two consumers (call them A and B) have utility functions over consumption...
Please give a detailed
solution, thank you!
4. Two consumers (call them A and B) have utility functions over consumption in period 1 and consumption in period 2 given by U (1,C2)n(c)ln(c2) In period 1, consumer A receives income of y 2, the endowments are reversed, consumer A gets y= 120 and consumer B gets y = 80 80 and consumer B receives y? = 120. In period (so they just a. First assume consumers are not allowed to save...
Starting with the dynamic consumption model seen in class, consider the case where the consumer is...
Starting with the dynamic consumption model seen in class, consider the case where the consumer is not facing lump-sum taxes, but proportional taxes. The tax is a linear tax on consumption. In first period, the consumer pays a tax t:c, in the second period T'.d. Note that t and t' need not be identical. The government wants to collect a total amount of revenue, which has a present value of R=G+ Now the government reduces t and increases t' in...
Problem 1. (Consumption smoothing) A consumer who lives for four periods have the following path of...
Problem 1. (Consumption smoothing) A consumer who lives for four periods have the following path of income y 60 0 60 0 Assume the consumer has log utility, a ct) 0 so that the real rate of return is 1 Inq, and is infinitely patient, β-1. Also aKsune the interest rate is (a) What is the optimal consumption profile of the consumer? (b) What is the value of assets, a, of the consumer at the beginning of period 47 (c)...
A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(c1,c2) = ccm, where Ct = consumption in period t and a + b = 1. Her income in period one is I1 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now that...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2) = ccm, where Ct = consumption in period t and a + b = 1. Her income in period one is 1 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2) = ccm where ct = consumption in period t and a + b = 1. Her income in period one is 11 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now...
1. Consider the following two period consumption savings problem. A consumer cares about consumption (c and future consumption c according to Assume that U(c) is given by for some constant y. In the present the consumer chooses how much to consume and how much to save out of her income y>0 This decision is made in the knowledge that in the future she will be retired, have no income, and thus future consumption will be entirely out of savings: c)a,...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and the budget constraint: C - 1+r 1+r where y = 100, y 120, and the interest rate r = 0.05. a) What is the optimal value of current consumption c*? b) What is the optimal value of future consumption, c*? c) Suppose the interest rate r -0.10. What is the new value of optimal current consumption c*? Suppose the new interest rate r =...
Please give a detailed
solution, thank you!
4. Two consumers (call them A and B) have utility functions over consumption in period 1 and consumption in period 2 given by U (1,C2)n(c)ln(c2) In period 1, consumer A receives income of y 2, the endowments are reversed, consumer A gets y= 120 and consumer B gets y = 80 80 and consumer B receives y? = 120. In period (so they just a. First assume consumers are not allowed to save...
Starting with the dynamic consumption model seen in class, consider the case where the consumer is not facing lump-sum taxes, but proportional taxes. The tax is a linear tax on consumption. In first period, the consumer pays a tax t:c, in the second period T'.d. Note that t and t' need not be identical. The government wants to collect a total amount of revenue, which has a present value of R=G+ Now the government reduces t and increases t' in...
Problem 1. (Consumption smoothing) A consumer who lives for four periods have the following path of income y 60 0 60 0 Assume the consumer has log utility, a ct) 0 so that the real rate of return is 1 Inq, and is infinitely patient, β-1. Also aKsune the interest rate is (a) What is the optimal consumption profile of the consumer? (b) What is the value of assets, a, of the consumer at the beginning of period 47 (c)...
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