Assume the representative consumer lives in two periods and his preferences can be described by the...
Assume the representative consumer lives in two periods and his preferences can be described
by the utility function
U(c; c') = c1/3 + B(c')1/3;
where c is the current consumption, c' is next period consumption, and B = 0.95. Let's assume
that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an
income y = 100 in the current period and y' = 110 in the next period. The government wants
to spend G = 30 in the current period and G' = 35 in the future period. The consumer pays a
lump sum tax t in period 0 and t' in period 0.
1. Write down the consumer's intertemporal budget constraint.
2. If the government sets t = 50, what will be the consumer's estimate of the value of t'?
3. Is it optimal for the consumer to consume his disposable income in each period?
4. Solve the consumer's problem by finding the optimal allocations c* and c'*.
5. Is the consumer a lender or a borrower?
6. Assume the consumer has to choose between two different jobs. Job 1 offers him the in-
come bundle (y1; y'1) = (100, 110) while job 2 offers (y2; y'2) = (110, 100). Which job will you
recommend to the consumer?
Homework Answers
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Assume the representative consumer lives in two periods and his
preferences can be described
by the...
Assume the representative consumer lives in two periods and his preferences can be described by U(c,...
Assume the representative consumer lives in two periods and his preferences can be described by U(c, c' ) = c ^(1/2) + β(c') ^(1/2) , where c is the current consumption, c' is next period consumption, and β = 0.95. Let’s assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y = 100 in the current period and y' = 110 in the next period. The government wants to...
Problem 1.Consider a consumer who lives for two periods. His income in period 1 equals 2000...
Problem 1.Consider a consumer who lives for two periods. His income in period 1 equals 2000 EUR and his income in period 2 equals 2500, Real interest rate equals 10% a) Use the appropriate diagram to show the consumer's intertemporal budget constraint and his consumption choice, assuming that he is a net lender in period 1 b) How will his consumption decision be affected if the interest rate increases to 20% Answr using the graph from part (a)? Will he...
3. A consumer lives for two periods. His income in period 1 is Y, and his...
3. A consumer lives for two periods. His income in period 1 is Y, and his income in period 2 is Y.,. The consumer is free to lend and borrow at zero interest rate (r=0 and R=1+r=1). Y, = Y, = 10. (a) What is the price of consumption in period 1 in terms of consumption in period 2? (How many units of period 2 consumption must the consumer give up to get an additional unit of consumption in period...
Question 1 (3 Points): Assume a consumer has current-period income y = 120, future-period income y'...
Question 1 (3 Points): Assume a consumer has current-period income y = 120, future-period income y' = 140, current and future taxes t = 20 and t' = 10, respectively, and faces a market real interest rate of r = 0.08, or 8% per period. The consumer has the following preferences over current and future consumption: U(c, c') = min(4c, 3c'). a) (1 points) Determine the consumer's lifetime wealth. b) (2 points) Determine what the consumer's optimal current-period and future-period...
Consider the two-period model from Chapter 9, and assume there is one representative consumer with utility...
Consider the two-period model from Chapter 9, and assume there is one representative consumer with utility function uc,d) = Iníc) + In(d), so the time discount factor is 3 = 1. There is also a government that levies lump-sum taxes in the current and future periods. The government has expenditures of G = 580 in the current period and G' = 630 in the future period. (a) Suppose the consumer has current and future income (w.y') = (3500, 6510), and...
A consumer's income in the current period is y=100, and income in the future period is...
A consumer's income in the current period is y=100, and income in the future period is y' =120. He or she pays lump-sum taxes t =20 in the current period and t' =10 in the future period. The real interest rate is 0.1, or 10%, per period. Also assume that this consumer likes to consume the same amount of consumption each period, that is, c = c. Questions: a) [5 points] Calculate the lifetime wealth for this consumer. b) [4...
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...
Consider a consumer who lives for two periods. The consumer gets utility from consumption in each...
Consider a consumer who lives for two periods. The consumer gets utility from consumption in each period. The consumer also gets an endowment of time in each period, L hours, which the consumer can use to work or consume as leisure . The consumer gets NO utility from leisure, however. There is no borrowing or lending. (a)(10%) Let w1 and w2 be the wage rates per hour in periods 1 and periods 2 respect- ively. In period 1, the consumer...
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...
Problem 1.Consider a consumer who lives for two periods. His income in period 1 equals 2000 EUR and his income in period 2 equals 2500, Real interest rate equals 10% a) Use the appropriate diagram to show the consumer's intertemporal budget constraint and his consumption choice, assuming that he is a net lender in period 1 b) How will his consumption decision be affected if the interest rate increases to 20% Answr using the graph from part (a)? Will he...
3. A consumer lives for two periods. His income in period 1 is Y, and his income in period 2 is Y.,. The consumer is free to lend and borrow at zero interest rate (r=0 and R=1+r=1). Y, = Y, = 10. (a) What is the price of consumption in period 1 in terms of consumption in period 2? (How many units of period 2 consumption must the consumer give up to get an additional unit of consumption in period...
Question 1 (3 Points): Assume a consumer has current-period income y = 120, future-period income y' = 140, current and future taxes t = 20 and t' = 10, respectively, and faces a market real interest rate of r = 0.08, or 8% per period. The consumer has the following preferences over current and future consumption: U(c, c') = min(4c, 3c'). a) (1 points) Determine the consumer's lifetime wealth. b) (2 points) Determine what the consumer's optimal current-period and future-period...
Consider the two-period model from Chapter 9, and assume there is one representative consumer with utility function uc,d) = Iníc) + In(d), so the time discount factor is 3 = 1. There is also a government that levies lump-sum taxes in the current and future periods. The government has expenditures of G = 580 in the current period and G' = 630 in the future period. (a) Suppose the consumer has current and future income (w.y') = (3500, 6510), and...
A consumer's income in the current period is y=100, and income in the future period is y' =120. He or she pays lump-sum taxes t =20 in the current period and t' =10 in the future period. The real interest rate is 0.1, or 10%, per period. Also assume that this consumer likes to consume the same amount of consumption each period, that is, c = c. Questions: a) [5 points] Calculate the lifetime wealth for this consumer. b) [4...
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...
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