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Suppose Sansa lives for two periods. Her preferences are represented as follows: u(c1, c2) = (1+0.8VC2...
2. Consider a consumer with preferences over current and future consumption given by U(C1, C2) = (c1)1/2 (c2)1/2 where...
2. Consider a consumer with preferences over current and future consumption given by U(C1, C2) = (c1)1/2 (c2)1/2 where cı denotes the amount consumed in period 1 and c2 the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is mı = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p1 = P2 = 1 and let r denote the interest rate. (a)...
Consider a consumer with preferences over current and future consumption given by U (c1, c2) =...
Consider a consumer with preferences over current and future consumption given by U (c1, c2) = c1c2 where c1 denotes the amount consumed in period 1 and c2 the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is m1 = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p1 = p2 = 1 and let r denote the interest rate. 1. Find...
2. Consider a consumer with preferences over current and future consumption given by U (C1, C2)...
2. Consider a consumer with preferences over current and future consumption given by U (C1, C2) = (c1)1/(c2)1/2 where c1 denotes the amount consumed in period 1 and ch the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is m1 = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that P1 = P2 = 1 and let r denote the interest rate. (a)...
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...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:5)1-y U(C1,C2) = - 1- ITBC: C1 + = yı + 1+1 a) Determine the marginal rate of substitution for this utility function and derive the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption...
Consider a household living for two periods
Consider a household living for two periods, t = 1, 2. Let ct and yt denote consumption and income in period t. s denotes saving in period 1, r is the real interest rate and β the weight the household places on future utility. The following must be true about the household’s consumption in the two periods:c1 = y1 − sandc2 = (1 + r)s + y2a. Derive the household’s intertemporal budget constraint.b. Assume that the preferences of the household can be represented by a log utility...
Problem 1 (2.5 marks). Suppose there are only two time periods, today (period 1) and tomorrow...
Problem 1 (2.5 marks). Suppose there are only two time periods, today (period 1) and tomorrow (period 2), and only one consumption good, let's call it food. Assume that food is a perfectly divisible good. Let ci and c2 denote the amount of food consumed today and tomorrow, respectively. Note that here we use subscripts to denote time periods. The price of food today is equal to Pi = P, but as the rate of inflation is > 0, the...
Consider a consumer that lives only for two periods. He works in period 1 (and gets...
Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and retires in period 2 (and gets income Y2 < Y1). This consumer has the usual preferences over time: u(C1) + βu(C2) Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse of? Could the consumer be better...
2. Consider a consumer with preferences over current and future consumption given by U(C1, C2) = (c1)1/2 (c2)1/2 where cı denotes the amount consumed in period 1 and c2 the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is mı = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p1 = P2 = 1 and let r denote the interest rate. (a)...
2. Consider a consumer with preferences over current and future consumption given by U (C1, C2) = (c1)1/(c2)1/2 where c1 denotes the amount consumed in period 1 and ch the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is m1 = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that P1 = P2 = 1 and let r denote the interest rate. (a)...
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...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:5)1-y U(C1,C2) = - 1- ITBC: C1 + = yı + 1+1 a) Determine the marginal rate of substitution for this utility function and derive the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption...
Problem 1 (2.5 marks). Suppose there are only two time periods, today (period 1) and tomorrow (period 2), and only one consumption good, let's call it food. Assume that food is a perfectly divisible good. Let ci and c2 denote the amount of food consumed today and tomorrow, respectively. Note that here we use subscripts to denote time periods. The price of food today is equal to Pi = P, but as the rate of inflation is > 0, the...
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