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2. Consumption-Savings Decision: The Household's decision problem is: 1- 1- max - C1,C2,8 1-7."1-7 s.t. Ci+s=(<)yi...
The consumer's problem is max u(C1, C2) s.t. C1 +5 < y1 C2 < y2 +...
The consumer's problem is max u(C1, C2) s.t. C1 +5 < y1 C2 < y2 + (1+r)s C1 > 0, c220 Characterize the solution
can anyone help me with this question? 2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consum...
can
anyone help me with this question?
2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consumption in perio You can assume that the price of consumption does not change between periods 1 and 2. The consumer has $100 at the beginning of period 1 and uses this money to fund consumption across the two periods (i.e. the consumer does not gain additional income...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow is p2. John gets an income of m, today and m2 tomorrow. (a) John also faces the interest rate, r. Write out John's intertemporal budget constraint in present value and future forms. (4 marks) (b) It turns out that John earns an income of £15000 today and...
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...
1. Consumer's Consumption Decision (Chapter 2 in Fabozi, Neave and Zhou - Fi- nancial Economics) Suppose...
1. Consumer's Consumption Decision (Chapter 2 in Fabozi, Neave and Zhou - Fi- nancial Economics) Suppose Amy's utility function for a two-period consumption problem is U(C1, C2) = C1026, (1) her income in period 1 yı = 2000; y2 = 1296 in period 2; and market borrowing and lending rate is 8%. Determine the optimal consumption expenditures in period 1 and 2 for Amy. Is Amy a borrower or lender?
Consider the following 2-period model U(C1,C2) = min{4C1,5C2} Ci + S = Y1-T C2 = Y2...
Consider the following 2-period model U(C1,C2) = min{4C1,5C2} Ci + S = Y1-T C2 = Y2 - T2 + (1+r)S Where C: first period consumption C2: second period consumption S: first period saving Y] = 20 : first period income Ti = 5 : first period lump-sum tax Y2 = 50 : second period income T2 = 10 : second period lump-sum tax r= 0.05 : real interest rate Find the optimal saving, S*
Question 1: Two-period model where Ci and C2 are perfect substitutes 1. Draw the budget constraint...
Question 1: Two-period model where Ci and C2 are perfect substitutes 1. Draw the budget constraint with Yi- 100, Y2 60, and 0.2 2. Draw the indifference curves for the preference that is represented by the lifetime utility function G +SC, where β-1. Do it for various levels of lifetime utility, such as 100, 150. and 200. 3. Using the budget constraint and the indifference curves, determine the optimal values of Ci and C2. Does the household have positive 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...
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...
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0)...
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0) Cl 1. Plot the household's indifference curve for U-80 for values of C andlless than 20 (i.e. find the curve containing all combinations of C and ( such that U(C, 0) 80) The household has a time endowment of h=16 hours per day. The wage rate per hour is w 1.25. The household's labour income is therefore wNs, where N-h-l-16- l is the time...
The consumer's problem is max u(C1, C2) s.t. C1 +5 < y1 C2 < y2 + (1+r)s C1 > 0, c220 Characterize the solution
can
anyone help me with this question?
2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consumption in perio You can assume that the price of consumption does not change between periods 1 and 2. The consumer has $100 at the beginning of period 1 and uses this money to fund consumption across the two periods (i.e. the consumer does not gain additional income...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow is p2. John gets an income of m, today and m2 tomorrow. (a) John also faces the interest rate, r. Write out John's intertemporal budget constraint in present value and future forms. (4 marks) (b) It turns out that John earns an income of £15000 today and...
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...
1. Consumer's Consumption Decision (Chapter 2 in Fabozi, Neave and Zhou - Fi- nancial Economics) Suppose Amy's utility function for a two-period consumption problem is U(C1, C2) = C1026, (1) her income in period 1 yı = 2000; y2 = 1296 in period 2; and market borrowing and lending rate is 8%. Determine the optimal consumption expenditures in period 1 and 2 for Amy. Is Amy a borrower or lender?
Consider the following 2-period model U(C1,C2) = min{4C1,5C2} Ci + S = Y1-T C2 = Y2 - T2 + (1+r)S Where C: first period consumption C2: second period consumption S: first period saving Y] = 20 : first period income Ti = 5 : first period lump-sum tax Y2 = 50 : second period income T2 = 10 : second period lump-sum tax r= 0.05 : real interest rate Find the optimal saving, S*
Question 1: Two-period model where Ci and C2 are perfect substitutes 1. Draw the budget constraint with Yi- 100, Y2 60, and 0.2 2. Draw the indifference curves for the preference that is represented by the lifetime utility function G +SC, where β-1. Do it for various levels of lifetime utility, such as 100, 150. and 200. 3. Using the budget constraint and the indifference curves, determine the optimal values of Ci and C2. Does the household have positive consumption...
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0) Cl 1. Plot the household's indifference curve for U-80 for values of C andlless than 20 (i.e. find the curve containing all combinations of C and ( such that U(C, 0) 80) The household has a time endowment of h=16 hours per day. The wage rate per hour is w 1.25. The household's labour income is therefore wNs, where N-h-l-16- l is the time...
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