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1. Suppose you are given the utility function: VC U = vc + 1.10 CI уг...
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 =...
Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + _u(Ct+1) that satisfies...
Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + _u(Ct+1) that satisfies all the standard assumptions listed in the book. The period t and t + 1 budget constraints are Ct + St = Yt Ct+1 + St+1 = Yt+1 + (1 + r)St (a) What is the optimal value of St+1? Impose this optimal value and derive the lifetime budget constraint. (b) Derive the Euler equation. Explain the economic intuition of the equa- tion. (c)...
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...
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...
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c)...
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c) + Bln(c'), where B is a parameter between 0 and 1, and assume that there is always an interior solution to the household's problem. 12. What is the marginal rate of substitution of current consumption for future con- sumption MRS given this utility function? How does it change with c and c'? 13. Solve the household's optimization problem with the lifetime budget constraint. That...
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...
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. A consumer's preferences over a and y are given by the utility function u(x,y) -...
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
Question 1. Suppose Kala's utility function is a function of consumption, with U = 150 cm...
Question 1. Suppose Kala's utility function is a function of consumption, with U = 150 cm Her income is 6. What is the expected value of a gamble where she wins 4 with probability 75% and loses 4 with probability 25%? Would Kala take this gamble? Question 2. What is the present value of $100 in two years, if the yearly interest rate is 7%? Question 3. Laura is deciding how much to consume in periods o, 1, and 2....
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 =...
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...
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...
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c) + Bln(c'), where B is a parameter between 0 and 1, and assume that there is always an interior solution to the household's problem. 12. What is the marginal rate of substitution of current consumption for future con- sumption MRS given this utility function? How does it change with c and c'? 13. Solve the household's optimization problem with the lifetime budget constraint. That...
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...
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. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
Question 1. Suppose Kala's utility function is a function of consumption, with U = 150 cm Her income is 6. What is the expected value of a gamble where she wins 4 with probability 75% and loses 4 with probability 25%? Would Kala take this gamble? Question 2. What is the present value of $100 in two years, if the yearly interest rate is 7%? Question 3. Laura is deciding how much to consume in periods o, 1, and 2....
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