![05 Suppose that Mingsongs utility function for inter-temporal co is: U(CO,C1) In(C0) n(C1)/(1 +p)] where CO is his current period consumption, CI is his future period consumption and ρ is his subject rate of time preference. Let ρ be 5%. If Mingsong is endowed with $100 this period and $100 in the next period. And suppose the risk-free interest rate is 10%. What is Mingsongs optimal consumption path (i.e., the optimal level of current and future consumption) if he can only allocate wealth through lending and borrowing?](http://img.homeworklib.com/questions/e98c5c30-7053-11ea-ae50-25f84dfd70ff.png?x-oss-process=image/resize,w_560)
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05 Suppose that Mingsong's utility function for inter-temporal co is: U(CO,C1) In(C0) n(C1)/(1 +p)] where CO...
Question 8: Suppose that Bibi's utility function for inter-temporal consumption is: U(C0.cl)-In(C0) + [0.4 * İn(C1)]...
Question 8: Suppose that Bibi's utility function for inter-temporal consumption is: U(C0.cl)-In(C0) + [0.4 * İn(C1)] where Cois his current period consumption, C, is his future period consumption. Bibi is endowed with mo 90,000 in this period (to) and mo -$500,000 in the next period (t1). And suppose there a perfect capital market in which Bibi can borrow and lend at 25% (risk-free). i. What is Bibi's optimal consumption bundle (i.e., the optimal level of current and future consumption) if...
1. Harvey Habit's utility function is U (C1, C2) = min {c1, c2}, where ci is...
1. Harvey Habit's utility function is U (C1, C2) = min {c1, c2}, where ci is his consumption of bread in period 1 and ca is his consumption of bread in period 2. The price of bread is $1 per loaf in period 1. The interest rate is 21%. Harvey earns $2,000 in period 1 and he will earn $1,100 in period 2. (a) Write Harvey's budget constraint in terms of future value. (b) How much bread does Harvey consume...
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 =...
1. Suppose you are given the utility function: VC U = vc + 1.10 CI уг...
1. Suppose you are given the utility function: VC U = vc + 1.10 CI уг and the budget constraint: c+ =yt 1+r 1+r where y = 5, y' = 10, and the interest rate r = 0.10. Now suppose that y=5 again, and there is only one consumer in the entire economy. If we add in government expenditures and taxation, the consumer's budget constraint is now: c+ y' = y + -t- +r 1+r 1+r If current and future...
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...
1. Harvey Habit's utility function is U (C1, C2) = min {c1, c2}, where cı is his consumption of bread in period 1 and c...
1. Harvey Habit's utility function is U (C1, C2) = min {c1, c2}, where cı is his consumption of bread in period 1 and c2 is his consumption of bread in period 2. The price of bread is $1 per loaf in period 1. The interest rate is 21%. Harvey earns $2,000 in period 1 and he will earn $1,100 in period 2. (a) Write Harvey's budget constraint in terms of future value. (b) How much bread does Harvey consume...
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 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
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?
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...
Question 8: Suppose that Bibi's utility function for inter-temporal consumption is: U(C0.cl)-In(C0) + [0.4 * İn(C1)] where Cois his current period consumption, C, is his future period consumption. Bibi is endowed with mo 90,000 in this period (to) and mo -$500,000 in the next period (t1). And suppose there a perfect capital market in which Bibi can borrow and lend at 25% (risk-free). i. What is Bibi's optimal consumption bundle (i.e., the optimal level of current and future consumption) if...
1. Harvey Habit's utility function is U (C1, C2) = min {c1, c2}, where ci is his consumption of bread in period 1 and ca is his consumption of bread in period 2. The price of bread is $1 per loaf in period 1. The interest rate is 21%. Harvey earns $2,000 in period 1 and he will earn $1,100 in period 2. (a) Write Harvey's budget constraint in terms of future value. (b) How much bread does Harvey consume...
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 =...
1. Suppose you are given the utility function: VC U = vc + 1.10 CI уг and the budget constraint: c+ =yt 1+r 1+r where y = 5, y' = 10, and the interest rate r = 0.10. Now suppose that y=5 again, and there is only one consumer in the entire economy. If we add in government expenditures and taxation, the consumer's budget constraint is now: c+ y' = y + -t- +r 1+r 1+r If current and future...
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...
1. Harvey Habit's utility function is U (C1, C2) = min {c1, c2}, where cı is his consumption of bread in period 1 and c2 is his consumption of bread in period 2. The price of bread is $1 per loaf in period 1. The interest rate is 21%. Harvey earns $2,000 in period 1 and he will earn $1,100 in period 2. (a) Write Harvey's budget constraint in terms of future value. (b) How much bread does Harvey consume...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
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?
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...
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