Suppose that the utility function of the consumer is U(c,c’)=ln(c) + b ln( c’ ) ....
Suppose that the utility function of the consumer is U(c,c’)=ln(c) + b ln( c’ ) . Analyze the solution of the model to show show that optimal consumption increases over time when
Question options:
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b (1+r)=1 |
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b (1+r)<1 |
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b (1+r)<0 |
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b (1+r)>1 |
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b > 1 |
Homework Answers
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Suppose that the utility function of the consumer is
U(c,c’)=ln(c) + b ln( c’ ) ....
1. If we=1,000 represents a two-period consumer's lifetime wealth and r=0.05 denotes the real rate of...
1. If we=1,000 represents a two-period consumer's lifetime wealth and r=0.05 denotes the real rate of interest, the slope of the consumer's budget line is equal to Question 12 options: a. -1.05 b. 50.05 c. -0.95 d. -0.00005 e. 50 2. Suppose that the utility function of the consumer is U(c,c’)=ln(c) + b ln( c’ ) . Analyze the solution of the model to show show that optimal consumption increases over time when Question 3 options: a. b > 1...
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...
Suppose the representative household has the following utility function: U (C; l) = ln C +...
Suppose the representative household has the following utility function: U (C; l) = ln C + 0:5 ln l where C is consumption and l is leisure. The householdís time constraint is l+N=1 where Ns is the representative householdís labour supply. Further assume that the production function is Cobb-Douglas zK0:5 (N)0:5 where z = 1 and K = 1: 2.1 Assuming that the government spending is G = 0; use the Social Plannerís problem to solve for Pareto optimal numerical...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
Suppose that utility is given by the following function: U= 10* ln(c) How large is marginal...
Suppose that utility is given by the following function: U= 10* ln(c) How large is marginal utility when real consumption is c=5?
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 =...
The weekly utility function of a consumer is: U = 2AB where A and B are...
The weekly utility function of a consumer is: U = 2AB where A and B are two goods in the consumer’s consumption bundle. Based on this utility function the marginal utility of good A is: MUA = 2B and the marginal utility of good B is: MUB = 2A, where A and B represent the quantities of good A and good B, respectively. The price of good A is $5 whereas the price good B is $10. a. Write the...
Problem 1 Suppose a single parent has the following utility function: U-20 in C+10 In L....
Problem 1 Suppose a single parent has the following utility function: U-20 in C+10 In L. The single parent is eligible for the TANF program which has the following characteristics: Benefit guarantee $1000, benefit reduction rate 50%. If the single parent works, her wage Is $20 an hour. She can spend her time (2000 hours) working or having leisure. What is the budget constraint of the single parent who is eligible for the TANF? C=1000-50%(2000-L)*20 O C=(2000-L)*20-1000 C=(2000-L)*20+1000-50%"(2000-L) 20 O...
3. Suppose a consumer's utility function is given by U(A, B) In(A)+In(B). Suppose the price of...
3. Suppose a consumer's utility function is given by U(A, B) In(A)+In(B). Suppose the price of each apple (A) is €6, and the price of a loaf of bread (B) Is €6 and the consumer's income is €120 ) Write down the Lagrangian for this problem and solve for the optimal consumption of apples and (ii) Report and interpret your solution for the Lagrange multiplier. bread. i) Evaluate the marginal utility of bread and the marginal utility of apples at...
please in part b graph it with identifying everything. 2. Consumer Theory. Ahn's utility function for...
please in part b graph it with identifying everything.
2. Consumer Theory. Ahn's utility function for goods X (pizzas) and Y (cola) is represented as U(X, Y) = 2ln(X)+ln(Y). The prices of X and Y are $1 and $1, respectively. Ahn's income is $12. 1) Calculate Ahn's optimal consumption bundle (X*, Y*). (X*, Y*)= 2) Suppose there is an increase in the price of X. Illustrate the net effect, income effect, and substitution effect on Ahn's optimal consumption choice.
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...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
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 =...
Problem 1 Suppose a single parent has the following utility function: U-20 in C+10 In L. The single parent is eligible for the TANF program which has the following characteristics: Benefit guarantee $1000, benefit reduction rate 50%. If the single parent works, her wage Is $20 an hour. She can spend her time (2000 hours) working or having leisure. What is the budget constraint of the single parent who is eligible for the TANF? C=1000-50%(2000-L)*20 O C=(2000-L)*20-1000 C=(2000-L)*20+1000-50%"(2000-L) 20 O...
3. Suppose a consumer's utility function is given by U(A, B) In(A)+In(B). Suppose the price of each apple (A) is €6, and the price of a loaf of bread (B) Is €6 and the consumer's income is €120 ) Write down the Lagrangian for this problem and solve for the optimal consumption of apples and (ii) Report and interpret your solution for the Lagrange multiplier. bread. i) Evaluate the marginal utility of bread and the marginal utility of apples at...
please in part b graph it with identifying everything.
2. Consumer Theory. Ahn's utility function for goods X (pizzas) and Y (cola) is represented as U(X, Y) = 2ln(X)+ln(Y). The prices of X and Y are $1 and $1, respectively. Ahn's income is $12. 1) Calculate Ahn's optimal consumption bundle (X*, Y*). (X*, Y*)= 2) Suppose there is an increase in the price of X. Illustrate the net effect, income effect, and substitution effect on Ahn's optimal consumption choice.
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