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Assume John has Cobb-Douglas utility function for bread (B) and whiskey (W): U- 2*B0.5w0.5 Marginal utilities...
Assume John has Cobb-Douglas utility function for bread (B) and whiskey (W): U= 2 BSWS Marginal...
Assume John has Cobb-Douglas utility function for bread (B) and whiskey (W): U= 2 BSWS Marginal utilities are as followed: MUB=B-05W. and MUw = 30.5W-0.5 a. Write down the expression for MRSow (i.e., you need to simplify the ratio and come up with a neat result) b. What is MRSBw at bundle A(4,4)? At bundle B(1,16)? C. Regarding MRSBw, we consider a movement along an indifference curve from the left to the righ (getting more of bread, the good on...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...
Q3: a. Consider a Cobb-Douglas Utility Function Find marginal utility of Y. Does marginal utility of...
Q3: a. Consider a Cobb-Douglas Utility Function Find marginal utility of Y. Does marginal utility of depend on the level of consumption of X? how do you know? Explain b. Find slope of the indifference curve. c. Find MRS and draw the indifference curve for above function.
Suppose Bill has preferences over chocolate,x, and ice cream,y, that are represented by the Cobb-Douglas utility...
Suppose Bill has preferences over chocolate,x, and ice cream,y, that are represented by the Cobb-Douglas utility function u(x, y) =x^2 y. 1. Write down two other Cobb-Douglas utility functions, besides the one above, that represent Bill’s preferences. 2. Write down two more Cobb-Douglas utility functions that do NOT represent Bill’s prefer- ences. 3. Draw 3 indifference curves that represents Bill’s preferences at 3 different levels of satsifaction. 4. What is Bill’s marginal rate of substitution between chocolate and ice cream?...
1. answer it only numerical values. 2. A person has a Cobb Douglas utility function for...
1.
answer it only numerical values.
2.
A person has a Cobb Douglas utility function for two goods X and
Y. If the price of a X increases and the budget stays the same, the
utility maximizing person __________.
Cannot be determined from the information
will consume less of Y
will only consume Y
will consume less of both goods
will have lower utility
Sara has $40 in her budget. Given the following graph, what is the MRS of her...
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function...
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function are MU1 = x23 and MU2 = 3x1x22. (a) Show that Alex’s utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (b) Find the MRS. [Note: find the MRS for the original utility function, not some monotonic transformation of it.] (c) Write down the tangency condition needed to find an optimal consumption bundle for well-behaved preferences....
2. Abagail has an estimated Cobb-Douglas utility function of U = 982592.75 for food, 91, and...
2. Abagail has an estimated Cobb-Douglas utility function of U = 982592.75 for food, 91, and housing, 92. The price for food is arbitrarily set at $1 per unit Pi = $1 and the average monthly rent near UCF, P2, is $1.50 per sq ft. Jackie, like the average UCF student spends $800 on food and housing per month. (a) (20 points) Using calculus, solve for Abagail's optimal quantities of housing and food. For 10 bonus points provide the marginal...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
Question-3 (Marginal Products and Returns to Scale) (30 points) Suppose the production function is Cobb-Douglas and...
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
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...
Assume John has Cobb-Douglas utility function for bread (B) and whiskey (W): U= 2 BSWS Marginal utilities are as followed: MUB=B-05W. and MUw = 30.5W-0.5 a. Write down the expression for MRSow (i.e., you need to simplify the ratio and come up with a neat result) b. What is MRSBw at bundle A(4,4)? At bundle B(1,16)? C. Regarding MRSBw, we consider a movement along an indifference curve from the left to the righ (getting more of bread, the good on...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...
Q3: a. Consider a Cobb-Douglas Utility Function Find marginal utility of Y. Does marginal utility of depend on the level of consumption of X? how do you know? Explain b. Find slope of the indifference curve. c. Find MRS and draw the indifference curve for above function.
1.
answer it only numerical values.
2.
A person has a Cobb Douglas utility function for two goods X and
Y. If the price of a X increases and the budget stays the same, the
utility maximizing person __________.
Cannot be determined from the information
will consume less of Y
will only consume Y
will consume less of both goods
will have lower utility
Sara has $40 in her budget. Given the following graph, what is the MRS of her...
2. Abagail has an estimated Cobb-Douglas utility function of U = 982592.75 for food, 91, and housing, 92. The price for food is arbitrarily set at $1 per unit Pi = $1 and the average monthly rent near UCF, P2, is $1.50 per sq ft. Jackie, like the average UCF student spends $800 on food and housing per month. (a) (20 points) Using calculus, solve for Abagail's optimal quantities of housing and food. For 10 bonus points provide the marginal...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
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...
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