A consumer has a utility of ?(?, ?) = 4??? + ? for the two goods ? and ?. If?x is 2, ?y is 10, the consumer’s income is 36, then the amount of ? he will consume is
A) 20
B) 18
C) 16
D) 0
Consider a consumer whose utility function is given by U(x, y) = x^1/4y^1/2, where x and y represent quantities of consumption of two consumer goods. (a) Derive and interpret the consumer’s Marshallian demand functions for x and y. (b) Derive and interpret the consumer’s Indirect Utility Function. (c) If the consumer’s income is $1000 and the prices of x and y are both $5, how should the consumer maximize her utility? What is her maximum level of utility? (d) Suppose...
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , available in arbitrary non-negative quantities (so the the consumption set is R 4 +). A typical consumption bundle is therefore a vector (q, r, x, y), where q ≥ 0 is the quantity of good Q, r ≥ 0 is the quantity of good R, x ≥ 0 is the quantity of good X, and y ≥ 0 is the quantity of...
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , available in arbitrary non-negative quantities (so the the consumption set is R 4 +). A typical consumption bundle is therefore a vector (q, r, x, y), where q ≥ 0 is the quantity of good Q, r ≥ 0 is the quantity of good R, x ≥ 0 is the quantity of good X, and y ≥ 0 is the quantity of...
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...
Consider the consumer Mr. Magnificent, who has the utility function u(x,y) = min{ x, 2y}. This consumer has an income of $234 and the price of both x and y is $6 a unit. Unfortunately for Mr. Magnificent, the federal government needs to raise tax revenue of $30. a. Find the consumer’s optimal basket and utility in the absence of taxes. b. If the government uses the lump‐sum approach for taxation, what is the resulting utility earned by Mr. Magnificent? c. Now,...
Question 2 A consumer purchases two goods, food (x) and clothing (y). He has the utility function U(X,Y) = XY, where X and Y denote amounts of X and Y consumed. Marginal utilities of X and Y are MUx = y and MUy = x. The consumer’s income is $72 per week and that the price of y is Py = $1 per unit and price of x is Px1 = $9 per unit. What are his initial quantities of X and...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function: U (X, Y) = X°.270.3 Budget Constraint: I = XP, + YP, a. What is the consumer's marginal utility for X and for Y? b. Suppose the price of X is equal to 4 and the price of Y equal to 6. What is the utility maximizing proportion of X and Y in his consumption? {construct the budget constraint) c. If the total amount...
Question 1 (20 marks) (a) A consumer maximizes utility and has Bernoulli utility function u(w)/2. The consumer has initial wealth w 1000 and faces two potential losses. With probability 0.1, the consumer loses S100, and with probability 0.2, the consumer loses $50. Assume that both losses cannot occur at the same time. What is the most this consumer would be willing to pay for full insurance against these losses? (10 marks) (b) A consumer has utility function u(z, y) In(x)...
A consumer has the utility function over goods X and Y, U(X; Y) = X1/3Y1/2 Let the price of good x be given by Px, let the price of good y be given by Py, and let income be given by I. Derive the consumer’s generalized demand function for good X. Solve for the Marshallian Demand for X and Y using Px, and Py (there are no numbers—use the notation). c. Is good Y normal or inferior? Explain precisely.
A consumer has the utility function over goods X and Y, U(X; Y) = X1/3Y1/2 Let the price of good x be given by Px, let the price of good y be given by Py, and let income be given by I. (a) Derive the consumer’s generalized demand function for good X. (b) Solve for the Marshallian Demand for X and Y using Px, and Py (there are no numbers—use the notation). (b) Is good Y normal or inferior? Explain...