Consumer Theory 13 Ordinary Goods 1. Let U(x, y) = x2/3743, MU2 = 173 MUY =...
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.
Suppose there are two consumers, A and B, and two goods, X, and Y. Consumer A's utility function is given by: Ua(X,Y) = X*Y^3 Consumer B's utility function is given by: Ub (X,Y) = X*Y Marginal Utilities for A: MUx =Y^3 , MUy = 3X*Y^2 Marginal Utilities for B: MUx = Y, MUy = X Initial endowments: Person A has 40 units of good X and 20 units of good Y Person B has 30 units of good x and...
QUESTION 10 Units of X MU MUx/Px $2 Units of Y MUy MUy/Py $4 20 1 48 18 2 40 3 16 36 14 4 32 12 24 6 1 6 12 If the prices of X and Y are $2 and $4 per unit, respectively, and this consumer has $10 in income to spend, to maximize total utility, this consumer should buy O 2 units of X and 2 units of Y 01 unit of X and 1 unit...
Suppose that a consumer’s utility function is U(x,y)=xy+10y. the marginal utilities for this utility function are MUx=y and MUy=x+10. The price of x is Px and the price of y is Py, with both prices positive. The consumer has income I. (this problem shows that an optimal consumption choice need not be interior, and may be at a corner point.) Assume first that we are at an interior optimum. Show that the demand schedule for x can be written as...
Assume an economy with two goods, x and y. A consumer has preferences u(x, y) = 2(Vx+ vý), (MU: = 1/VX, MUY = 1/./). Prices are px=1 and py=1. The consumer has an income of M=195.0. Calculate the CV (Compensating Variation) if the price of good x increases to Px'=2. No units, no rounding. Important: Don't round! Leave the numbers under the square root as they are and see if they simplify later without having to round! Do the same...
Given two utility functions U(x, y) = x2/3 y4/5 and U(x, y) = x2 + y, with Px = 2, Py = 1, budget is 10 unit, show the consumer choice respectively.
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
2. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 2 units of good X and 3 units of good Y. Consumer B is given an initial endowment of 6 units of good X and 5 units of good Y. Consumer A’s utility function is given by: UA(X,Y) = X1/2*Y1/2, And consumer B’s utility function is given by UB(X,Y) = X1/4*Y3/4. Therefore, consumer A’s marginal utilities for...
1. A consumer is considering to buy only two products, X, and Y. The amount of total utility yielded by their consumption is shown in the table below. Assume that the prices of X, and Y are $8, and $2 respectively, and that the consumer has an income of $24 to spend. a) Complete the following table by computing the marginal utility and the marginal utility per dollar for successive units of product X and Y. (4 marks) b) How...