Utility Function: U = ln (x) + ln (z)
Budget Constraint: 120 = 2x + 3z
(a) Find the optimal values of x and z
(b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z
Problem 4
(a) Derive the demand functions for the utility function
(b) Let a = 2, b = 5, px = 1, pz = 3, and Y = 75. Find the optimal values for x and z.
Problem 5
Utility Function:
Time Constraint: H=24-
Income Constraint: Y=wH
w=16
Solve for the optimal values of and Y using the Substitution Method
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z
4. A consumer’s utility function is U = x + z . If the budget constraint has a slope ( − px / pz ) = -2, which statement is true? a. z* >0,x* =0 b. z* = x* > 0 c. z* =0,x* >0 d. Not possible to say, given the information provided. e. None of the above.
(a) Derive the demand functions for the utility function U=(a)sqrt(x)+(b)sqrt(z) +xz (b) Let a = 2, b = 3, px = 1, pz = 2, and Y = 50. Find the optimal values for x and z.
A household's utility function is given by U(x, y, z) = 6 In x + 9 ln y + 15 In z, where x,y and z are the quantities of products X, Y and Z respectively, consumed by the household each month. The prices per unit for these three goods are px = $6, Py = $15 and pz = $24, respectively. The household's monthly budget for these goods is B = $4800. Question 11 2 pts This continues the...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint px + p2x2 = m. Derive the consumer's demand functions for x1 and x2. (25 marks)
2.Optional Question on duality for those who welcome a challenge Consider the same utility function as given by: U(X, Y) = X-Y For the primal problem, find the Marshallian uncompensated demand functions, X(Px Ру and y(Rs Py, by maximizing utility subject to budget constraint Px. X + Ру.Y - I. After obtaining the optimal consumption choices, write down the indirect utility function. Give a simple diagrammatic and economic interpretation. Illustrate the use of the indirect utility function by plugging in...
Vasco's utility function is: U = 10x²z The price of X is px = $2, the price of Z is pz = $4, and his income is $60. What is his optimal bundle? (round your answer to two decimal places) X= Z. = units units
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y = 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (b) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x, y)? Compare with the value found in (a) for the Lagrange multiplier. (C) Suppose we change the budget constraint to px + y = m, but keep the same utility...
(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...