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
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 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...
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.
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...
(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...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find the initial optimal bundle. ii. If the prices change to (6, 2), find the new optimal bundle. Show this in your graph in (i). iii. How much of the change in demand for x1 is due to the substitution effect? How much due to...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the indifference curves for u = 50, 72 and 98. e indifference Carved forbise banta un b. Sketch budget constraint of 5x +10y = 30. Label intercepts (where it crosses the axes). 00:0 VE c. Solve for calculate) the optimal bundle (x, y) and sketch the optimal solution.
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)
A person with the following utility function, u(x) = ln(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: E{u(.)] = 0.91n(x) +0.1ln(y) where x would be the wealth under no identity theft and y the wealth under identity theft. This means that the marginal utilities are: MU 0.9, MUy = 0.1 Using this information answer the following questions 1) What is...
Mustapha’s utility function is as follows: U = 10x0.8 y0.6 Budget constraint: 100 = 6x + 4y a. Solve for the utility-maximizing bundle b. Find the equation of the indifference curve that contains the utility-maximizing bundle. c. Sketch the solution, labeling all relevant items, x on the horizontal axis and y on the vertical axis. d. At the utility-maximizing bundle, what is the increase in Mustapha’s utility from the last dollar spent on good X? What about for good Y?...
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...