1. A consumer is faced with the Utility function U = InX + InY. The budget...
Suppose the following equations represent an individual’s utility maximization problem: U(X,Y) = X0.5 + Y0.5 And the budget constraint is: I = PxX + PyY (a) Set up the individual’s maximization problem using the Lagrange technique. (b) Find the individual’s demand function for X and Y (Derive from first order condition). (c) Find the indirect utility function. (d) Find the expenditure function. (e) Find the share of X and Y on expenditure. (f) Find the marginal utility of income.
2. A consumer has a utility function u(xj, X2) = max Inx, Inx2. What is the consumer's demand function for good 1? What is her indirect utility function? What is her expenditure function?
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)
Derive the demand for x for a person with income (I) and Utility=min(x,y) with budget constraint I= pxX+pyY. Find the own price elasticity of demand for x and the income elasticity of demand for x.
1. (Consumer theory) Consider the utility function u(x) = √x1 + √x2 ; and a standard budget constraint: p1x1+p2x2=I. a. Are the preferences convex? (1 pt) b. Are the preferences represented by this function homothetic? (1 pt) c. Formally write the utility maximization problem, derive the first order conditions and find the Marshallian demand function. (2 pt) d. Verify that the demand function is homogeneous of degree 0 in prices and income. (1 pt) e. Find the indirect utility function. (1 pt) f. Find the expenditure function by...
Suppose that the budget constraint is given as: PxX + PYY = M and the formulation of a utility function is given as: U(X, Y) = ??2/2 + ?????????? with 0 < ??, ?? < 1 and constants C, δ > 0. Answer for following questions and show all your calculation/ proof. (15 points) a. Derive the formula of income-consumption curve and draw its graph. (15 points) b. Derive the demand function of good X and Y respectively as functions...
Suppose a person has a utility function U(x1,x2)= xa1+xa2, which she maximizes subject to her budget constraint, px1 + qx2 = m, where p, q, m are all positive. Use the Lagrangian method to solve the maximization problem, and find the demand functions for the consumer. Show that the demand functions are homogeneous of degree zero in prices (p, q) and income (m) (2.5 marks) Suppose a person has a utility function U(x1, x2) = xq +xm, which she maximizes...
Suppose that the budget constraint is given as: PxX + PyY = M and the formulation of a utility function is given as: Answer for following questions and show all your calculation/ proof. a. Derive the formula of income-consumption curve and draw its graph. b. Derive the demand function of good X and Y respectively as functions of income and price of good X and Y. c. Calculate the amount of income spent for good X and Y respectively. χαΥβ...
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...
Given the following utility function: Where, q1 and q2 are consumer goods and the budget constraint is given as. With p, and p the prices of the goods and the month the income. Find. 1. The Marshallian Demands for (q1 and 92. 2. The Indirect Utility Function, V (p1, p2, m) 3. The Hicksian Demands for q1 and q2. 4. The Expenditure Function, m (p1, p2, U) U(992)=9, +10 log2 U(992)=9, +10 log2