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Consider the indirect utility function: v(p1; p2; m) = m /(p1 + p2). What is the Hicksian demand function?
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- A consumer has Hicksian demand functions h(p1 p2, ü)=a()*"ū and h(p1 P2, u)=(1 a)()"ū. Determine this consumer's expenditure function, e(p1.P2, ū). Next, invert it obtain the indirect utility function, v(p1, p2, m). Finally, use Roy's Identity to obtain the Marshallian demand function, r(p1, P2, m), and apply Slutsky's Equation to obtain P2 P2 ahiI A Consumer has utility function U(X,Y)= X¹/4*y3/4 Find the Marshallian demand x(p, w) and the indirect utility function v(p, w) Find the Hicksian demand h(p, u) and expenditure function e(p, u).Suppose Marcel's preferences over consumption bundles (X, Y) can be represented by the utility function U(X, Y) = X³Y. Which of the following expressions gives Marcel's Marshallian demand? (a) (X*,Y*) = ( 31 3px+py' (b) (X*,Y*) = (px (PX+py)) (d) (X*,Y*) : = 3px' +py) 3px+py (c) (X*,Y*) = (-1,0) Ipx px (px+py)' py (py+PX) 1 I 3 I 4px' 4 py (e) (X*,Y*) = = ( px + 4py ² : 31 px +4py' 4px+py
- Suppose an individual has preferences over goods x and y, and their expenditure minimization problem has the following expenditure function: E(px, Py, U) = (px + 3p,)U. What is the person's Hicksian demand? O(h, hy) = (2p U, pU) O(h, hy) = (U, 3U) O(h, hy) = (Up,',Up,) O(hx, hy) = (3U, U) What is the individual's indirect utility? OV = 3p! p OV = P.+3p, OV = P Py OV = P.PConsider the indirect utility function: V(P1, P2, m) = (m+p,+p,) - 4p;p2 4p,P2 Derive the expenditure function. Derive the Hicksian demand function for good 1. a. b.Consider the following indirect utility function: V(p,I) = II,( Pi where E-1 a; = 1, and a; + 0 , Vi 1. What's the demand function for x;? (Hint: Take logarithm to both sides of the equation) 2. What's the original utility function? (Hint: If n is too abstract, let n = = 2)
- Consider the following indirect utility function:ʋ(P,y) = y(P1r + P2r)-1/r Wherer = ρ/(ρ-1, Pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi (P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity). b) Derive the Hicksian demand functions xih (P,u)Naomi has the following utility function, U(x, y) = x + 3y. Suppose that py > 4pr. What are the hicksian demands of x and y? (a) (hr, hy) = (U, 0) (b) (h, hy) = (0, U/3) (c) (ha, hy) = (U, U/3) (d) (ha, hy) = (In (U), In (U/3))Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U = 100(X^(0.75) + Y^(0.75)). Income of 1000, the price of Good X is 10 and the Price of Good Y is 20 a) Find the Marginal Rate of Substitution as a function of the quantities consumed of Good X and Good Y. b) Write out the Lagrangian for this problem. c) Solve to find the demand for Good X, the demand for Good Y, and the highest level of utility for this individual. d) Now consider an increase in the price of Good X to 20. What is the demand for Good X and Good Y? What is the Utility of the consumer following the price change? e) Considering the change in demand for each good between parts c) and d), how much is due to the substitution effect and how much is due to the income effect? f) Show your answers on a graph.
- An individual utility function is given by U(x,y) = x·y. This individual demand (optimal purchase) equation for x is a factor a of I/px: x* = a (I/px). In this specific case, factor a is equal to?For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x and x2 are p₁ and p₂ respectively and income is m. i) U(x1x2) = ln(x1+ x2) ii) U(x1x2) = (x1+ x2)1. For each of the following utility function, compute the Hicksian demand function h(p, v), the expenditure function e(p, v) and the Slutsky (Substitution) matrix S(p, w). In your com- putation procedure, feel free to use your (or my) answers in Assignment 5. 3 a) u(*1, 12) = VI, + ¤2 b) u(x1, 12) = log(1) +3 log r2 c) u(r1, 12) = min(r1, 12) d) u(x1,r2) = max(r1, r2) %3D %3D %3D %3D