ECON211 Chapter Notes - Chapter 8: Hicksian Demand Function, Expenditure Function, Lagrange Multiplier

• School: University of Waterloo
• Department: Economics
• Course: ECON211
• Professor: John Burbidge

Document Summary

An example of an expenditure-minimizing consumer and a utility-maximizing consumer: consider a price-taking, expenditure-minimizing consumer in a two-good world. De- note goods prices by p1, p2, and suppose preferences are represented by the following utility function u (h1, h2) = 2h1/2. Answer (a) upper contour sets are strictly convex if. 1u22 < 0. u1 (h1, h2) = 2 u2 (h1, h2) = 1. 2 u11 (h1, h2) = u12 (h1, h2) = 0 u22 (h1, h2) = 0, h 3/2. < 0 if h1 > 0 from which it is clear that upper contour sets are strictly convex for h1 > 0. L = p1h1 + p2h2 + (cid:16)u0 (cid:16)2h1/2. Take the ratio of equations (1) and (2) and re-arrange: Substitute this result into equation (3) and solve for h2. h2 = u0 2h1/2. Then e (p1, p2, u0) p1h1 (p1, p2, u0) + p2h2 (p1, p2, u0) = p2u0 .