Microeconomic Theory - Problem Set 3 16th November 2020 The solutions to these exercises will be made available on Monday November 23rd

Microeconomic Theory - Problem Set 3 16th November 2020 The solutions to these exercises will be made available on Monday November 23rd. You can submit your own solutions by 23:59 (CET) on Sunlay November 22nd. 1. Let u: R2 + R where: with a, 3 € 10,1). Assume P1:P2 > 0 and that the consumer's income is Recall that, in Problem Set 2 we derived the following Marshallian demand functions: (P.12, y) = (a + 3). By a 3)2 (a) Compute the indirect utility function (P1, P2, y). (b) Show that the indirect utility function is homogeneous of degree 0 in (p,y). (c) Use Roy's identity to derive the Marshallian demand function for 2; using the indirect utility function. 2. A consumer has pre?erences over the single good, I and all other goods”, m represented by the utility function, u(x.m.) = ln() + m. Let the price of r be p, the price of m bel and let income bey. (a) Derive the Marshallian demands for I and m. (b) Derive the indirect utility function, up,y). (c) Use the Slutsky equation to decompose the effect of an own-price change on the demand for x into an income and substitution effect. Interpret you result bricfly. 1