Consider a consumer with quasi-linear preferences over bundles of strictly positive amounts of each of two commodities that can be represented by a utility function of the form U(x1,x2) = x1 +ln(x2). This consumer is a price taker that faces a budget constraint of the form p1x1 + p2x2 = y. Suppose that this consumer has enough income to always want to consume a strictly positive amount of each commodity. 4

1. Find the Marshallian demand functions, Hicksian demand functions, indirect utility function, and expenditure function for this consumer.

2. Suppose that the initial price and income vector is (p01, p02, y0). Follow- ing an exogenous shock, the final price and income vector is (p1, p12, y1). Calculate both the equivalent variation and the compensating variation measures of the welfare impact of this shock.

3. Suppose now that the shock only affects the price of commodity two, 01010 so that the final price and income vector is (p1,p2,y ). (Let p2 > p2.) How does this simplify the general formulae that you obtained for the equivalent variation and the compensating variation measures of the welfare impact of this shock. Calculate the change in Marshallian con- sumer surplus measure of the welfare impact of this shock and compare it to the equivalent variation and the compensating variation measures. What do you notice?

4. Suppose now that the shock only affects the price of commodity one, 10010 so that the final price and income vector is (p1,p2,y ). (Let p1 > p1.) How does this simplify the general formulae that you obtained for the equivalent variation and the compensating variation measures of the welfare impact of this shock. Calculate the change in Marshallian con- sumer surplus measure of the welfare impact of this shock and compare it to the equivalent variation and the compensating variation measures. What do you notice?

5. Compare and contrast your answers to the preceding two parts of this question, paying particular attention to the factors that influence the marginal utility of income for this consumer.