Consider a consumer whose preferences can be represented by the utility functionU(q1,q2)=q1+q2.

This consumer has an income ofyand faces a price ofp1per unit of commodity one and a price ofp2per unit of commodity two.

1. Find this consumer's uncompensated (Marshallian) demand functions for commodi- ties one and two. You may assume both that the budget constraint binds and that the consumer has sufficient income to guarantee consumption of a positive amount of each good. (8 marks.)
2. Find this consumer's indirect utility function. (5 marks.)
3. Find this consumer's expenditure function. (5 marks.)
4. Find this consumer's compensated (Hicksian) demand functions for each of the two commodities. (5 marks).
5. Suppose that this consumer has an income ofy=y0= 100. Find this consumer's optimal consumption bundle when the price vector isp0= (p01, p02) = (4,1). (1 mark.)
6. Suppose that this consumer has an income ofy=y0= 100. Find this consumer's optimal consumption bundle when the price vector isp1= (p1, p12) = (10,2). (1 mark.)