Question 1 (75 marks). Consider a consumer with wealth to who consumes two goods, which we shall call goods 1, 2. Let the amount of good 6 that the consumer consumes be me and the price of good 6 be pg. Suppose that the consumer's preferences are described by the utility function mm as as : (17 2) (331+I2) for any ($1,902) # (0,0). If both 391 and $2 are 0 then this function is 0/0 and thus indeterminate. In this case we dene u(0, U) to be 0. (1) Neatly and accurately graph the indifference curves through the consumption bundles (1,1) and (2,2). Do these indifference curves ever hit the axes? If so, at what points? If not, explain why you know that they do not. If the indifference curve does hit the mlraxis what is the slope of the indifference curve at that point? Explain why with this utility function a utility maximising consumer will, for any budget set with p1, p2, and u) all strictly positive, consume strictly positive amounts of both goods. (10 marks) (2) Set up the utility maximisation problem and write down the Lagrangian. (5 marks) (3) Give the rst order necessary conditions for an interior solution to this problem, (5 marks) (4) Solve these conditions to obtain the Marshallian (or uncompens sated) demand functions. You may, and should, assume that the solution will be interior, that is that, at the maximum, all goods will be consumed in strictly positive amounts. (5 marks) (5) Substitute the Marshallian demands back into the utility func tion to obtain the indirect utility function