Problem 1 (30 p) You are asked to plan a budget of University of Connecticut for the next year. The two major expenses involve computers, r , and classroom furniture, r 2. The university's utility function is given by U(x], x;)=In x1 + 2lm x2 a) Find optimal "consumption" of computers and furniture if P,=2 and P,=4 and the available funds are m= 60. b) Is computer an ordinary or a Giffen good ? Determin whether computer is a gross complement, gross substitute or neither, for classroom furniture. (Explain these questions using partial derivatives) c) Please draw the price offer curve for x, given p1=4 and m = 60. Problem 2 (42 p) Given preferences represented by the utility function u($1, 12) = min {211, r2}, let's figure out the following: a) Derive demand for I, and 12 as a function of prices and income. b) Let m = 100, pi = 2, and pa = 4. Find the demands for r, and 12. (two numbers) c) Suppose py increases to pi = 10. Now what is the optimal bundle? (two numbers) d) Decompose this change into the income and substitution effects. (show detailed steps)