Art is a finance major. He has to take two courses, mathematics and psychology. He is relatively good at the former, but not so much at the latter. He needs to spend 1 hour studying for mathematics in order to improve his grade by one point, while he needs to spend 2 hours studying psychology in order to do the same. Art has a total of 50 hours to study for the two subjects. Suppose that he would get 50 points on each course if he didn't study at all. Also, assume what he cares is the total score on the two subjects.

(a) We want to analyze Art's problem with consumption theory. What are the goods, prices and income? Write down the budget constraint. Illustrate it with a graph.(hint: consider the improvements on his grades, rather than the levels. That is, let good 1 be improvements in his grade on mathematics, and good 2 be improvement in his grade on history.)

(b) Now, Art has to pass both subjects by obtaining at least 60 points on both courses. Illustrate his new budget set in the graph.

(c) Can you give a utility function that represents his preferences? Draw two indifference curves, and indicate what their utility levels are.

(d) If he does not care about his grade on mathematics, write utility function that represents his preferences? Draw two indifference curves, and indicate what their utility levels are.