1. TRUE or FALSE (Determine if each of the following statements is true or false. Explain your reasoning. All credits are assigned to
explanations).
a. In a two-good model, the consumer remains as well-o if both prices decrease by half and income is also reduced by half.
b. If a consumer's preferences do not satisfy transitivity, then we cannot represent her preferences with a utility function.
c. Indi erence curves representing di erent levels of preference can cross each other.
2. Are the following functions monotonic transformations? You can determine it by drawing a graph or calculating their derivatives. Assume u > 0 throughout.
3. Art is a history 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 for psychology in order to do the same. Art has a total of 40 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 he only cares about 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.)
b. Can you give two utility functions that represents his preferences?
Draw two indi erence curves, and indicate what their utility levels are for each utility function.
c. Now Art has to pass both subjects by obtaining at least 60 points on both courses. Illustrate his new budget set in the graph.