1. Paul deduces utility only from CDs and DVDs.
His utility function is: U = √C.D
a) Draw Paul's indifference curves for U = 5, U = 10, and U = 20.
b) Assume Paul has $200 to spend and that CDs cost $5 and DVDs cost $20. Sketch Paul's budget constraint on the same graph as his indifference curves.
c) Assume Paul spends all of his income on DVDs. How many can he buy and what is his utility?
d) Illustrate that Paul's income will not permit him to reach the U = 20 indifference curve.
e) If Paul buys 5 DVDs, how many CDs can he buy? What is his utility?
f) Use carefully drawn graph to show that utility find outd in part e is highest Paul can achieve with his $200.
2. Sometimes it is convenient to think about consumer's problem in its "dual" form. This alternative approach asks how a person could achieve a given target level of utility at minimal cost.
a) Create a graphical argument to illustrate that this approach will yield same choices for this consumer as would the utility-maximization approach.
b) Returning to problem 1, suppose that Paul's target level of utility is U = 10. Compute the costs of attaining this utility target for the following bundles of goods:
i. C = 100, D = 1
ii. C = 50, D = 2
iii. C = 25, D = 4
iv. C = 20, D = 5
v. C = 10, D = 10
vi. C = 5, D = 20.
c) Which of the bundles in part b gives the least costly way of reaching the U = 10 target? How does this compare to utility-maximizing solution found in problem 1?