Sometimes it is convenient to think about the 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. Develop a graphical argument to show that this approach will yield the same choices for this consumer as would the utility maximization approach.
b. Returning to problem 2.3, assume that Paul’s target level of utility is U = 10. Calculate 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 provides the least costly way of reaching the U = 10 target? How does this compare to the utility-maximizing solution found in problem 2.3?