8.17. A packaging firm relies on the production function Q ! KL " K, with MPL ! K and MPK ! L " 1.

Assume that the firm’s optimal input combination is interior (it uses positive amounts of both inputs). Derive its long-run total cost curve in terms of the input prices, w and r. Verify that if the input prices double, then total cost doubles as well.

K ! 9).

MPK ! [L 1

2 " K1 2 ]K$1 2

MPL ! [L 1

2 " K1 2 ]L$1 2

Q ! (1L " 1K)

2

.