Consider a widget maker named Jimmy. He hires labor (L) at the rate w = 30 and rents capital at the rate r = 10.
(a) When Jimmy's technology is given by: f(L,K) = min(5L,2K) What are the long-run, cost-minimizing values of L and K when his production target is 100 widgets?
(b) When Jimmy's technology is given by: f(L,K) = 5L + 2K What are the long-run, cost-minimizing values of L and K when his production target is 100 widgets?
(c) When Jimmy's technology is given by: f(L,K) = 5L + 2K What is the long-run total cost associated with producing 100 widgets?
(d) When Jimmy's technology is given by: f(L,K) = 5L + 2K What are the long-run, cost-minimizing values of L and K when his production target is 100 widgets?
(e) When Jimmy's technology is given by: f(L,K) = 5L + 2K What are the short-run, cost-minimizing values of L and K when his production target is only 50 widgets?