Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q = F(L,K) = 10L0.5k0.5, where L is their number of workers and K is units of capital. The wage rate is $1000, and a unit of capital costs Hannah and Sam $1000 per week.
(a) Graph the isocost curves F (L, K) = 10 and F (L, K) = 20.
(b) What is their least-cost input combination for remodeling 100 square feet a week?
(c) What is their total cost?
(d) What is their cost function C(Q)?
(e) What is their average cost function AC(Q) and marginal cost function MC(Q)?