A film studio in Hollywood produces movies according to the function (yes, they can also produce fractions of movies... Think of half a movie as a B-movie or so.) q = F(K, L) = K0.5L 0.5 /100.(reads as K to the power of 0.5 times L to the power of 0.5 divided by 100) In the short run, capital (studios, gear) is fixed at a level of 100. It costs $4,000 to rent a unit of capital and $1,000 to hire a unit of labor (actors, stuntmen, camera crew etc.).
(a) What is the fixed cost? What is the variable cost as a function of output q?
(b) What is the marginal cost (MC) and the average cost (AC) of a movie? What is the average variable cost and average fixed cost?
(c) Where do the average and marginal cost curves intersect? What is the derivative of the AC curve and what value does it take at the intersection? What does it tell you about minimum average cost?