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You have just inherited Willy Wonka's chocolate factory. The production function for chocolate candy bars is given by F (K,L)=(K^ (1 /4) + L^(1/4))^2. Oompa Loompa workers receive wages w =2 and rental rate ofcapital is r =4 :
a) Solve for the cost function in terms of q when the ?rm is free to choose both labor and capital. (You will need to solve the cost minimization problem and ?nd the optimal K,L in terms of q in order to ?nd cost in terms of q).
b) Solve for the marginal cost function using your result from part a).
c) Suppose p = 50 and that the ?rm is a price taker. What is the optimal amount of output the ?rm should produce?
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