Problem Set 7 1. Suppose Farmer Frank grows watermelons. The production function is defined in terms of labor (L), capital (K), and acres (A) and is given by q = L3 K3 A3 . Expen- ditures are equal to wL trk + mA. (a) Does the production function exhibit increasing, decreasing, or constant re- turns to scale? (b) Set up the Lagrangian for the cost minimization problem. Take the four first order conditions. (c) Solve for L as a function of w, r, m, and q. "Solve" for K and A by symmetry. (d) Find the cost function for watermelons (e) Now suppose that for this particular production process, the amount of land, A, is fixed in the short term so that A = 1; neither K nor L is fixed in the short term for this firm. Solve the new new cost minimization problem. What are the optimal amounts of K and L? (f) What is the short run cost function