For each of the following production functions, calculate (note: some numbers don't come out that nicely, feel free to round) (a) Whether the function is increasing, decreasing, or constant returns to scale (b) Contingent demands for L and K (assuming both are chosen optimally by the firm) as a function of m, 'U and Q (c) The long run cost function and marginal cost assuming both labor and capital are chosen optimally as function of w, v and Q (d) Contingent demand for L assuming K fixed at K = 64 (Keep K fixed at 64 for all remaining parts) (e) The short run cost function and short run marginal cost (for simplicity assume w and u are both equal to 1 for the rest of the question) (f) The short run supply curve for a single firm (g) The (partial) equilibrium price given a single consumer with a utility function of U(m, y) = sci/43:3\" and an income ofI = 1000 and a single firm with the given production function and K = 64 (assume we are looking at the market for at) (h) The profit of the firm in equilibrium (i) F(K,L) = K1/3L2/3 (ii) F(K,L) = K1/3L1/3 (iii) F(K,L) : KL3/4 (iv) F(K,L) : K2122 (Only do a-e. Challenge: explain why f and g won't make sense in this