I would like to confirm the answer from 1 to 4 as follows (esp. want you to expand on (f) and (g))

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 w, v and @) (c) The long run cost function and long run marginal cost as a function of w, v and @ (d) Contingent demand for L assuming K fixed at K = 64 (e) The short run cost function and short run marginal cost (for simplicity assume w and v 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(z,y) = z1/4y3/4 and an income of I = 1000 and a single firm with the given production function and K = 64 (assume we are looking at the market for z) (h) The profit of the firm in equilibrium 1. F(K,L)= K'/3L%/3 2. F(K,L) = K'/3L'/3 3. F(K,L)= KL%* 4. F(K,L) = K2L? (Only do a-e. Challenge: explain why f and g won't make sense in this case)