W= Continuing to use the three production functions: q = h(K, L) = K(1/3) [(1/3), q=g(K,...
W= Continuing to use the three production functions: q = h(KL) K(1/3) L(1/3) q = g(K, L) = min{:K, L}, and q = f(K, L) = K (1/4)(3/4). (h) (6 points) What is the Long Run Cost curve for each of these when r = $4 and $16? (i) (6 points) What are the Long Run Average Cost here? How about the Marginal Cost? (j) (4 points) Provide a convincing argument that a firm using with h(K, L) or 9(K,...
just answer e,f,g,h,i,j. (a) (3 points) To begin, assume that a firm is producing using q = h(K, L) = K(1/3) L (1/3). Suppose the firm currently owns 128 machines, the price of the good is P = $96, the rental rate of capital is r = $4, and the wage rate is w = $16. What level of Labour would be hired? How much would be produced? Would the firm make a profit or a loss? Suppose there are...
Provide a convincing argument that a firm using with g(K,L) =min{K/4, L/5} would select K*= 128 in the Long Run given P=$96, w=$16 and r=$4??
(3 points) To begin, assume that a firm is producing using a h(K, L) K(1/3) L(1/3). Suppose the firm currently owns 128 machines, the price of the good is P $96, the rental rate of capital is r = $4, and the wage rate is w = $16. = Suppose there are two other methods of production using the same machines: q = g(K, L) = min{ĀK, ŽL} or q = f(K, L) = K(1/4)[(3/4). (e) (2 points) Using production...
(3) Consider the ﬁrm of the previous question (with f(L,K) = 2K√L and with w = 1 and r = 4). For the following questions suppose that this ﬁrm currently uses K = 4 machine hours, and that this can’t be changed in the short-run. f(L) = 8√L L = Q^2/64 C= 16 + Q^2/64 AC = 16/Q + Q/64 MC = Q/32 (e) In one graph draw the average cost and marginal cost curves. The graph should show the...
4. Production of bikes requires 3 workers for every 2 machines, such that bikes are prodaced according to F(K.L) min(3K, 2L) (a) Setup the short run cost minimization problem when R-6. (2 points) 5 (b) Solve for the short run optimal amount of labor Lsle) and short run minimized cost Csa(w,r.q). (3 points) (e) Now suppose the bike shop can freely choose capita! (K) and labor (L). Setup the long run cost minimiza- tion problem. (2 points) (d) Solve for...
Let the production function be as follow: 2. L0.7 K.3 q(L, K) Also assume w 2 and r=4 Find out if we have increasing, decreasing or constant return to scale. a. Derive the long-run cost function. TC(q) b. Derive the average cost curve. Is it increasing or decreasing or constant in q? С. Let the production function be as follow: 3. q(L, K) LK3 Also assume w-4 and r=3 Find out if we have increasing, decreasing or constant return to...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion for producing cars is: F(K, L) = min(2K,5L) (a) Setup the short run cost minimization problem when K = 10. (2 points) (b) Solve for the short run optimal amount of labor Lsr() and short run minimized cost Csr(w,r,q). Circle your answer. (4 points) (c) Now suppose the car factory can freely choose capital (K) and labor (L). Setup the long run cost minimization...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...