Please someone help out with these two questions! Consider a firm with the produ
ID: 1201102 • Letter: P
Question
Please someone help out with these two questions!
Consider a firm with the production function, q = (K^1/2 + L^1/2) In the shon-run, the level of capital is fixed. Determine the equations for MPl and APl. Solve for the shon-run cost function (i.e. total costs as a function of output) Determine the equations for MC, ATC, AVC, and AFC. Using the same production function as in question 4, suppose that the firm is now operating in thclangjm Solve for the long-run cost function (i.e. total costs as a function of input prices and output). Consider your answer from questions 5a and 4b. How does shon-run total cost compare to long-run total cost when the fixed level of capital in the shon-run equals the optimal level from the long-run cost minimization problem? Prove your statement mathematically.Explanation / Answer
q = (K1/2+L1/2)2 = K + L + 2K1/2L1/2
MPL = dq/dL = 1+ (K/L)1/2
APL = q/L = (K/L) + 1 + 2(K/L)1/2
b) Let wage is w and rate of capital is r
L1/2 = q1/2 - K1/2
L = (q1/2-K1/2)2
TC = wL+ rK = w(q1/2-K1/2)2 + rK
c) ATC = TC/q = w(q1/2-K1/2)2 /q + rK/q
AVC = w(q1/2-K1/2)2 /q
AFC = rK/q
MC = dTC/dq = d(w(q+K-2q1/2K1/2) + rK)/dq = wc(1-(K/q)1/2