Answer to Question #99044 in Economics for Dareal

Question

The production function of a competitive firm is given by Q=10K^0.5L^0.5
And sells its output at the price of GHS2 per unit. Suppose the price of labour per hour is GHS10 and the cost of hiring a machine per hour is GHS20 and the operating budget for the firm is GHS10,000.
a. Calculate the optimal levels of labour and capital usage.​
b. Is the firm experiencing abnormal profit, normal profit or loss? Assume it is operating in the short run.​​​​​​​
c. Based on your answer to B, should the firm continue to operate or shut down? Explain
d. What is the total profit at the optimal levels of capital and labour usage?

Answer 1

a) To answer the question we should resolve the system of equations: TC=w×L+r×K; MP(L)/w=MP(K)/r; where MP is the first derivative of PQ. So, TC=10L+20K; MP(L)=2×(10K^0.5L^0.5)'=20×0.5×K^0.5/L^0.5=10K^0.5/L^0.5;

MP(K) is analogically 10L^0.5/K^0.5

So, 10K^0.5/L^0.5/10=10L^0.5/K^0.5/20; after simplification L=2K. Then, 10×2K+20K=10000; K=250, L=500.

b) TC=10×500+20×250=10000; PQ=2×10×250^0.5×500^0.5=7071, it is less than TC, so the firm is ecperiencing loss

c) A firm should continue to produce in short run, if its revenue more than variable costs. Usually capital is fixed cost, labor is variable cost. VC=500×10=5000, 7071>5000; so the firm should continue

d) TP=7071-10000=-2929