# Econ_102A_PS5_Answer - wage is 10 dollars per worker. What...

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Econ 102A Problem Set 5 Consider a firm operating in the short run in a perfectly competitive market using a production technology given by F(K,L)=K ½ L ½ . Suppose that the firm is utilizing 100 units of capital input in the short run but the firm can hire and fire workers anytime it wants (ie: capital is a fixed input and labor is a variable input). #1) What type of returns to scale does this technology exhibit? F(2K,2L)=(2K)^.5*(2L)^.5 = 2*(K*L)^.5 = 2*F(K,L) Thus, we doubled each input and the output has exactly doubled Constant returns to scale. a) What is the short run production function? What type of returns does it exhibit? Q=10*L^(1/2) Now becomes decreasing returns to labor when capital is fixed. b) If the firm hired 49 workers, how many units of output could it produce? Q=10*(49)^(1/2) = 70 units c) How many workers would the firm need to hire in order to produce 100 units of output? Q=10*L^(1/2) L=[Q^2]/100 = ([100]^2)/100 = 100 workers d) Suppose that the rental rate on capital is 5 dollars per unit of capital equipment and the

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Unformatted text preview: wage is 10 dollars per worker. What are the total, fixed, and variable costs for this firm (as a function of quantity produced)? TC= wL+rK = 10L+ 500 but L=[Q^2]/100 => TC= [Q^2]/10 + 500 Fixed Costs = 500 on capital expenditure Variable Costs = (Q^2)/10 e) What is the marginal cost of producing an additional unit of output (hint: take dTC/dQ)? What is the short run supply curve? dTC/dQ = MC = Q/5. To maximize profits, firms set price equal to MC Q/5=P Then the supply curve for a firm is given by Q=5P. f) Suppose the price in the market is 100 dollars. How many units of output should the firm produce in the short run? From above, if P=100, Q=500. g) How much profit will the firm make in the short run? Profit = Total Revenue – Total Cost Profit = P*Q – [(Q^2)/10+500] P=100, Q= 500 and substitute. h) How much profit will the firm make in the long run? Perfectly competitive firms make ZERO profit in the LONG RUN....
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## This note was uploaded on 02/03/2010 for the course ECON econ102a taught by Professor Bandy during the Winter '09 term at UC Riverside.

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Econ_102A_PS5_Answer - wage is 10 dollars per worker. What...

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