w10_ps5_econ100

# 6 l is the amount of labor measured in person hours k

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0.6 L is the amount of labor (measured in person-hours), K is the amount of capital (measured in machine hours), and Q is the number of egg cartons produced. The price of labor (w) is \$8, and the price of capital (r ) is \$16. a. Find the marginal rate of technical substitution of labor for capital. b. If Acme wishes to produce 2000 egg cartons at minimum cost, how much labor and capital should they employ? c. What will be Acme’s to tal cost of producing these 2000 egg cartons, assuming labor and capital are their only costs? 3. Consider a firm that produces with a Cobb-Douglas production function in labor and capital, given by F(L,K) = 5L 0.6 K 0.4 a. Demonstrate that this firm’s product ion function exhibits CONSTANT returns to scale. b. It can be shown that this firm’s cost function will be given by: C = w 0.6 r 0.4 [(2/3) 0.6 + (2/3) -0.4 ](1/5)Q (optional: can you derive this cost function?) What does this c ost function imply about the firm’s cost -output elasticity? Show that this firm has neither economies of scale or diseconomies of scale. (Hint: calculate MC/AC) 4. Draw graphs including curves for marginal costs, average total costs, average variable costs, and the market price of output for a single perfectly competitive firm that: a. will produce a positive quantity of output and earn positive economic profits. b. will produce no output this period. c. will produce a positive quantity of output, but earn negative economic profits.

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5. A perfectly competitive, profit-maximizing firm faces the following total cost function. TC = 26Q 4Q 2 + (1/3)Q 3 + 50. a. Find the firm’s average total cost function, average variable cost function, and its marginal cost function. Find the firm’s fixed costs. b. At what non-zero quantity are average variable costs equal to marginal costs? What do we know about this point on the average variable cost curve?
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