Homework answers / question archive / University of Ottawa - ECON 2142 1)A firm’s long-run total cost curve is TC(Q) = 40Q − 10Q2 + Q3, and its long-run marginal cost curve is MC(Q) = 40 − 20Q + 3Q2

University of Ottawa - ECON 2142 1)A firm’s long-run total cost curve is TC(Q) = 40Q − 10Q2 + Q3, and its long-run marginal cost curve is MC(Q) = 40 − 20Q + 3Q2

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University of Ottawa - ECON 2142

1)A firm’s long-run total cost curve is TC(Q) = 40Q − 10Q² + Q³, and its long-run marginal cost curve is MC(Q) = 40 − 20Q + 3Q². Over what range of output does the production function exhibit economies of scale, and over what range does it exhibit diseconomies of scale?

 

 

2.  A packaging firm relies on the production function Q = KL + K, with MP_L = K and MP_K = L + 1.

Assume that the firm’s optimal input combination is interior (it uses positive amounts of both inputs). Derive its long-run total cost curve in terms of the input prices, w and r. Verify that if the input prices double, then total cost doubles as well.

 

 

3.  A perfectly competitive industry consists of two types of firms: 100 firms of type A and 30 firms of type B. Each type A firm has a short-run supply curve s_A(P) = 2P. Each type B firm has a short-run supply curve s_B(P) = 10P. The market demand curve is D(P) = 5000 − 500P. What is the short-run equilibrium price in this market? At this price, how much does each type A firm produce, and how much does each type B firm produce?

 

 

4.  A market contains a group of identical price taking firms. Each firm has a marginal cost curve SMC(Q) = 2Q, where Q is the annual output of each firm. A study reveals that each firm will produce if the price exceeds $20 per unit and will shut down if the price is less than $20 per unit. The market demand curve for the industry is D(P) = 240 − P/2, where P is the market price. At the equilibrium market price, each firm produces 20 units. What is the equilibrium market price, and how many firms are in this industry?

 

 

5.  The global propylene industry is perfectly competitive, and each producer has the long-run marginal cost function MC(Q) = 40 − 12Q + Q². The corresponding long-run average cost function is AC(Q) = 40 − 6Q + Q²/3. The market demand curve for propylene is D(P) = 2200 − 100P. What is the long-run equilibrium price in this industry, and at this price, how much would an individual firm produce? How many active producers are in the propylene market in a long-run competitive equilibrium?