Suppose that the market for toothbrushes is perfectly competitive and has 100 pr

Question

Suppose that the market for toothbrushes is perfectly competitive and has 100 producers. Out of these producers, 60 are "low-cost" producers whose individual average variable cost and marginal cost curves are AVC = 1 + 0.4Q MC = 1 + 0.8Q and 40 firms are "high-cost producers whose individual average variable cost and marginal cost curves are AVC 1 0.50 MC = 1 + Q where Q is the quantity of toothbrushes produced (in thousands per day) a. Derive the short-run supply curves for a low-cost producer and for a high-cost producer. b. Derive the market short-run supply curve. c. If the market demand curve for toothbrushes is given by Q230 - 57.5P, what are the market equilibrium price and quantity of toothbrushes? d. At the market price, how many toothbrushes does each low-cost firm produce? Each high-cost firm? LLe. When the market is in equilibrium, what is the industry producer surplus?

Explanation / Answer

a) Supply curve of a firm is the rising portion of MC beyond the minimum of AVC. For both producer type, the supply curves are

P = 1 + 0.8Q and P = 1 + Q

or

0.8Q = P - 1 and Q = P - 1

or

Q = 1.25P - 1.25 and Q = P - 1

b) Market supply curve is the addition of individual supply curves

60Q = 60*1.25P - 60*1.25 and 40Q = 40P - 40

QL = 75P - 75 and QH = 40P - 40

Total Q = 105P - 105

c) Market demand Q = 230 - 57.5P

Equilibrium price and quantities are

105P - 105 = 230 - 57.5P

P = 2, Q = 115 (approx)

d) Low cost tooth brushes QL = 75P - 75 = 75*2 - 75 = 75 andHigh cost toothbrushes QH = 40*2 - 40 = 40

e) Surplus = 0.5*(4 - 1)*115 = 172.50

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