A number of stores offer film developing as a service to their customers. Suppos

Question

A number of stores offer film developing as a service to their customers. Suppose that each store offering this service has a cost function (C) C(q) = 25 + 0.40q + 0.0625q2 and a marginal cost (MC) of MC(q) = 0.40 + 0.125q. If the going rate for developing a roll of film is $8.00: is the industry in long-run equilibrium? Find the price associated with long-run equilibrium. The market will be in long-run equilibrium when the price is $ 2.90. Suppose now a new technology is developed that will reduce the cost of film developing by 20 percent. Assuming that the industry is in long-run equilibrium, how much would any one store be willing to pay to purchase this new technology? Assuming that the market price remains at the above long-run equilibrium level, a firm would be willing to pay $ for the new technology.

Explanation / Answer

c.

If the total cost is reduced by 20%, C(q) would be as below:

(25 + 0.4q + 0.0625q^2) × (1 – 0.20)

20 + 0.32q + 0.05q^2

Marginal cost (MC) would the first order derivative of the new C(q)

MC = 0.32 + 0.1q

Since the above equilibrium is maintained, q would be 20.

MC = 0.32 + 0.1 × 20 = $2.32

Now the difference of equilibrium price, $2.9 and the new MC would be the amount of additional cost.

Answer: A firm would be will to pay ($2.9 - $2.32 =) $0.58.

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