Question

The global DVD manufacturing industry is perfectly competitive. Each firm has a shout-run total cost function T = 100 + 3 − 82 + 30, where is the firm’s annual output and all of the firm’s fixed cost is sunk. There are currently 15 identical firms in the industry. The market demand for DVD is = 132 − P. What is each firm’s producer surplus when the market price is $25?

Answer 1

Each firm's producer surplus when the market price is $25 is -$168 by calculations.

Step-by-step explanation:

In order to calculate the producer surplus for each firm in the global DVD manufacturing industry, we first need to determine the equilibrium quantity in the market. To do this, we set the market demand equation equal to the market supply equation:

Qd = Qs

132 - P = 15Q

Where Qd represents the quantity demanded, Qs represents the quantity supplied, and P represents the price. Substituting the market price of $25 into the equation:

132 - 25 = 15Q

107 = 15Q

Q = 7.13

Since production quantities must be whole numbers, each firm will produce 7 DVD units. To calculate the producer surplus for each firm, we need to find the area between the market price and the firm's marginal cost curve up to the quantity produced. The marginal cost curve can be calculated by taking the derivative of the total cost function with respect to output:

MC = dT/dQ = 3 - 164 + 30Q

MC = 3 - 164 + 30(7)

MC = 3 - 164 + 210

MC = 49

Therefore, each firm's producer surplus when the market price is $25 is the area between the market price ($25) and the marginal cost curve up to the quantity produced (7 units):

Producer Surplus = (P - MC) * Q

Producer Surplus = (25 - 49) * 7

Producer Surplus = -24 * 7

Producer Surplus = -168