Assume a firm is a monopoly has a fixed cost of 500000000 a

Assume a firm is a monopoly, has a fixed cost of $5,000,000.00, a constant average variable cost of $95.00, and faces the following price-demand relationship q(p)-200,000- 800 p a. Compute the profit maximizing price level for the firm and state whether the firm is a price taker or a price setter b. Compute the elasticity of demand at the price level which maximizes profit. c. Compute the maximum profit. d. State and explain why the firm would be better of operating or shutting down.

Solution

a) Find inverse demand

800p = 200,000 - q

p = 200,000/800 - q/800

p = 250 - 0.00125q

TR = 250q - 0.00125q^2

Marginal revenue MR = 250 - 0.0025q

Monopolist produces where MR = MC

250 - 0.0025q = 95

q = 62000

price P = 250 - 0.00125*62000 = 172.50

It is a price setter as it sets the price

b) elasticity = slope of demand x price / quantity

= -800 x 172.50/62000

= -2.2258

c) Profit = TR - TC = 172.50*62000 - 5,000,000 - 95*62000 = -195,000

d) If it shuts down it bears a loss of fixed cost which is 5,000,000. In operations, it is bearing a smaller loss of 195,000 so continued business operations is a better / economical option.