Question

# Please show all work. 3) Based on the best available econometric estimates, the market elasticity of...

3) Based on the best available econometric estimates, the market elasticity of demand for your firm’s product is -2. The marginal cost of producing your product is constant at \$50.

a. What is your optimal per unit price if you are a monopolist?
b. What is your optimal per unit price if you compete against one other firm in a Cournot

oligopoly? What is your optimal per unit price if you compete against 20 other firms in a

Cournot oligopoly?
c. What price pattern are you seeing between parts a and b? Explain why this makes intuitive

sense (hint: at what price will you eventually sell your product if the number of firms

continues to increase?).

Market elasticity is -2. Marginal cost is \$50. We have P = MC * (NE/NE + 1) where N is number of firms, MC is marginal cost and E is price elasticity of demand (market).

a) A monopoly has 1 seller. This implies N = 1. Hence the price is P = 50*(-2*1/-2*1+1) or 50*(-2/-1) = \$100.

b) Cournot has N = 2. This gives a price P = 50*(-2*2/-2*2 + 1) or 50*(-4/-3) = \$66.67. Now when N = 21 (including the incumbent seller), price is P = 50*(-2*21/-2*21 + 1) = \$51.22

c) As the number of firms increases, the market power declines and the firm is not able to charge a higher price. This shows that competition decreases the price of the product.

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