Please show all work.
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
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
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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