Question

Based on the best available econometric estimates, the market elasticity of demand for your firm’s product is -1.5. The marginal cost of producing the product is constant at $125, while average total cost at current production levels is $190. Determine your optimal per unit price if:

a) You are a monopolist. $_____

b) You compete against one other firm in a Cournot oligopoly. $____

c) You compete against 19 other firms in a Cournot oligopoly. $_____

Answer 1

a).

If you are a monopolist, then you can determine the optimal unit price by using this formula:

Price = Markup * Marginal Cost

Here markup = [Elasticity of demand / (1 + Elasticity of demand)]

Here, Elasticity of demand = - 1.5.

So, Markup = [(- 1.5) / {1 + (- 1.5)}] = (- 1.5) / (- 0.5) = 3

So, if you are a monopolist then the optimal per unit price is (3 * $125) = $375.

So, Optimal per unit price, if you are a monopolist, is $375.

b)

Now if you compete against one other firm, then there is total two firms.

In that case, the formula for markup became:

Markup = [(No. of firm * Elasticity of demand) /{1 + (No. of firm * Elasticity of demand)}]

So, in this case, Markup = [{2 * (- 1.5)}] / [1 + {2 * (- 1.5)}] = (- 3) / (- 2) = 1.5.

If you compete against one other firm in a Cournot oligopoly then the optimal per unit price is (1.5 * $125) = $187.5.

So, Optimal per unit price, if you compete against one other firm is a Cournot oligopoly, is $187.5.

c)

Now if you compete against 19 other firms, then there is total 20 firms.

In that case, the formula for markup became:

Markup = [(No. of firm * Elasticity of demand) /{1 + (No. of firm * Elasticity of demand)}]

So, in this case, Markup = [{20 * (- 1.5)}] / [1 + {20 * (- 1.5)}] = (- 30) / (- 29) = 1.03.

If you compete against 19 other firms in a Cournot oligopoly then the optimal per unit price is (1.03 * $125) = $128.75.

So, Optimal per unit price, if you compete against 19 other firms is a Cournot oligopoly, is $128.75.