A duopoly faces the demand curve D(p)= 30 - .5p.Both firms in the industry have a total cost function given by C(q)= 4q.Suppose that firm 1 is a Stackelberg leader in choosing its quantity first.Firm 1's profit function can be written as A)q₁ = 14 - .5q₂. B)q₂ = 14 - .5q₁. C)28q1 - q²₁. D)56q1 - q²₁. E)60q - q².

Question

Quizplus · Accepted Answer

The correct answer is C because the profit function for firm 1 is given by:π1 = (p - 4)q1where p is the market price and q1 is firm 1's quantity.Substituting the demand curve into the profit function, we get:π1 = (30 - .5p - 4)q1= 26q1 - .5p * q1= 26q1 - .5 * (30 - .5q1) * q1= 26q1 - 15q1 + .25q1^2= 11q1 + .25q1^2= 28q1 - q^2₁

A Duopoly Faces the Demand Curve D(p)= 30 -