Question

#4 only please

ZOOM + 3. Suppose that Firm 1 and Firm 2 are Cournot competitors. Each still has a marginal cost of 2 and the inverse demand curve is given by: P 5 - .5Q. Calculate the equilibrium price and profit for both firms. Calculate the HHI 4. For the two firms in the previous question, suppose that Firm 1 lowers its marginal cost to 1. Calculate the new price and the prosit levels for each firm 5. Based on your answers to the previous two questions, are industry profits higher or lower after Firm 1 cuts its marginal cost? Is the HHI higher or lower

Answer 1

Market demand is given by P = 5 - 0.5(Q1 + Q2).

Now we have the profit function for firm 1 as π1 = (P - MC)Q1 and for firm 2 as π2 = (P - MC)Q2. This gives

π1 = (5 - 0.5Q1 - 0.5Q2 - 1)Q1 and π2 = (5 - 0.5Q1 - 0.5Q2 - 2)Q2

π1 = 4Q1 - 0.5Q1^2 - 0.5Q1Q2 and π2 = 3Q2 - 0.5Q2^2 - 0.5Q1Q2

Maximize profits and keep π1'(Q1) = π2'(Q2) = 0

4 - Q1 - 0.5Q2 = 0 and 3 - Q2 - 0.5Q1 = 0

Q1 = 4 - 0.5Q2 and Q2 = 3 - 0.5*(4 - 0.5Q2)

This gives Q2 = 1 + 0.25Q2 or Q2 = 1.33 and so Q1 = 3.33

New price = 5 - 0.5*(3.33 + 1.33) = $2.67

Profit for firm 1 = (2.67 - 1)*3.33 = $5.56 and for firm 2 profit = (2.67 - 2)*1.33 = $0.88