Working together through collusion

Chapter 11: Oligopoly: I Need You

By solving this set of equations simultaneously, the cartel’s profit-maximizing quantity of output and price are determined. In addition, the quantity of output each firm produces to minimize production cost is determined.

1. Determine total revenue as a function of quantity.

Because firms A and B are acting together, the market demand curve becomes the cartel’s demand curve. Determine total revenue as a function of quantity by multiplying price from the market demand curve times quantity.

201

2. Determine marginal revenue.

To determine marginal revenue, take the derivative of total revenue with respect to Q.

3. Set MR = MCA.

4. Substitute qA + qB for Q.

Because the total quantity of output the cartel sells, Q, is produced in some combination from firms A and B, the quantities produced by each firm added together must equal the quantity sold by the cartel.

5. Solve the equation in Step 4 for qA.

6. Set MCA equal to MCB.

7. Substitute qA = 200 – 0.5qB in the equation in Step 6.