# Chapter 1. Figure It Out 11.2

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OilPro and GreaseTech are the only two firms who provide oil changes in a local market in a Cournot duopoly. The oil changes performed by the two firms are identical, and consumers are indifferent about which firm they will purchase an oil change from. The market inverse demand for oil changes is P = 100 – 2Q, where Q is the total number of oil changes (in thousands per year) produced by the two firms, qO + qG. OilPro has a marginal cost of \$12 per oil change, while GreaseTech has a marginal cost of \$20. Assume that neither firm has any fixed cost.

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### Question

How many oil changes will each firm produce in a Cournot equilibrium?

OilPro will produce zhw5AiG32jY= thousand oil changes.

GreaseTech will produce DDH6Tw1RFEk= thousand oil changes.

The profit-maximizing number of oil changes can be found by combining the two firms’ reaction functions and then solving for output. OilPro’s reaction function is qO = 22 – 0.5qG; GreaseTech’s is qG = 20 – 0.5qO. Substitute GreaseTech’s reaction function into OilTech’s to find that qG = 22 – 0.5(20 – 0.5qO), and solve to find qO = 16. Then, substitute 16 for qO in GreaseTech’s reaction function to find that qG = 12. For further review see section “Oligopoly with Identical Goods: Cournot Competition”.

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### Question

What will the market price for an oil change be?

The price of oil changes will be \$ LOXpWXxH6ie30/5l .

To determine the market price, substitute each firm’s output into the inverse demand curve, P = 100 – 2(qO + qG). OilTech produces 16 units; GreaseTech produces 12. So, the market price is 100 – 2(16 + 12), or \$44. For further review see section “Oligopoly with Identical Goods: Cournot Competition”.

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### Question

How much profit does each firm earn?

OilPro earns \$ GoudNZ/Oz9vIoPjR thousand profit.

GreaseTech earns \$ zqXJ9fv1hq+d2wqv thousand profit.

OilPro sells 16,000 oil changes for \$44 each. Because OilPro’s marginal cost is \$12 (and there are no fixed costs), OilPro earns \$32 profit on each oil change. So, OilPro’s profits are \$32 × 16,000, or \$512,000. GreaseTech sells 12,000 oil changes for \$44 each. Because GreaseTech’s marginal cost is \$20 (and there are no fixed costs), GreaseTech earns \$24 profit on each oil change. So, GreaseTech’s profits are \$24 × 12,000, or \$288,000. For further review see section “Oligopoly with Identical Goods: Cournot Competition”.