Chapter 1. Figure It Out 11.3

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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. Neither firm has any fixed cost. In FIO 11.2, it was determined that OilPro’s reaction function is qO = 22 – 0.5qG; GreaseTech’s reaction function is qG = 20 – 0.5qO.

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Question

To maximize profit, how many oil changes should OilPro perform?

OilPro should perform 7dfNq0tWt7c= thousand oil changes.

To determine the profit-maximizing level of output, equate OilPro’s marginal revenue and marginal cost. OilPro’s demand is P = 60 – qO, so OilPro’s marginal revenue is MR = 60 – 2qO. Setting marginal revenue equal to OilPro’s \$12 marginal cost, 12 = 60 – 2qO, which can be solved to find qO= 24. For further review see section “Oligopoly with Identical Goods: Stackelberg Competition”.

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Question

How many oil changes will GreaseTech produce?

GreaseTech will produce L6bSXEGJIC8= thousand oil changes.

GreaseTech’s profit-maximizing output can be found by substituting OilPro’s chosen output into GreaseTech’s reaction function, qG = 20 – 0.5qO. First-mover OilPro maximizes profit by producing 24 thousand oil changes, so qG = 20 – 0.5(24), or 8 thousand oil changes. For further review see section “Oligopoly with Identical Goods: Stackelberg Competition”.

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Question

How much profit will each firm earn?

OilPro will earn \$ AesOOFia2+y+8DLP thousand dollars.

GreaseTech will earn \$ Oi7XmnZ0Z7MvoKbx thousand dollars.

To find the firms’ profits, first determine the market price. Demand is given by P = 100 – 2Q, where Q is the combined output of the two firms, 32,000 oil changes. Substituting 32 for Q, the market price of an oil change must be \$36. OilPro, with a marginal cost of \$12, performs 24,000 oil changes, and earns (\$36 – \$12) on each change, for total profit of 24,000 × (\$36 – \$12), or \$576,000. GreaseTech, with marginal cost of \$20, performs 8,000 oil changes and earns (\$36 – \$20) on each one, for total profit of (\$36 – \$20)8,000 × (\$36 – \$20), or \$128,000. For further review see section “Oligopoly with Identical Goods: Stackelberg Competition”.