Suppose that the market demand for rose hips is given by P 100 Q There are two

# Suppose that the market demand for rose hips is given

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20. Suppose that the market demand for rose hips is given by P= 100 Q. There are two firms, A and B, producing rose hips, each at a constant marginal and average total cost of \$5. Fill in the table below for each market structure.Collusive MonopolyCournot OligopolyBertrand OligopolyStackelberg Oligopoly (A is first- mover)A’s Quantity B’s QuantityIndustry QuantityPriceA’s ProfitB’s ProfitIndustry Profit20. Collusive MonopolyCournot OligopolyBertrand OligopolyStackelberg Oligopoly (A is first- mover)A’s Quantity 23.7531.6747.5047.50B’s Quantity23.7531.6747.5023.75Industry Quantity47.5063.339571.25Price\$52.50\$36.67\$5\$28.75A’s Profit\$1,128.13\$1,002.70\$0\$1,128.13B’s Profit\$1,128.13\$1,002.70\$0\$564.06Industry Profit\$2,256.25\$2,005.40\$0\$1,692.19Goolsbee1e_Solutions_Manual_Ch11.indd 167Goolsbee1e_Solutions_Manual_Ch11.indd 16711/15/12 3:09 PM11/15/12 3:09 PM
168Part 3 Markets and PricesThe Collusive Monopoly CaseFirms produce exactly the same output and sell it at the price where MC= MR, that is,MR= 100 2Q= 5 = Q= 47.50Thus, each firm produces 23.75 units of output. The monopolistic price isP= 100 Q= \$52.50Both Firm A and Firm B generate the same profit, which is equal toTRTC= (\$52.50 \$5) × 23.75 = \$1,128.13The profit for the industry is \$2,256.25.The Cournot Oligopoly CaseThe inverse demand function isP= 100 q Aq The residual marginal revenue for Firm i= {A, B} isMR= 100 2q Aq Therefore, the reaction function for Firm iis100 2q Aq Bq A= 47.5 0.5 Therefore, the output produced by Firm A and Firm B isq1= 47.5 0.5 q2= 47.5 0.5(47.5 0.5q1) = 23.75 + 0.25 q A= 31.67 = q The output for the industry is 63.33. The price isP= 100 q Aq B= \$36.67Both firms earn the same profit, which is equal toTRTC= (\$36.67 \$5) × 31.67 = \$1,002.70Hence, the profit for the industry is\$1,002.70 × 2 = \$2,005.40The Bertrand Oligopoly CaseBoth firms will sell the product at the marginal cost of \$5 and each will produce exactly the same quantity, that is,5 = 100 2 q q i= 47.50Since firms sell output at the marginal cost, each firm’s profit is \$0; thus, the industry profit is also equal to \$0.The Stackelberg Oligopoly CaseThe reaction function for Firm B is100 q A2q Bq B= 47.5 0.5 Assuming that Firm A is the first-mover, the inverse demand function faced by Firm A isP= 100 q Aq B= 100 q A47.5 + 0.5 q A= 52.5 MCBB= 5q Bq1Bi= 5q A0.5 q AGoolsbee1e_Solutions_Manual_Ch11.indd 168Goolsbee1e_Solutions_Manual_Ch11.indd 16811/15/12 3:09 PM11/15/12 3:09 PM
Imperfect Competition Chapter 11 169Equating the marginal revenue with marginal cost, the quantity produced by Firm A isMR= 52.5 q A= 5q A= 47.50Thus, Firm B producesq B= 47.5 0.5 q A= 47.5 0.5 × 47.5 = 23.75The industry quantity is 71.25. The price isP= 100 q Aq B= \$28.75Firm A generates a profit ofT R ATC A= (\$28.75 \$5) × 47.50 = \$1,128.13Firm B generates a profit ofTR BT C B= (\$28.75 \$5) × 23.75 = \$564.06Thus, the industry’s profit is \$1,692.19.Goolsbee1e_Solutions_Manual_Ch11.indd 169Goolsbee1e_Solutions_Manual_Ch11.indd 16911/15/12 3:09 PM11/15/12 3:09 PM
Goolsbee1e_Solutions_Manual_Ch11.indd 170Goolsbee1e_Solutions_Manual_Ch11.indd 17011/15/12 3:09 PM11/15/12 3:09 PM