1. Investment in Bertrand competition with differentiated goods In the market for electric cars, firm 1 is a pioneer who invests k₁ in R&D for efficient production. Firm 1's total production cost is given by C₁(9₁) = (10-k₁)q₁+k². The demand for firm 1's electric cars is given by q1 = 20-2p1+P2. On the other hand, firm 2 is a latecomer whose total production cost is given by C₂ (92) 1092. The demand for firm 2's electric cars is given by q2 = 20 - 2p2 + P₁. Assume the two firms compete by setting prices after firm 1 invests k₁. = 1.1. What are the equilibrium prices, (p₁, p2), in terms of k₁? (Hint: find the best response func- tions.) 1.2. What is firm 1's optimal level of investment, k₁? 1.3. Use your answers to questions 1 and 2 to compute the equilibrium profits. Does firm 1 have an advantage over firm 2? 1.4. Suppose firm 2 charges p2 = 12.60 regardless of p₁. Note that P2 = 12.60 is roughly how much firm 2 would charge in equilibrium in question 2. What is firm 1's optimal level of investment, k₁, in this case? 1.5. Compare firm 1's optimal investment level in questions 2 and 4. Explain whether firm 1 has a strategic incentive to overinvest or underinvest using Fudenberg and Tirole (1984)'s taxonomy.
1. Investment in Bertrand competition with differentiated goods In the market for electric cars, firm 1 is a pioneer who invests k₁ in R&D for efficient production. Firm 1's total production cost is given by C₁(9₁) = (10-k₁)q₁+k². The demand for firm 1's electric cars is given by q1 = 20-2p1+P2. On the other hand, firm 2 is a latecomer whose total production cost is given by C₂ (92) 1092. The demand for firm 2's electric cars is given by q2 = 20 - 2p2 + P₁. Assume the two firms compete by setting prices after firm 1 invests k₁. = 1.1. What are the equilibrium prices, (p₁, p2), in terms of k₁? (Hint: find the best response func- tions.) 1.2. What is firm 1's optimal level of investment, k₁? 1.3. Use your answers to questions 1 and 2 to compute the equilibrium profits. Does firm 1 have an advantage over firm 2? 1.4. Suppose firm 2 charges p2 = 12.60 regardless of p₁. Note that P2 = 12.60 is roughly how much firm 2 would charge in equilibrium in question 2. What is firm 1's optimal level of investment, k₁, in this case? 1.5. Compare firm 1's optimal investment level in questions 2 and 4. Explain whether firm 1 has a strategic incentive to overinvest or underinvest using Fudenberg and Tirole (1984)'s taxonomy.
Chapter8: Perefect Competition
Section: Chapter Questions
Problem 11SQ
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Transcribed Image Text:1. Investment in Bertrand competition with differentiated goods
In the market for electric cars, firm 1 is a pioneer who invests k₁ in R&D for efficient production.
Firm 1's total production cost is given by C₁(9₁) = (10− k₁)q1+k². The demand for firm 1's electric
cars is given by 91 20−2p₁+p2. On the other hand, firm 2 is a latecomer whose total production
cost is given by C2(92) = 10q2. The demand for firm 2's electric cars is given by q2 = 20 − 2p2 +P₁.
Assume the two firms compete by setting prices after firm 1 invests k₁.
1.1. What are the equilibrium prices, (p₁,P2), in terms of k₁? (Hint: find the best response func-
tions.)
1.2. What is firm 1's optimal level of investment, k₁?
1.3. Use your answers to questions 1 and 2 to compute the equilibrium profits. Does firm 1 have
an advantage over firm 2?
=
1.4. Suppose firm 2 charges p2 12.60 regardless of p₁. Note that p2 12.60 is roughly how much
firm 2 would charge in equilibrium in question 2. What is firm 1's optimal level of investment, k₁,
in this case?
=
1.5. Compare firm l's optimal investment level in questions 2 and 4. Explain whether firm 1 has a
strategic incentive to overinvest or underinvest using Fudenberg and Tirole (1984)'s taxonomy.
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