Problem 2 Cournot Competition and Acquisition (16 points) Firm A and rm B compete in the same market by simultaneous quantity competition. Firms can choose any quantity Q 2 U. The inverse market demand curve is P (Q) : 40 2Q. Both rms have cost functions C (Q) : 2Q2, implying a marginal cost function of -f C (Q) : 4Q. 1. Determine Firm A's best response function, QA (QB), to any quantity choice by rm B, Q3 2 0. By similar argument determine B's best response function, QB (QA). 2. Determine the Cournot equilibrium of the economy. (Hint: In this case, the equilibrium is symmetric with each rm choosing the same quantity.) (a) State the equilibrium quantity provided by each rm, QC. (b) State the equilibrium market price. (c) State the prots of each individual rm in the equilibrium, H9. 3. Firm A is considering the (likely illegal) possibility of bribing rm B to leave the market. Specically, Firm A can make rm B set Q B = 0 by giving a bribe of HG. ls it advantageous for Firm A to do so? 4. Firm A is considering acquiring rm B at a price equal to B's Cournot prots. Once acquired, Firm A would then have access to two plants each with a cost function of C (Q) = 2Q2. If rm A wanted to produce Q units it is then optimal to divide the production equally across the two plants, each plant producing Q / 2. (a) State Firm A's new cost function where production of Q units is spread equally across the two plants, that is the combined production cost across the two plants. (b) Having acquired rm B, rm A is now a monopolist in the market. Determine its prots given its new production function determined in question 4(a). Make sure to subtract the acquisition cost from A's prots. Given your calculations, is it advantageous for rm A to acquire rm B ? Make sure to show your calculations. 5. Questions 3 and 4 are both cases where Firm A achieves monopoly at a price of HG. Explain the core difference between the two cases. Problem 2 Cournot Competition and Acquisition (16 points) Firm A and rm B compete in the same market by simultaneous quantity competition. Firms can choose any quantity Q 2 U. The inverse market demand curve is P (Q) : 40 2Q. Both rms have cost functions C (Q) : 2Q2, implying a marginal cost function of -f C (Q) : 4Q. 1. Determine Firm A's best response function, QA (QB), to any quantity choice by rm B, Q3 2 0. By similar argument determine B's best response function, QB (QA). 2. Determine the Cournot equilibrium of the economy. (Hint: In this case, the equilibrium is symmetric with each rm choosing the same quantity.) (a) State the equilibrium quantity provided by each rm, QC. (b) State the equilibrium market price. (c) State the prots of each individual rm in the equilibrium, H9. 3. Firm A is considering the (likely illegal) possibility of bribing rm B to leave the market. Specically, Firm A can make rm B set Q B = 0 by giving a bribe of HG. ls it advantageous for Firm A to do so? 4. Firm A is considering acquiring rm B at a price equal to B's Cournot prots. Once acquired, Firm A would then have access to two plants each with a cost function of C (Q) = 2Q2. If rm A wanted to produce Q units it is then optimal to divide the production equally across the two plants, each plant producing Q / 2. (a) State Firm A's new cost function where production of Q units is spread equally across the two plants, that is the combined production cost across the two plants. (b) Having acquired rm B, rm A is now a monopolist in the market. Determine its prots given its new production function determined in question 4(a). Make sure to subtract the acquisition cost from A's prots. Given your calculations, is it advantageous for rm A to acquire rm B ? Make sure to show your calculations. 5. Questions 3 and 4 are both cases where Firm A achieves monopoly at a price of HG. Explain the core difference between the two cases