CHAPTER 11 • Pricing with Market Power 441 What about the engine manufacturer? It chooses the price of engines, PE, to maximize its profit: pE = (PE - cE)Q(PE) = (PE - cE) (A - PE) (A11.6) You can confirm that the profit-maximizing price of engines is:3 PE* = (A + cE) (A11.7) The profit to the engine manufacturer is then equal to: pE* = (A - c E)2 (A11.8) Now go back to Equation (A11.5) for the profit to the automobile manufacturer, and substitute in Equation (A11.7) for the price of engines You will see that the automobile company’s profit is then: pA* = (A - c E)2 16 (A11.9) Hence the total profit for the two companies is: p TOT* = p A* + p E* = (A - cE)2 16 (A11.10) Also, the price of cars paid by consumers is: P* = (3A + cE) (A11.11) VERTICAL INTEGRATION Now suppose that the engine company and the automobile company merge to form a vertically integrated firm The management of this firm would choose a price of automobiles to maximize the firm’s profit: p = (P - cE)(A - P) (A11.12) The profit-maximizing price of cars is now: P* = (A + cE)/2 (A11.13) (A - cE)2 (A11.14) which yields a profit of: p* = Now take the derivative of pE with respect to PE and set it equal to zero