You are working as an economist for Tesla. Tesla needs to price its newest car, the Model K. However, there is some overlap in the customer base between the Model K and its existing Model Y. Suppose pK is the price of the Model K and pY is the price of the Model Y. The demand for the Model K is given by qK = 1002pK +pY and the demand for the Model Y is given by qY = 50 pY + 1 /2 pK..

aCalculate the own-price elasticity of the Model K (the elasticity of qK with respect to pK) and the own-price elasticity of the Model Y (the elasticity of qY with respect to pY ). Hint: Your answer should be a function of pK and pY .

bSuppose you are the manager of the Model K line. The marginal cost of the Model K is constant and equal to 10. Given some price pY , what price should you set to maximize profits?

cNow suppose you are the manager of the Model Y line. The marginal cost of the Model Y is constant and equal to 20. Given some price pK, what price should you set to maximize profits?

dSuppose that Tesla is poorly managed, and each line is priced independently. Use your answers to the previous two parts to find the prices, quantities, and profits for each line. What are the Tesla's total profits?

eNow suppose that the firm sets both prices simultaneously. What are the resulting prices? What is the total profit? How does it differ from what you found in the previous part?