Brake repair and muffler repair require many tools and other capital equipment that can be classified as shared or common inputs.
a. What are some of these shared or common inputs in muffler and brake repair?
b. Are brake repairs and muffler repairs joint products? Why or why not?
Firms that produce only muffler repair services must spend $900,000 on common inputs used in brake and muffler repair. The marginal cost of muffler repair is $50. The long-run total cost function for a firm specializing in muffler repair is

LTC(Q_M) = 900,000 + 50Q_M

Firms that produce only brake repair services must also spend $900,000 on common inputs used in brake and muffler repair. The marginal cost of brake repair is $50. The long-run total cost function for a firm specializing in brake repair is

LTC(Q_B) = 900,000 + 60Q_B 

Firms that do only muffler repair work or only brake repair work can extend their service line to include the other type of repair work by spending $25,000 to train their mechanics to do the new type of repair work and to undertake initial advertising costs to inform consumers of the new service.
c. Write the mathematical expression for the multi product long-run total cost function LTC(Q_M,Q_B), which gives the long-run total cost for a repair shop doing Q_M muffler repairs and Q_B brake repairs.
d. A small company, All Brakes and Mufflers, Inc., plans to perform 5,000 muffler repairs and 4,000 brake repairs annually. Use the multi product cost function in part c to calculate the long-run total cost for All Brakes and Mufflers to produce this combination of services.
Down the street from All Brakes and Mufflers are two rival firms, Just Brakes Inc. and Just Mufflers Inc., which each specialize in doing only one type of repair work.
e. Just Mufflers, Inc. plans to perform 5,000 muffler repairs annually. Calculate the total costs for Just Mufflers, Inc. to do 5,000 muffler repairs.
f. Just Brakes, Inc. plans to perform 4,000 brake repairs annually. Calculate the total costs for Just Brakes, Inc. to do 4,000 brake repairs.
g. Do you find evidence of economies of scope in brake and muffler repair? Explain why using your answers in parts d, e, and f.
h. What are the implications of your finding in part g for the nature of competition in this brake and muffler repair market? How do you explain the fact that specialty companies like Just Brakes or Just Mufflers sometimes do compete successfully with multiservice rivals that do both brake and muffler repair?