Jim Scott owns Jim's automated Car Wash which operates in a medium size southeastern city. Jim's main competition comes from the local franchise of Clean-Car, which is part of a nationwide chain. Jim's has been washing an average of 1000 cars per week at a price of $5.00 per car. Clean Car recently reduced its price from $10 to 7.50 per car causing a weekly total for Jim to fall to 750 cars.
a. What is the cross-price elasticity between Jim's car washes and Clean Car?
b. Jim has heard a reliable rumor that Clean Car plans to cut price again to $5.00. Assuming that the cross-price elasticity is constant, how many cars can Jim expect to wash if clean car's price is actually lowered to $5.00?
c. Assume that Clean-Car has in fact lowered its price to $5.00 and Jim decides to counter by altering his price. What price would Jim have to charge in order to regain his original market share of 1000 cars? (Note: you must reason this out. There is no mathematical solution)