The Hidden Dog Fence company sells invisible electric fences to contain dogs within yards. For a half-acre lot, the cost is $2,000 for the system and installation. The market for invisible dog fencing is competitive: Several companies sell similar products at about the same price. In each case, the dog wears a battery-powered collar. The collar give the dog a shock if it gets near the boundary of the property. Hidden Fence uses a specially designed collar that uses batteries made specifically for Hidden Fence by the Battery-O-Vac Company. The batteries last for 3 months and cost $25 apiece. Hidden Fence has a patent on these batteries, and there are no alternative source of supply. Other fence companies produce products that use generic batteries. Currently, the battery costs of these other systems are the same as for Hidden Fence.

a. Suppose that you purchase the system from Hidden Fence. After you purchase the system, how much will Hidden Fence be able to raise the price of its batteries before you discontinue use of the system and buy a different system from another company? (Suppose that you do want to maintain an invisible fence.) For this question, assume a 10 percent annual discount rate, no inflation, and an infinite life for the invisible fence, yourself, and the patent for the batteries. 

b. As the management of Hidden Fence Company, what might you do to convince a worried prospective customer that opportunistic behavior with respect to battery prices is not a likely occurrence?