A consumer is trying to decide between 2 long-distance calling plans. The first one charges a...

A consumer is trying to decide between 2 long-distance calling plans. The first one charges a flat rate of 10 cents/min, while the second charges a flat rate of 99 cents for calls up to 20 minutes and then 10 cents for each additional minute exceeding 20 minutes (assume that calls lasting a noninteger number of minutes are charged proportionally, e.g. 6 seconds is 1/10 of a minute and so 6 seconds over 20 minutes would be charged 1 cent). Suppose the consumer’s distribution of call duration is exponential with parameter λ.

a. Explain intuitively how the choice of calling plan should depend on what the expected call duration is.

b. Which plan is better if expected call duration is 10 min? 15 min? [Hint: Let h1(x) denote the cost for the first plan when call duration is x minutes and let h2(x) be the cost function for the second plan. Give expressions for these two cost functions, and then determine the expected cost for each plan.]

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orchestra answered 1 year ago

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