Question from Past Microeconomics Qualifying ExamEdit
Spring 2006 - Section II, Question two, George Mason University
Suppose MCI, the long distance telephone company, offers two calling plans. If you sign up for the full-price plan, you pay $1 for each hour of long-distance calls that you make. Under the discount plan, you only pay 25¢ per hour, but you must pay a monthly fee of $6. So a person who makes eight hours worth of calls per month pays the same amount under either plan.
(a)Draw the budget lines under the two plans between hours of long-distance calls and all other goods for a person with income equal to I and price of all other goods equal to $1.
(b)After analyzing a year's worth of data, MCI finds that no one under either plan makes exactly eight hours of calls per month. Use your diagram in part (a) to show why.
(a) Take Long Distance Calls on Y and All other goods on X axis.
Full-price plan budget constraint is a straight line with intercepts I and I on each axis where I is Income.
Discount plan budget constraint is also a straight line, with intercept (I-6) on X and (I-6)/0.25 on Y axis.
This should give you two budget constraints that cut each other at (I-8,8).
(b) Since the two budget constraints cut each other, there is a region in each where it is strictly better than the other budget. A telephone customer's ex ante consumption set (combinations he can possibly consume with one or the other plan) is thus the union of the two budget constraints. This locus is discontinous at (I-8,8). Using the assumption of smooth Indifference curves (i.e. not kinked), this implies that any indifference curve that passes through (I-8,8) MUST be dominated by at least one point in the consumption set. Hence, no customer will be satisfied by the intersection point at which 8 calls are made.
The rough intuition goes as follows: assume you are currently consuming 8 calls with the full-price plan. You are at least as well off by a switch to the discounted plan. If you make the switch however, your marginal cost per call goes down and you are more likely to make more calls. Alternatively, if you were on a discounted plan and switch to a full-price plan, the marginal savings from reducing calls increases from 25cents to one dollar, making you likely to reduce your number of calls. Either way, you may do better by switching. Note that this is NOT a rigorous answer.
Essentially I think MCI's data shows that none of their customers value their 8th call at more than $1 but their 9th call at less than 25 cents.