Joe buys two goods, internet usage and \"all other\" goods. His marginal utility

Question

Joe buys two goods, internet usage and "all other" goods. His marginal utility for each hour of internet usage, H, is 1/H, and his marginal utility for each unit of all other goods, A, is 4/A. For the questions that follow, assume that the price of each unit of all other goods is $1 and that his total expenditure is $100. Suppose internet usage costs SI per hour. Find Joe's optimum point and illustrate it with an indifference curve and budget line diagram. Derive and draw Joe's demand curve for internet usage. The government decides to subsidize pay-as-you-go Internet access, lowering Joe's hourly internet usage price to $0.25 per hour. Find Joe's new optimum point for both internet usage and all other goods, and illustrate it on the diagram from part a. The company allows Joe two options: he can continue to purchase Internet access at the subsidized price, OR he can switch to a plan that costs a $20 monthly fee for unlimited Internet access, but caps internet usage at 80 hours per month. Illustrate this plan as a budget constraint in a new diagram. Will Joe choose this plan?

Explanation / Answer

At the optimum level,

            MRSHA= MUH/MUA

                                = (1/H)/(4/A)

                        = A/4H

The budget constraint is

            PHH + PAA = 100

            PHH + A = 100

            PHH + 4PHH = 100

            H= 20/PH

which is the demand function of H.

When the price of internet usage is $1, then

H = 20/1

    = 20 hours

and

A = 4 (1) 20 = 80 units

(b) When the price of internet usage is $0.25, then

H = 20/0.25

    = 80 hours

and

A = 4 (0.25) 80 = 80 units

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