With some services, e.g., checking accounts, phone service, or pay TV, consumers

Question

With some services, e.g., checking accounts, phone service, or pay TV, consumers choose between two or more payment plans. One can either pay a high entry fee and get a low price per unit of the service or pay a low entry fee and a high price per unit of the service. Suppose you have an income of $100. There are two plans. Plan A has an entry fee of $20 with a price of $2 per unit of the service. Plan B has an entry fee of $40 with a price of $1 per unit of service. Let x be expenditure on other goods (in dollars) and y be consumption of the service. (a) Write down the budget equation that you would have after you paid the entry fee for each of the two plans. (b) If your utility function is U(x; y) = xy, how much y would you choose in each case? (c) Which plan would you prefer? Explain.

Explanation / Answer

(a)

Option 1:

Budget line is

100 = X + 20 + 2Y

80 = X + 2Y

Option 2:

Budget Line is

100 = X + 40 + Y

60 = X + Y

(b)

U = XY

MUX = dU / dX = Y

MUY = dU / dY = X

So, MRS = MUX / MUY = Y / X

In optimum condition, MRS = PX / PY

Or,

(Y / X) = 2 / 1 = 2

Y = 2X

Substituting in budget line:

(i) Option 1:

80 = X + 2Y

80 = X + (2 x 2X) = 5X

X = 16

Y = 2X = 32

(ii) Option 2:

60 = X + Y

60 = X + 2X = 3X

X = 20

Y = 2X = 40

(c)

Total utility, option 1: XY = 16 x 32 = 512

Total utility, option 2: XY = 20 x 40 = 800

Since total utility is higher in option 2, I would choose option 2.

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