Question

With some services, e.g., checking accounts, phone service, or pay TV, a consumer is offered a choice of two or more payment plans. One can either pay a low entry fee and get a high price per unit of service or pay a high entry fee and a low price per unit of service. Suppose you have an income of $1000. There are two plans. Plan A has an entry fee of $20 with a price of $10 per unit. Plan B has an entry fee of $40 with a price of $5 per unit for using the service. Let ?2 be expenditure on other goods (i.e., ?2 is the numeraire) and let ?1 be the consumption of the service. Your utility function is given by ?(?1, ?2) = 100(?1)^(1/2) + ?2.

1. 1) Write down the budget equation that you would have after you paid the entry fee for each of the two plans. (6 points)

2. 2) Find the demand functions. (10 points)

3. 3) How much service would you use in each case? And how much would you

   spend on other goods? Clearly derive your results. (8 points)

4. 4) Which plan would you prefer? Explain. (6 pints)

Answer 1