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.

Find the demand functions:

Answer 1

Budget constraint

Plan a

10 x1 + x2 =1000-20

10x1 + x2= 980

Plan b

5x1 + x2 = 1000-40

5x1 + x2 = 960

Utility function, U:

So MRS= MUx1/MUx2

=

Plan a

MRS=px/py

=10/1

x1=25

put the value of x1 in the budget constraint

10(25)+x2=980

x2=980-250=730

Plan b

MRS=px/py

=5/1

x1= 100

put the value of x1 in budget constraint

5(100)+x2=960

x2=460