Question

Sally is an MTSU student. She is interested in shopping for a new cell phone plan. Currently, there are two cell phone companies that offer service in her area: AT&T and Verizon. Being a diligent consumer, Sally visits both AT&T and Verizon to find out about their current prices. AT&T charges customers $200 for a phone, but then charges $0.10 per minute for all calls. Verizon, on the other hand, gives customers a free phone but charges $0.50 per minute for all calls.

Sally has the following utility function for minutes of cell phone calls (M) and all other goods (A): U = A^3/4M^1/4. Assume that Sally’s income is $400 and the price of all other goods is $1 (i.e. P_A = $1).

a. On the same graph, draw Sally’s two budget constraints: one constraint if she chooses AT&T and another budget constraint if she chooses Verizon. Put “all other goods” on the vertical axis and cell phone minutes on the horizontal axis. Be sure to label ALL relevant information (intercepts, etc.).

b. Fill in the blank in the following sentence: “Sally will definitely prefer AT&T if she plans to talk at least ______ minutes on the cell phone.” Explain your answer. Note: you should not solve the utility maximization problem to answer this question.

c. Find Sally’s utility maximizing choices of A and M if she purchases AT&T’s plan. What is her utility?

d. Find Sally’s utility maximizing choices of A and M if she purchases Verizon’s plan. What is her utility?

e. Which plan does she – ultimately – prefer?

Answer 1

b,c for ATnt

a+0.10m = 400 - 200

a+0.10m = 200

b.c for verizon

a+0.50m = 400

  

b) 800 minutes

c) fo rmaximization

mrs =pa/pm

mua/mum = pa/pm

(3/4a^-1/4 *m^1/4 ) / 1/4m^-3/4 . a^3/4 = 1 / 0.10

3m/a = 10

3m = 10a

m = 10a/3

putting in in b.c

a+0.1m = 200

a + 0.1*10a/3 = 200

4a/3 =200

a = 150

m = 500

U = 42.86 *4.72 = 202.2

d) For verizon'

mua/mum = pa/pm

(3/4a^-1/4 *m^1/4 ) / 1/4m^-3/4 . a^3/4 = 1 / 0.50

3m/a = 2

m = 2a/3

putting it in b.c

a + 0.5m = 400

a+0.5*2a/3 = 400

4a/3 = 400

a = 300

m = 200

U = 72.08*3.76 = 271.08

e) She will prefer plan Verizon , as her total utility is higher.