Question

Suppose the local zoo hires you to assist them in setting admission prices. The zoo’s managers recognize that there are two distinct groups of consumers for zoo admission: adults (A) and children/senior citizens (CS). The demand and marginal revenue functions for the two groups are as follows:       

           

            P_A = 9.6 – 0.08Q_A        MR_A = 9.6 – 0.16Q_A

            P_CS = 4 – 0.05Q_CS        MR_CS = 4 – 0.10Q_CS

Suppose the zoo is large enough so that crowding is not a problem at the zoo. The managers therefore consider marginal cost to be zero. Answer the following questions: [5 pts. each]

A. If the zoo decides to price discriminate, what are the profit-maximizing price and quantity in each sub-market? Calculate the total revenue in each sub-market.

B. If the zoo decides not to price discriminate, it faces a combined demand and marginal revenue function of P = 6.15 – 0.03Q and MR = 6.15 – 0.06Q. What are the profit-maximizing price and quantity of admission if the zoo charges one admission price for all. Calculate the total revenue in this case.

Mostly need help on B

Answer 1

Solution:-

For Adults

(A). PA = 9.6 – 0.08QA       MRA = 9.6 – 0.16QA , MC =0

Profit = TR - TC = P*Q - MC*Q

For profit to be maximized

MRA = MC

  9.6 – 0.16QA = 0

QA = 60

PA = 9.6 – 0.08QA = 9.6 – 0.08*60 = 4.8

Total Revenue = P*Q = 4.8*60 = 288

For Children and Senor Citizen

PCS = 4 – 0.05QCS        MRCS = 4 – 0.10QCS , MC = 0

In case also , for profit to be maximized,

MRCS = MC

4 – 0.10QCS = 0

QCS = 40

PCS = 4 – 0.05QCS   = 4 – 0.05*40 = 2

Total Revenue = PCS*QCS = 2*40 = 80

(B). No Price Discrimination

  combined demand P = 6.15 – 0.03Q and

MR = 6.15 – 0.06Q

For profit to be maximized

MR = MC

6.15 – 0.06Q = 0

Q = 102.5

P = 6.15 – 0.03Q  =  6.15 – 0.03*102.5 = 3.07

Total Revenue = P*Q = 3.07*102.5 = 315.18