Suppose the local zoo hires you to assist them in setting admission prices. The

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:      

            PA = 9.6 – 0.08QA       MRA = 9.6 – 0.16QA

            PCS = 4 – 0.05QCS        MRCS = 4 – 0.10QCS

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:

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.

C) Would you recommend charging one admission price for all or different prices for adult and for children/senior citizens? Why do you make that recommendation?

Explanation / Answer

For Adults

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

c. I would recommend charging different prices for adult and for children/senior citizens. I make this recommendation because In case of different prices the total Revenue and hence the total profit is more for the Zoo then charging Single price as total revenue in case of different price is 368 while in case of one price it is 315.18. And also due to lesser price for children/senior citizen ,They can come to the zoo in more numbers.

If you don't understand anything then comment , Iill revert back on the same.

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