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**

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