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The local zoo has hired you to assist them in setting admission prices. The zoo’s managers recognize that there are two distinct demand curves for zoo admission. One demand curve applies to those ages 12 to 64, while the other is for children and senior citizens. The two demands and marginal revenue curves are:

PA = 9.6 - 0.08QA

MRA = 9.6 - 0.16QA

PCS = 4 - 0.05QCS

MRCS = 4 - 0.10QCS

Where PA = adult price, PCS = children’s/senior citizen’s price, QA = daily quantity of adults, and QCS = daily quantity of children and senior citizens. Crowding is not a problem at the zoo, so that the managers consider marginal cost to be zero.

  1. If the zoo decides to price discriminate, what should the price and quantity be in each market? Calculate total revenue in each sub-market.
  2. What is the elasticity of demand at the quantities calculated in (a) for each market. Are these elasticities consistent with your understanding of profit maximization and the relationship between marginal revenue and elasticity?
Category : Economics | Answer: 1 1 Year Ago

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a.

Optimal price discrimination requires the zoo to set MRA = MRCS = MC.

Setting MRA = 0

9.6 - 0.16QA = 0

9.6 = 0.16QA

QA = 60

PA = 9.6 - 0.08(60)

PA = $4.8

MRCS = 4 - 0.10QCS = 0

4 = 0.10QCS

QCS = 40

PCS = 4 - 0.05(40) = $2

PCS = $2

TRA = PA · QA

TRA = 4.8 · 60 = $288

TRCS = PCS · QCS

TRCS = 2 · 40 = $80

TR = 288 + 80 = $368

b.

To calculate elasticities, solve for Q.

PA = 9.6 - 0.08QA

PA - 9.6 = -0.08QA

QA = 120 - 12.50PA

QA = 120 - 12.5PA

EA = ΔQA/ΔPA·PA/QA

EA = -12.50 · 4.8/60

EA = -60/60 = -1.0

PCS = 4-0.05QCS

PCS = 4 - 0.05QCS

PCS - 4 = -0.05QCS

QCS = 80 - 20PCS

ECS = -20 · 2/ 40

ECS = -1

Yes it is consistent. When MC - 0, profit maximization requires that MR = 0.

1 Year Ago
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