Question

An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows: Qa = 20 – Pa where a is adult market Qc = 30 – 2 Pc Where c is children market QT = 50 – 3 PT where T is the two markets combined Assume that the marginal cost of each unit of quantity is $5 (constant), the owners of the park want to maximize profit: A) Calculate the price, quantity and profit if the amusement park charges a different price in each market. B) Calculate the price, quantity and profit if the amusement park charges the same price in the two markets combined.

Answer 1

Answer:

	Price($)	Quantity	Profit($)
Adult Market	7.5	13	28.75
Children Market	6.25	18	58.43
Total Market	7.5	28	178.75

To find out the price ,quantity and profit ,we need to follow the steps:

1) Find out total revenue (Total Revenue = Quantity * price)

2) Find Marginal revenue by differentiating the total revenue with respect to price .

3) Put Marginal revenue = Marginal Cost (At this point , Profit is maximum).

4)We will be able to find price from above condition.

5)Put the price value in the demand function to obtain quantity.

6)To find out the profit ,put all the values in this equation :

Total Profit = Total Revenue - Total cost

Total Revenue = Price * Quantity

Total cost = Marginal Cost * Quantity

A)

Adult Market:

Qa = 20-Pa

Total revenue = Quantity *Price

TR=20Pa-P2a

MR=20-2Pa

MC=5

MR=Mc

20-2Pa=5

Pa=$7.5

Qa=20-7.5

=12.5 units or 13 units approx

Profit = TR=TC

Profit = (20Pa-P2a)-5Qa

=20*7.5-7.52-5*13

=$28.75

Children Market:

Qc=30-2Pc

Total revenue = Quantity *Price

TR=30Pc-2P2c

MR=30-4Pc

MC=5

MR=Mc

30-4Pc=5

Pc=$6.25

Qc=30-6.25

=17.5 units or 18 units approx

Profit = TR=TC

Profit = (30Pc-2P2c)-5Qc

=30*6.25-6.252-5*18

=$58.43

B) Total Market

QT=50-3PT

Total revenue = Quantity *Price

TR=50PT-3P2T

MR=50-6PT

MC=5

MR=Mc

50-6PT=5

PT=$7.5

QT=50-7.5

=27.5 units or 28 units approx

Profit = TR=TC

Profit = (50PT-3P2T)-5QT

=50*7.5-7.52-5*28

=$178.75

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