refer to the scenario that follows. An amusement park, whose customer set is mad
ID: 1189487 • Letter: R
Question
refer to the scenario that follows. An amusement park, whose customer set is made up of two markets, adult and children, has developed demand schedules as follows:
Price ($)
Quantity, Adults
Quantity, Children
5
15
20
6
14
18
7
13
16
8
12
14
9
11
12
10
10
10
11
9
8
12
8
6
13
7
4
14
6
2
The marginal operating cost of each unit of quantity is $5. (Hint: Because marginal cost is a constant, so is average variable cost. Ignore fixed cost.) The owners of the amusement park want to maximize profits.
Calculate the price, quantity, and profit for each segment if the amusement park charges a different price in each market. (Hint: calculate profit at each price in the adult market, then in the child market, and choose profit maximizing in each. Using a spreadsheet would make this task manageable.)
Adult market price (in dollars): [a]
Adult market quantity: [b]
Adult market profit (in dollars): [c]
Child market price (in dollars): [d]
Child market quantity: [e]
Child market profit (in dollars): [f]
Total profit (adult + child, in dollars): [g]
Calculate the price, quantity, and profit if the amusement park charges the same price in the two markets combined. (Hint: Add adult and child quantities together, and treat this total and the entire market quantity at each price.)
Market price (in dollars): [a]
Quantity (child + adult at this price): [b]
Profit: [c]
Is profit higher, lower, or the same when the market is split with different prices for adults and for children?
Higher profit with split pricing
Lower profit with split pricing
Same profit with split pricing
Cannot determine with the information available
Price ($)
Quantity, Adults
Quantity, Children
5
15
20
6
14
18
7
13
16
8
12
14
9
11
12
10
10
10
11
9
8
12
8
6
13
7
4
14
6
2
Explanation / Answer
Working Note:
Profit = TR - TC
(1) Separate Market
The calculation table as follows.
So,
(i)
In Adult market, Maximum profit = 56
The profit is maximized at 2 prices: $12 & $13.
When P = $12, Q = 8, profit = $56
When P = $13, Q = 7, Profit = $56
(ii) In Children's Market
Profit is maximized at price = $10
When P = $10, Q = 10 & Profit = $50
(iii) Total maximized price = $56 + $50 = $106
(2) Unified market
The calculations are as follows.
So,
Profit is maximized at price = $11, Q = 17 & Maximum profit = $102
(3)
Total maximum price = $106 when markets are separate, and maximum price = $102 when markets are split.
Therefore, profit is higher when the market is split.
P QA QC TR(A) TR(C) MC = AVC TC(A) = AVC x Q(A) TC(C) = AVC x Q(C) Profit(A) Profit(C) 5 15 20 75 100 5 75 100 0 0 6 14 18 84 108 5 70 90 14 18 7 13 16 91 112 5 65 80 26 32 8 12 14 96 112 5 60 70 36 42 9 11 12 99 108 5 55 60 44 48 10 10 10 100 100 5 50 50 50 50 11 9 8 99 88 5 45 40 54 48 12 8 6 96 72 5 40 30 56 42 13 7 4 91 52 5 35 20 56 32 14 6 2 84 28 5 30 10 54 18Related Questions
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