Question
In: Accounting
An amusement park, whose customer set is made up of two markets, adults and children, has...
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:
- Calculate the price, quantity and profit if the amusement park charges a different price in each market.
- Calculate the price, quantity and profit if the amusement park charges the same price in the two markets combined.
Solutions
Expert Solution
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Given, |
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Qa = 20 – Pa where a is adult market |
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Qc = 30 – 2 Pc Where c is children market |
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QT = 50 – 3 PT where T is the two markets combined |
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where Q represents Quantity and P reprents Price |
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Assuming Marginal Cost of each unit =$5 |
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Using the following equations , we found the following Quantities |
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Assumed Minimum Price to be set at Marginal Cost |
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| Refer this Price, Quantity table for calculations done below:- | |||
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Price($) |
Quantity |
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|
Adult |
Children |
Combined |
|
|
5 |
15 |
20 |
35 |
|
6 |
14 |
18 |
32 |
|
7 |
13 |
16 |
29 |
|
8 |
12 |
14 |
26 |
|
9 |
11 |
12 |
23 |
|
10 |
10 |
10 |
20 |
|
11 |
9 |
8 |
17 |
|
12 |
8 |
6 |
14 |
|
13 |
7 |
4 |
11 |
|
14 |
6 |
2 |
8 |
Answer to Question A:
Computation of Price, Quantity & Profit if it charges different price in each market:-
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Computation of Price, Quantity & Profit for Adult Market |
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Price($) |
Quantity |
Total Revenue |
Marginal Revenue(MR) |
Marginal Cost(MC) |
Total Cost |
MR-MC |
Profit |
|
|
14 |
6 |
84 |
0 |
5 |
30 |
-5 |
54 |
|
|
13 |
7 |
91 |
7 |
5 |
35 |
2 |
56 |
|
|
12 |
8 |
96 |
5 |
5 |
40 |
0 |
56 |
|
|
11 |
9 |
99 |
3 |
5 |
45 |
-2 |
54 |
|
|
10 |
10 |
100 |
1 |
5 |
50 |
-4 |
50 |
|
|
9 |
11 |
99 |
-1 |
5 |
55 |
-6 |
44 |
|
|
8 |
12 |
96 |
-3 |
5 |
60 |
-8 |
36 |
|
|
7 |
13 |
91 |
-5 |
5 |
65 |
-10 |
26 |
|
|
6 |
14 |
84 |
-7 |
5 |
70 |
-12 |
14 |
|
|
5 |
15 |
75 |
-9 |
5 |
75 |
-14 |
0 |
|
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Profit is maximum at Price = $12 |
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Quantity =8 |
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Profit =$56 |
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Computation of Price, Quantity & Profit for Children Market |
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|
Price($) |
Quantity |
Total Revenue |
Marginal Revenue(MR) |
Marginal Cost(MC) |
Total Cost |
MR-MC |
Profit |
|
|
14 |
2 |
28 |
0 |
5 |
10 |
-5 |
18 |
|
|
13 |
4 |
52 |
24 |
5 |
20 |
19 |
32 |
|
|
12 |
6 |
72 |
20 |
5 |
30 |
15 |
42 |
|
|
11 |
8 |
88 |
16 |
5 |
40 |
11 |
48 |
|
|
10 |
10 |
100 |
12 |
5 |
50 |
7 |
50 |
|
|
9 |
12 |
108 |
8 |
5 |
60 |
3 |
48 |
|
|
8 |
14 |
112 |
4 |
5 |
70 |
-1 |
42 |
|
|
7 |
16 |
112 |
0 |
5 |
80 |
-5 |
32 |
|
|
6 |
18 |
108 |
-4 |
5 |
90 |
-9 |
18 |
|
|
5 |
20 |
100 |
-8 |
5 |
100 |
-13 |
0 |
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Profit is maximum at Price = $10 |
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Quantity =10 |
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Profit =$50 |
Answer to Question B:-
Computation of Price, Quantity & Profit if it charges different price in Combined market:-
| Computation of Price, Quantity & Profit for Combined Market | ||
| Price($) | Quantity |
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