Question

In: Economics

2. If an airlines’ demand function in a specific market is: D=-8*P+100*F+1000, Where: D represents the...

2. If an airlines’ demand function in a specific market is:
D=-8*P+100*F+1000,
Where:
D represents the total number of passengers;
P represented the average price charged to passengers ($);
F represents the daily service frequency in that market.
And the cost function is:
C=800*F+3*D+100,000
Where:
C represents the total cost ($);
F and D are the same as defined above.

1) If the airlines’ daily service frequency is fixed at 15; the airlines can charge $100, $150, $185 and $200 to passengers, which ticket price will give airlines maximum traffic? maximum revenue? least cost? maximum profit?

2) If the airlines’ ticket price is fixed at $185; the airlines can provide service 10, 12, 15 or 18 times per day, which service frequency will give airlines maximum traffic? maximum revenue? least cost? maximum profit?

3) If the airlines can charge $150 or $185, and can fly 12 or 15 times per day, which combination of the price and frequency will give the airlines maximum traffic?

Solutions

Expert Solution

(1) Total revenue (TR) = P x D and Profit = TR - TC

We construct following data table.

F P ($) D TR ($) = D x P TC ($) Profit ($) = TR - TC
15 100 1,700 1,70,000 1,06,600 63,400
15 150 1,300 1,95,000 1,05,400 89,600
15 184 1,028 1,89,152 1,04,584 84,568
15 200 900 1,80,000 1,04,200 75,800

(i) Maximum traffic (D) (= 1,700) when P = $100

(ii) Maximum revenue (= $195,000) when P = $150

(iii) Least cost (= $104,200) when P = $200

(iv) Maximum profit (= $89,600) when P = $150

(2)

We construct following data table.

F P ($) D TR ($) = D x P TC ($) Profit ($) = TR - TC
10 185 520 96,200 1,02,560 -6,360
12 185 720 1,33,200 1,03,360 29,840
15 185 1,020 1,88,700 1,04,560 84,140
18 185 1,320 2,44,200 1,05,760 1,38,440

(i) Maximum traffic (D) (= 1,320) when F = 18

(ii) Maximum revenue (= $244,200) when F = 18

(iii) Least cost (= $102,560) when F = 10

(iv) Maximum profit (= $138,440) when F = 18

(2)

We construct following data table.

F P ($) D TR ($) = D x P TC ($) Profit ($) = TR - TC
12 150 1,000 1,50,000 1,04,200 45,800
12 185 720 1,33,200 1,03,360 29,840
15 150 1,300 1,95,000 1,05,400 89,600
15 185 1,020 1,88,700 1,04,560 84,140

Maximum traffic (D) (= 1,300) when P = $150 and F = 15.


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