Pricing Concepts -Transportati
Pricing Concepts -TransportationEngineering
A transportation firm is producing a transport service (withquantity Q trips) with the following cost and revenuefunctions:
Total Cost: TC=$36,000 + $200Q + $0.4Q^2
Total Revenue: TR=$900Q-$0.1Q^2
Set up a table or spreadsheet for trip output/supply (Q), price(P), total revenue (TR), marginal revenue (MR), total cost (TC),marginal cost (MC), average cost (AC), total profit (π), andmarginal profit (Mπ). Establish a range for Q from 0 to 1,000 inincrements of 100 (i.e., 0, 100, 200, …, 1,000). Using thisspreadsheet, create a graph with AC and MC as dependent variablesand trip output/supply (Q) as the independent variable.
a) At what combination of price P and supply Q is profitmaximized? Why?
b) At what price P and supply Q is average cost (AC) minimized?Why?
Answer:
TR = 900Q – 0.1Q2
TC = 36,000 + 200Q + 0.4Q2
- P = TR/Q = 900 – 0.1Q
- MR =
TR/Qand MC = TC/Q - AC = TC/Q = (36,000/Q) + 200 + 0.4Q
- Profit (
) =TR – TC - Marginal profit = /Q
TR/
) =TR – TC(1)
Data table:
| Q | TR | TC | P | MR | MC | AC | Profit | Marginal profit |
| 0 | 0 | 36,000 | -36,000 | |||||
| 100 | 89,000 | 60,000 | 890 | 890 | 240 | 600 | 29,000 | 650 |
| 200 | 1,76,000 | 92,000 | 880 | 870 | 320 | 460 | 84,000 | 550 |
| 300 | 2,61,000 | 1,32,000 | 870 | 850 | 400 | 440 | 1,29,000 | 450 |
| 400 | 3,44,000 | 1,80,000 | 860 | 830 | 480 | 450 | 1,64,000 | 350 |
| 500 | 4,25,000 | 2,36,000 | 850 | 810 | 560 | 472 | 1,89,000 | 250 |
| 600 | 5,04,000 | 3,00,000 | 840 | 790 | 640 | 500 | 2,04,000 | 150 |
| 700 | 5,81,000 | 3,72,000 | 830 | 770 | 720 | 531.43 | 2,09,000 | 50 |
| 800 | 6,56,000 | 4,52,000 | 820 | 750 | 800 | 565 | 2,04,000 | -50 |
| 900 | 7,29,000 | 5,40,000 | 810 | 730 | 880 | 600 | 1,89,000 | -150 |
| 1,000 | 8,00,000 | 6,36,000 | 800 | 710 | 960 | 636 | 1,64,000 | -250 |
(2)
Graph:
(a) Profit is maximized (= 209,000) when Q = 700 and P =830.
(b) AC is minimized (= 440) when Q = 300 and P = 870.
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