# 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?

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

(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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