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
(a) Profit is maximized (= 209,000) when Q = 700 and P =830.
(b) AC is minimized (= 440) when Q = 300 and P = 870.