Question

WestLink is a company that owns the only bridge between a city and its western suburbs. Therefore, it is a monopoly with price making powers. The daily demand curve for the toll bridge is given by the following formula:

Q = 800 - 100P

Where: Q represents the daily number of bridge crossings and P represents the bridge toll expressed in dollars per crossing.

Assume that the bridge operation does not incur any daily fixed costs. Finally, suppose the total variable cost curve is given by:

TVC = 2Q

From the information provided, complete the following columns: TR, TC, MR, MC and Profit (Ignore any dollar signs and round any decimals to the closest whole number)

P	Q	TR	TC	MR	MC	Profit
8	0
7	100
6	200
5	300
4	400
3	500
2	600
1	700
0	800

Use the marginal approch to determine the profit maximising number of bridge crossings.

What is the toll rate at the this point? $

What is the maximum profit the bridge operator earns? $

What is consumer surplus under perfect competition? $

What is consumer surplus under monopoly? $

What is the Deadweight Loss to society as a result of the monopoly pricing? $

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Answer 1

P	Q	TR	TC	MR	MC	Profit
8	0	0	0			0
7	100	700	200	7	2	500
6	200	1200	400	5	2	800
5	300	1500	600	3	2	900
4	400	1600	800	1	2	800
3	500	1500	1000	-1	2	500
2	600	1200	1200	-3	2	0
1	700	700	1400	-5	2	-700
0	800	0	1600	-7	2	-1600

Profit would be maximized at a quantity where MR > = MC for the last unit

Q = 300 and P = 5

Consumer surplus = Area bounded by the demand curve, price axis and the price level

Consumer surplus (perfect competition) = (Y intercept - Price) x Qc/2

Qc = 600, Y intercept = 8 and Price = 2 = MC

CS (perfect competition) = 6 x 600/2 = 1800

CS (monopoly) = (Y intercept - MC + Price - MC) x Qm/2 = (8 - 2 + 5 - 2) x 300/2 = 1350

DWL = (P - MC) x (Qc - Qm)/2

P = 5 , MC = 2 , Qc (under perfect competition) = 600, Qm = 300

DWL = 3 x 300/2 = 450