The Tricities Bus Company is a regional bus line providing transit service betwe
ID: 1216462 • Letter: T
Question
The Tricities Bus Company is a regional bus line providing transit service between Coquitlam, Port Moody and Port Coquitlam. An analysis of the monthly demand for transit reveals the following demand equation:
Qx = 1,750 - 40Px - 15PC + 30BAI - 1,700S
Where Qx is quantity measured by the number of passengers per month, Px is the price, PC is a price index for connecting bus routes, BAI is a business activity index and S, a binary or dummy variable, equals 1 in summer months, zero otherwise.
Currently Px = 50, PC = 120, and BAI = 175.
(a) Calculate the quantity demanded during the winter month of January if all price-related variables are as specified above.
(b) Calculate the price elasticity of demand in winter for transit services and the cross-price elasticity of demand for transit with respect to the level of business activity.
(c) What price would you recommend the Tricities Bus company charge in the winter months if they were primarily interested in maximizing revenue?
(d) Calculate the quantity demanded during the summer month of August if all price-related variables are as specified above.
(e) Calculate the price elasticity of demand in summer for transit services and the cross-price elasticity of demand for transit with respect to the level of business activity.
(f) What price would you recommend the Tricities Bus company charge in the summer months if they were primarily interested in maximizing revenue?
Explanation / Answer
Qx = 1,750 - 40Px - 15PC + 30BAI - 1,700S
= 1,750 - (40 x 50) - (15 x 120) + (30 x 175) - 1,700S = 1,750 - 2,000 - 1,800 + 5,250 - 1,700S
Qx = 3,200 - 1,700S
(a) In winter, S = 0
Qx = 3,200 - 0 = 3,200
(b) In winter:
Price elasticity of demand = (dQx / dPx) x (Px / Qx) = - 40 x (50 / 3,200) = - 0.625
Cross price elasticity = (dQx / dBAI) x (BAI / Qx) = 30 x (175 / 3,200) = 1.64
(c) In winter,
Qx = 1,750 - 40Px - (15 x 120) + (30 x 175) - (1,700 x 0) = 1,750 - 40Px - 1,800 + 5,250 = 5,200 - 40Px
40Px = 5,200 - Qx
Px = 130 - 0.025Qx
Total revenue, TR = Px. Qx = 130Qx - 0.025Qx2
Total revenue is maximized when dTR / dQx = 0
130 - 0.05Qx = 0
0.05Qx = 130
Qx = 2,600
Px = 130 - 0.025Qx = 130 - (0.025 x 2,600) = 130 - 65 = 65
(d) In summer, S = 1
Qx = 3,200 - 1,700S = 3,200 - (1,700 x 1) = 3,200 - 1,700 = 1,500
Note: First 4 sub-parts are answered.
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