The demand for imported Honda automobiles is given by the following equation: Q
ID: 1216467 • Letter: T
Question
The demand for imported Honda automobiles is given by the following equation:
QH = 1200 – 20PH + 10PC + 200PG
The price of Hondas, PH = 60, the price of Chevrolets, PC = 70, and the price of gasoline, PG = 1.5.
(a) Calculate the point elasticity of demand for Hondas with respect to its own price, the price of Chevrolets, and the price of gasoline.
(b) For each of Chevrolets and gasoline, is it a substitute or complement for Hondas?
(c) Calculate consumer surplus at the revenue-maximizing price for Hondas.
(d) If the cost per Honda is 50 and the Honda importing agency behaves as a monopolist, how many will be imported and at what price will they sell?
(e) Redo part (d) on the assumption gasoline price rises to PG = 2.5.
Explanation / Answer
QH = 1200 – 20PH + 10PC + 200PG
= 1200 - (20 x 60) + (10 x 70) + (200 x 1.5) = 1200 - 1200 + 700 + 300 = 1000
(a)
Elasticity with own price = (dQH / dPH) x (PH / QH) = - 20 x (60 / 1000) = - 1.2
Elasticity with Chevrolet price = (dQH / dPC) x (PC / QH) = 10 x (70 / 1000) = 0.7
Elasticity with gasoline price = (dQH / dPG) x (PG / QH) = 200 x (1.5 / 1000) = 0.3
(b)
Elasticity with respect to price of Chevrolet is positive, so Honda and Chevrolet are substitutes.
Elasticity with respect to price of gasoline is positive, so Honda and gasoline are substitutes.
(c)
QH = 1200 - 20PH + (10 x 70) + (200 x 1.5) = 1200 - 20PH + 700 + 300
QH = 2200 - 20PH
20PH = 2200 - QH
PH = 110 - 0.05QH
Total revenue, TR = PH x QH = 110QH - 0.05QH2
TR is maximized when dTR / dQH = 0
110 - 0.1QH = 0
0.1QH = 110
QH = 1,100
PH = 110 - (0.05 x 1,100) = 110 - 55 = 55
From demand function, when QH = 0, PH = 110 (Reservation price)
So, Consumer surplus = Area between demand curve & market price
= (1/2) x (110 - 55) x 1100 = (1/2) x 55 x 1100 = 30,250
(d) Monopolist maximizes profit by equating marginal revenue (MR) with MC (= 50).
MR = dTR / dQH = 110 - 0.1QH
Equating with MC,
110 - 0.1QH = 50
0.1QH = 55
QH = 550
PH = 110 - (0.05 x 550) = 110 - 27.5 = 82.5
Imports = 1100 - 550 = 550
Note: First 4 sub-parts are answered.
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