Question

Frank Buckley sells his famous bad tasting but very effective cough medicine in Toronto and Montreal. The demand functions in these two urban areas, respectively, are:

PT = 18 − QT and PM = 14 − QM .

Buckley’s plant is located in Kingston, Ontario, which is roughly midway between the two cities. As a result, the cost of producing and delivering cough syrup to each town is:

2 + 3Qi where i = T, M .

a. Compute the optimal price of Buckley’s cough medicine in Toronto and Montreal if the two markets are separate.

b. Compute the optimal price of Buckley’s medicine if Toronto and Montreal are treated as a common market.

Answer 1

Frank Buckley is the only producer of effective medicine, i.e. Monopoly market

For Toronto:

PT =18 - QT

TR = 18QT - QT²

MR = 18 - 2QT

TC = 2 + 3QT

MC = 3

At Equilibrium, MR = MC

=> 18 - 2QT = 3

=> 2QT = 15

=> QT = 7.5, PT = 18 - 7.5 = 10.5

For Montreal

PM = 14 -QM

TR = 14QM - QM²

MR = 14 - 2QM

TC = 2 + 3QM

MC = 3

At Equilibrium, MR = MC

=> 14 - 2QM = 3

=> 2QM = 11

=> QM = 5.5, PM = 14 - 5.5 = 8.5

b.

If the markets are common

Demand: P = 32 - (QT + QM)

TC = 2 + 3(QT + QM)

TR_T = 32QT - QT² - QTQM; TR_M = 32QM - QTQM - QM²

= TR_T - TC

= 32QT - QT² - QTQM - 2 - 3(QT + QM)

= 29QT - QT² -QTQM -2 - 3QM

= 29 - 2QT - QM =0

=> QT = 1/2(29 - QM) ... REACTION FUNCTION OF TORONTO (i)

Similarly for, = 29 - 2QM - QT =0

=> QM = 1/2(29 - QT) ... REACTION FUNCTION OF MONTREAL (ii)

Solving (i) and (ii), we get

QT = 14.5, QM = 7.25

P = 32 - (14.5 + 7.25) = 32 - 22 = 10 => Optimal price