8) Suppose a monopolist firm produces a medicine and can engage in 3rd degree pr

Question

8) Suppose a monopolist firm produces a medicine and can engage in 3rd degree price discrimination. The firm's marginal cost is constant at $8 per unit. In the United States, the demand for this medicine is given by: Qus = 20-0. SP. In Canada the demand is given by: QCan-20-P. If the monopolist has to charge the same price in the US and Canada, the relevant portion of demand curve is given by Qtotal = 40-1.5P. b. c. Determine the inverse demand function for the United States If the firm has to charge the same price in both markets, it will charge Determine the marginal revenue function, of just the Canadian market P = 40-20s $17.33 MR=20-2Q d. If the monopolist can charge separate prices in Canada and the US, in Canada it will charge $14.00 If the monopolist can charge separate prices in Canada and the US it will (circle one) e. ii. Charge a higher price in Canada iv. Charge a higher price in the US f. If the firm has no fixed costs, determine the change in profit from moving from a single-price monopolist to a 3"d degree pce discriminator (be sure to include sign). +$33.33

Explanation / Answer

a) Qus = 20 - 0.5P

0.5P = 20 - Qus (Multiply both sides by 2)

P = 40 - 2Qus

b)

MC = $8

TR = Qt x P = Qt x (40 - Qt)/1.5

MR = d(TR)/dQt = 26.67 - 1.33Qt

Profit would be maximized where MR = MC:

26.67 - 1.33Qt = 8

Qt = 14 and P = (40 - 14)/1.5 = $17.33

c)

Qcan = 20 - P

P = 20 - Qcan

TRcan = PQcan = 20Qcan - Qcan2

MRcan = d(TRcan)/dQcan = 20 - 2Qcan

d)

Profit would be maximized when MRcan = MC = 8

20 - 2Qcan = 8

Qcan = 6 and P = 20 - 6 = $14

e)

A higher price would be charged in the US because the demand is less price elastic in comparison to Canada.

(PE = dQ/dP x P/Q)

f)

In case of a single price:

Total profit = 14 x (17.33 - 8) = $ 130.67

In case of 3rd degree price discrimination:

Canada:

Profit = 6 x (14 - 8) = $36

USA:

MR = d(PQus)/dQus = 40 - 4Qus

MC = 8

40 - 4Qus = 8

Qus = 8 and P = 24

Profit = 8 x (24 - 8) = $ 128

Total profit = 128 + 36 = $ 164

Change in profit = 164 - 130.67 = $ 33.33

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