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2. Consider UCB Pharma, Belgium originated international pharma firm, found a vaccine against Covid-19 and would like to sell it only in Turkey and Belgium. Vaccines can be produced at a constant average cost of €10 per unit. The demand for vaccines in Turkey and Belgium is given by: PTURKEY = 50 -0.5Q PBELGIUM = 20 -0.25Q a. If UCB can charge different prices to each country, what price and quantity will it sell to each? b. If UCB cannot price discriminate, what price and quantity of guns will it sell to each country? c. Will UCB make more profit from price discriminating? Briefly explain. Why is it that the manufacturer will likely be able to price discriminate? d. Is the deadweight loss higher under price discrimination or a single-price? Show mathematically
Expert Solution
Since averge cost is constant,
MC = AC = 10
(a)
(i) In Turkey:
Pt = 50 - 0.5Qt
TRt = Pt x Qt = 50Qt - 0.5Qt2
MRt = dTRt/dQt = 50 - Qt
Setting MRt = MC,
50 - Qt = 10
Qt = 40
Pt = 50 - 0.5 x 40 = 50 - 20 = 30
(ii) In Belgium:
Pb = 20 - 0.25Qb
TRb = Pb x Qb = 20Qb - 0.25Qb2
MRb = dTRb/dQb = 20 - 0.5Qb
Setting MRb = MC,
20 - 0.5Qb = 10
0.5Qb = 10
Qb = 20
Pb = 20 - 0.25 x 20 = 20 - 5 = 15
(b)
Without price discrimination, market quantity (Q) = Qt + Qb and Common price (P) = Pt = Pb
Since Pt (P) = 50 - 0.5Qt
Qt = (50 - P) / 0.5 = 100 - 2P
Since Pb (P) = 20 - 0.25Qb,
Qb = (20 - P) / 0.25 = 80 - 4P
So,
Q = 100 - 2P + 80 - 4P
Q = 180 - 6P
P = (180 - Q)/6
TR = P x Q = (180Q - Q2)/6
MR = dTR/dQ = (180 - 2Q)/6
Setting MR = MC,
(180 - 2Q)/6 = 10
180 - 2Q = 60
2Q = 120
Q = 60
P = (180 - 60)/6 = 120/6 = 20
(c)
With price discrimination, Total profit = TRt + TRb - MC x (Qt + Qb)
= (30 x 40) + (15 x 20) - 10 x (40 + 20)
= 1200 + 300 - 10 x 60
= 1500 - 600
= 900
Without price discrimination, Total profit = TR - TC = Q x (P - MC)
= 60 x (20 - 10)
= 60 x 10
= 600
So, UCB makes more profit from price discriminating.
The COVID pandemic has restricted international travel and postal services, therefore nobody can buy the product at lower price in Belgium and sell at higher price in Turkey, by shipping it from Belgium to Turkey. Since resale is not possible, price discrimination is effective.
(d)
Deadweight loss (DWL) = (1/2) x Difference in price x Difference in quantity
(I) With price discrimination
Setting Pt = MC for Turkey,
50 - 0.5Qt = 10
0.5Qt = 40
Qt = 80
Pt = MC = 10
DWLt = (1/2) x (30 - 10) x (80 - 40) = (1/2) x 20 x 40 = 400
Setting Pb = MC for Belgium,
20 - 0.25Qb = 10
0.25Qb = 10
Qb = 40
Pb = MC = 10
DWLb = (1/2) x (15 - 10) x (40 - 20) = (1/2) x 5 x 20 = 50
Total DWL = DWLt + DWLb = 400 + 50 = 450
(II) Without price discrimination
Setting P = MC,
(180 - Q)/6 = 10
180 - Q = 60
Q = 120
P = MC = 10
DWL = (1/2) x (20 - 10) x (120 - 60) = (1/2) x 10 x 60 = 300
So, DWL is higher under price discrimination.
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