ANSWERS
Ans 1. a) p = 100 −2y
Revenue, R = p*y = (100-2y)*y = 100y – 2y2
MR = dR/dy = 100 – 4y
For a monopolist, MR = MC
=> 100 – 4y = 20
=> ym = 80/4 = 20 units
b) Optimum price for Monopolist, pm = 100 – 2*20 = Rs 60
c) The socially optimum price will be the price that a perfectly competitive market sets.
For a perfectly competitive market, p = MC
=> pc = Rs 20
d) The socially optimal quantity: p = 100 – 2y
=> yc = (100 – p)/2 = (100 – 20)/2 = 40 units
e) For the deadweight loss:
Price, p A
100
60 M
B
Demand
MR
D Q C
20
20 25 40 50 Quantity, y
Under Monopoly,
Consumer Surplus = ΔABM = ½*AB*BM = ½*(100-60)*(20-0) = 400
Producer Surplus = BMQD = BD*DQ = (60-20)*(20-0) = 800
Deadweight Loss = ΔMQC = ½*MQ*QC = ½*(60-20)*(40-20) = 400
, f) If the monopolist can operate as a perfectly discriminating monopolist and sell each unit of
output at the highest price it would fetch, there will be NO deadweight loss as the monopolist
will sell upto 40 units and charge each unit at the price the consumer is willing to pay,
thereby capturing the entire area ΔADC.
Ans 2. a) P(y) = 120 – y
Revenue, R = p*y = 120y – y2
MR = 120 – 2y
c(y)= y2
𝑑𝐶
=> MC = 𝑑𝑦 = 2𝑦
For a monopolist, MR = MC
=> 120 – 2y = 2y
=> ym = 30 units
Price charged by the monopolist, pm = 120 – 30 = Rs 90
b) The Social Planner will choose the price ceiling which is equal to the price set by a
perfectly competitive market.
Hence, pc = MC
=> 120 – y = 2y
=> yc = 40 units
Price ceiling, pc = 120 – yc = Rs 80
c) The output to be produced at the price ceiling = yc = 40 units
d) When a tax of Rs 20/unit of output is imposed, the cost of the monopolist rises by Rs
20/unit. So the new MC’ = 2y + 20
Again, for a monopolist, MR = MC’
=> 120 – 2y = 2y + 20
=> ym = 25 units
New price charged by the monopolist, pm = 120 – ym = Rs 95.
Ans 3.
Here q1 is the quantity produced for Market 1, p1 is the price charged in Market 1, q2 is the
quantity produced for Market 2 and p2 is the price charged in Market 2.
Ans 1. a) p = 100 −2y
Revenue, R = p*y = (100-2y)*y = 100y – 2y2
MR = dR/dy = 100 – 4y
For a monopolist, MR = MC
=> 100 – 4y = 20
=> ym = 80/4 = 20 units
b) Optimum price for Monopolist, pm = 100 – 2*20 = Rs 60
c) The socially optimum price will be the price that a perfectly competitive market sets.
For a perfectly competitive market, p = MC
=> pc = Rs 20
d) The socially optimal quantity: p = 100 – 2y
=> yc = (100 – p)/2 = (100 – 20)/2 = 40 units
e) For the deadweight loss:
Price, p A
100
60 M
B
Demand
MR
D Q C
20
20 25 40 50 Quantity, y
Under Monopoly,
Consumer Surplus = ΔABM = ½*AB*BM = ½*(100-60)*(20-0) = 400
Producer Surplus = BMQD = BD*DQ = (60-20)*(20-0) = 800
Deadweight Loss = ΔMQC = ½*MQ*QC = ½*(60-20)*(40-20) = 400
, f) If the monopolist can operate as a perfectly discriminating monopolist and sell each unit of
output at the highest price it would fetch, there will be NO deadweight loss as the monopolist
will sell upto 40 units and charge each unit at the price the consumer is willing to pay,
thereby capturing the entire area ΔADC.
Ans 2. a) P(y) = 120 – y
Revenue, R = p*y = 120y – y2
MR = 120 – 2y
c(y)= y2
𝑑𝐶
=> MC = 𝑑𝑦 = 2𝑦
For a monopolist, MR = MC
=> 120 – 2y = 2y
=> ym = 30 units
Price charged by the monopolist, pm = 120 – 30 = Rs 90
b) The Social Planner will choose the price ceiling which is equal to the price set by a
perfectly competitive market.
Hence, pc = MC
=> 120 – y = 2y
=> yc = 40 units
Price ceiling, pc = 120 – yc = Rs 80
c) The output to be produced at the price ceiling = yc = 40 units
d) When a tax of Rs 20/unit of output is imposed, the cost of the monopolist rises by Rs
20/unit. So the new MC’ = 2y + 20
Again, for a monopolist, MR = MC’
=> 120 – 2y = 2y + 20
=> ym = 25 units
New price charged by the monopolist, pm = 120 – ym = Rs 95.
Ans 3.
Here q1 is the quantity produced for Market 1, p1 is the price charged in Market 1, q2 is the
quantity produced for Market 2 and p2 is the price charged in Market 2.
