Download 1. Rose growing is a perfectly competitive industry and all rose

1. Rose growing is a perfectly competitive industry and all rose growers have
the same cost curves. The market price of roses is Rs. 15 a bunch and each
grower maximizes profit by producing 1500 bunches a week. The average cost
of producing roses is Rs. 21 a bunch. Minimum average variable cost is Rs.12
a bunch and the minimum average total cost is Rs.18 a bunch.
(a) Assuming U-shaped AV C, ATC, draw MR, AV C, ATC and MC in the
same graph and show where each rose grower is operating at this
moment.
(b) What is a rose grower’s economic profit or loss in the short run?
Show this area in the graph.
Answer
Marketing Price, P = Rs 15 / bunch
Qty, Qs = 1500 bunches /week
AC = 21
AVC = 12
= TC /Q
; TC = AVC X Q = 150 X 12 = 18,000
ATC = 18
Profit maximisation takes place when,
MR = MC
TR = P x Qs
= 15 x 1500
=
12,500
P = MC
P > AVC
(15 > 12)
ATC = AVC + AFC
(18 = 12 + 6)
Grower is operating in the loss condition, but since the market price is above the AVC hence
the rose grower should continue growing. It is not the shut down condition for him.
(b)
Since the market Price, P = MR < ATC
When, MC = MR =15
At this point the ATC = 21
The total loss is defined by area PQRS = (21 – 15) x 1500
= 6 x 1500 = Rs 9000
2. Consider the following market demand and supply:
P = 100 - 2QD,
P = 20 + 2QS,
(a) Calculate the equilibrium price/output solution.
(b) Graphically determine the amount of market buyer surplus and seller
surplus in the equilibrium.
(c) The government sets a price ceiling of Rs.30 in this market.
Determine the excess demand or excess supply, and the amount of
deadweight loss.
Answer
P = 100-2Qd …………………….. Eqn (1)
(a)
P = 20+2Qs …………………….. Eqn (2)
At the point of equilibrium, we know that,
Demand = Supply
Hence, we equate the two equations
100 - 2Qd = 20 + 2Qs
(solving for Qs)
Qs = (80-2Qd)/2 ……... Eqn (3)
Also, at equilibrium, Qs = Qd ………………..Eqn (4)
Solving (4) and (3), we get
Qd = (80 – 2Qd) / 2
Or,
2Qd = 80 – 2Qd
Or,
4Qd = 80
Or,
Qd = 20
Now putting the value of Qd in Eqn (3) above
We get,
Qs = 20 …..(5)
Qd = 20 …..(6)
Solving for P from (1) and (6), we get,
P = 100 - 2(20)
Equilibrium Price = 60
(Answer)
(b)
For Demand Curve:
P
100 0
60
90
Qd
0
20
5
50
For Supply Curve:
P
20
0
60
Qs
0
-10 20
Area for consumer surplus:
Consumer surplus = ½(20)(100 - 60)
= ½(20) (40)
= 400
(c)
Price ceiling = Rs 30
at P=30,
Qd = (100-P)/2 = 35 and,
Qs = (P-20)/2 = 5
Hence, excess demand = 35 - 5 = 30
Dead weight loss
3. A monopolist sells a product with total cost function TC = 1200 + 0.5Q 2. The
market demand is: P = 300 – Q.
(a) Find the profit maximizing profit and price. Is this monopolist making
a positive profit?
(b) Verify that the IEPR (see your notes) holds at the profit maximizing
price and quantity.
Answer
TC = 1200 + 0.5Q2
Demand Curve is P = 300 – Q
The profit will be maximised when marginal revenue is equal to marginal cost.
i.e.
MR = MC
_____________ Condition for monopoly
We know that,
Max. Profit = Total Revenue (TR) – Total Cost (TC) = TR – TC
Total Revenue (TR) = Price (P) x Quantity (Q) = P.Q
= (300 – Q). Q
TR
We Know,
Now equating,
MR = ∂TR
∂Q
MC = ∂TC
∂Q
MR = MC
∂TR
∂Q
= 300Q – Q2
= 300 – 2Q
= 0 + 0.5 x 2Q = Q
= ∂TC
∂Q
300 – 2Q = Q
Therefore,
Q = 100
And
P = 200
(Answer)
Profit maximising profit = TR – TC = 300Q – Q2 – (1200 + 0.5Q2)
π = 300(100) – 10000 – (1200 + 5000)
Profit (max.)
= 13,800
(Answer)
The monopolist is making a positive profit.
(b)
GGGGGGGGGGGGGGGGGG
4. Resort Phi Phi is the only resort in the island of Ko Phi Phi in Thailand. Both
bargain travellers and high-end travellers visit this island. The demand curve
for bargain travellers is: Q1 = 400 – P1. The demand curve for rge high-end
travellers is Q2 = 500 – P2. The resorts marginal cost is $20. The resort wants
to price discriminate.
(a) Suggest a suitable price discrimination scheme, i.e., a price and
quantity scheme for each of kind of customer group.
(b) Calculate the total producer surplus.
Answer
Price Discrimination Demand Curve
For bargain travellers -------------------------------Q1 = 400 – P1________Eqn (1)
For high end travellers------------------------------ Q2 = 500 – P2________Eqn (2)
The marginal Cost = 20
The Total Revenues (TR) will be
TR1 = P1.Q1 = 400Q1 – (Q1)2
TR2 = P2.Q2
MR1 = ∂TR1 = 400-2Q1
∂Q
Similarly, TR2 = 500Q2 – (Q2)2
MR2 = ∂TR2 = 500 - 2.Q2
∂Q
Now, MR = MC
500 – 2Q2 = 20
Q2 = 240
Putting value of Q2 in Eqn (2) and value of Q1 in Eqn (1)
(b)
400 – 2Q1 = 20
Q1 = 190
(Answer)
P2 = 500 – 240
P1 = 400 – 190
P2 = 260
P1 = 210
Producers Surplus
The area will be
= 1\2 .X 190 X (400 – 210)
= ½ X 190 X 190
= 18050
The area will be
= 1\2 X 240 X (500 – 260)
= ½ X 240 X 240
= 28800