Student Number:
Name (Last Name, First Name):
Econ 212 Section 001
Quiz 5
Question 1: [10pt] Suppose there are identical firms in the industry. For
each firm, let total cost be TC(q) = 10q - 4q2 + q3 for positive q and TC(q) = 0
for q = 0.
(a) What will be the quantity produced by each firm in long-run equilibrium?
[3pt] What will be the long-run competitive equilibrium price? [3pt]
Answer:
LAC(q) = 10 - 4q + q2
LMC(q) = 10 -8q + 3q2
set LMC = LAC → -8q + 3q2 = - 4q + q2
→
each firm produce
q* = 2
substitute q* into LAC or LMC to find p* = 10 – 4(2) + (2)2 = 6
(b) Suppose that market demand takes the form QD = C – 100p, where p is
the price and C is some constant. If there are 200 firms in the industry at
long-run equilibrium, find the value of C . [4pt]
Answer:
Industry demand in long-run : QD = C – 100p* = C – 100(6) = C - 600
Industry output in long-run : QS = n*q* = 200(2) = 400
QS = QD implies C = 1000
Question 2: [10pt] Consider a perfectly competitive market with demand
and supply functions as QD = 200 - p and QS = p - 100.
(a) Calculate the competitive market equilibrium quantity and price. [2pt]
Answer:
at equilibrium: QD = QS
→
200 - P = P - 100
→
P* = 150 and Q* = 50
(b) Suppose there is an excise tax of T = 10 is imposed on suppliers.
Calculate the new equilibrium quantity and price paid by consumers. [4pt]
Answer:
If T = 10 on suppliers, then the new supply curve is QS = (p - 10) - 100.
at new equilibrium: QD = QS
→
200 – P = P - 110
→
P* = 155 and Q* = 45
(c) Suppose instead of tax there is a price ceiling of Pc is imposed in this
market, and there is a 20-unit excess demand in the market. Calculate the
value of price ceiling, Pc , which causes the 20-unit excess demand. [4pt]
Answer:
If a price ceiling of Pc is imposed, then QS = Pc – 100 is the amount sellers
are willing to supply, and QD = 200 - Pc is the amount demanded. 20-unit
excess demand means QD - QS = 20 implies Pc = 140