Prof. Gustavo Indart
Department of Economics
University of Toronto
ECO 100Y
INTRODUCTION TO ECONOMICS
Solution to Problem Set 8
1.a) i) Po = $10 and Qo = 2,000 units
ii) q = 100 units and Profit = 0
iii) # Firms = Q/q = 2000/100 = 20
iv) Yes. Economic Profit = 0 => long-run equilibrium
b) i) Ps = $15 and Qs = 3,000
ii) Each firm increases q from 100 to 150 (where MC = new MR)
iii) Profit = 150 (15 - AC) = 150 (15 - 13) = $300
c) Entry shifts Supply right until P = $10 gives 0 economic profit and long-run equilibrium
d) i) P1 = 10 and Q1 = 4,000
ii) q = 100 and Economic Profit = 0
iii) # Firms = Q/q = 4000/100 = 40
2.a) Q = 700 where P = SMC2
Profit = (P-AC)Q = ($12 - $9.50)*700 = $1,750
b) The larger plant's profit ($1,750) is at the moment larger than the smaller plant's profit
(approximately ($12 - $9)*500 = $1,500) at $12. [Note that total profit for the larger plant is
larger even though profit per unit for the smaller plant is larger].
However, in the long-run, firms enter the industry pushing economic profit to 0; price will
therefore fall to $8 (break-even point for smaller plant) leaving the larger firm with economic
losses and eliminating the larger plant. [Owners may operate the larger plant at economic
losses less than fixed costs until the plant wears out but no new such plants will be built).
Moreover, there must exist a plant size that generates even lower average costs than plant
1, i.e., the plant that produces minimum long-run average cost of @$7.60 at 550.
c) The long-run industry supply is horizontal (perfectly elastic) at P = $8, the break-even
price (0 economic profit) of the smaller firm. (In reality, the firm capable of minimum
average cost at @$7.60 will displace this firm size). Long-run equilibrium is at Q = 16,000
where QLRS = QD.
d) Since each smaller plant produces 400 units at 0 economic profit and the industry produces
16,000, there must be 16,000/400 = 40 of the smaller plants operating at long-run
equilibrium.
The short-run supply curve for the industry is the horizontal sum of the short-run supply
curves (SMC above SAVC) of all the firms in the industry. Therefore, short-run supply for
the industry is horizontal at $6 - the shut-down price where firms may or may not produce up to 1400 units (40 firms * shut-down output of 350), and is the quantity supplied by a firm
times 40 (the number of firms) at each price above $6.
e) Short-run equilibrium is at P = $12 and Q = 20,000 units. Each firm produces at MC = P at
Q = 500 where profit is approximately ($12 - $9)*500 = $1,500.
f) In the long-run, firms enter until P falls to $8.
Equilibrium is at 28,000 for the industry and 400 units for each firm with 0 economic profits.
# of firms = 28,000/400 = 70
3.
Initial Equilibrium:
Industry Supply is firm Marginal Cost curve (above AVC) * # of firms and Demand is
arbitrary.
Industry: Quantity Supplied (QS) = Quantity Demanded (QD)=> Qo and Po where Supply
intersects Demand
Firm:
Short-run Equilibrium => qo at Po = SMC
Long-run Equilibrium => 0 economic profits => qo at Po = min SAC (=SMC)
Decrease in Licensing Fee
=> decrease in fixed costs => no change in SMC
=> no change in S (SMC*#firms)
=> no change in Po or Qo
=> no change in qo
=> decrease in SACo to SAC1
(Decrease in SAC falls as FC spread over Q but min SAC1 = SMC). Firms still maximize
profits at Po and Qo but economic profits have risen from (Po-ACo)qo = 0 to (Po - AC1)q1
Long-run Equilibrium:
Short-run economic profits => firms enter the industry
=> S increases - shifts right
=> Decrease in P and increase in Q
=> Remaining firms decrease output
(P = SMC => decrease in q)
Constant Costs => no change in variable costs due to change in output
=> Long-run Equilibrium occurs when rightward shift in Supply (as firms enter) intersects
Demand at the price (P1) where SMCo = min SAC1.
Q1 > Qo but q1 < qo and there are more firms in the industry.
4.
The diagram shows the short and
long run equilibria but the answer
need only give the long run
equilibrium.
MC and AC fall by $2 per unit as
does S (to Ss). Short-run
equilibrium is at Ps and Qs in the
industry and qs for the firm giving
economic profits. In the long-run,
entrance of firms shifts short run
supply to the right until economic
profits are eliminated at minimum
AC1. In the long-run then, S1
intersects D at Po-$2 and Q1 and each firm produces output equal to initial output q1.
Hence the statement that Price falls by $2 and firms enter the industry is correct but
industry output, not firm output, increases and firm output, not industry output, is the same.
5.
This question reverses the shift of question 4, i.e., an increase in per unit costs rather than
a decrease in per unit costs. The diagram is simply the diagram for #5 in reverse except
that Ss is a vertical, not a horizontal shift relative to S1 (original supply) and So (final supply)
is a horizontal shift left, not a vertical shift relative to Ss.
Hence, only the third part of the statement is incorrect: in the long-run the full burden on the
tax falls on the consumer not the producer. The parts that are true are that price rises by
the full $2 /unit, industry output falls, firm output is unchanged, and firms leave the industry.
6.
Draw two short run average cost curves, each representing a fixed capital, tangent to a long-run
average cost curve with one curve (SRACa) tangent to minimum long-run average cost. Both
firms will make an economic profit if Supply (So) intersects Demand above minimum average
cost for each. Since P > minimum SRAC, both firms make an economic profit and firms enter
the industry. Supply shifts right lowering price below minimum average cost for SRACb.
However, the firm with SRACa still makes an economic profit inducing firms to enter with a
capital similar to SRACa. Entry of new firms with plant size to give SRACa will shift supply until
P falls to minimum SRACa and minimum LRAC. Firms with any other capital will make
economic losses and eventually leave. As long as no technological change alters mimimum
LRAC, competition over time will eventually eliminate all firms except those with SRACa. Perfect
competition is thus a logical outcome of competition between differenct sized firms.