Questions Chapter 9

1
Questions Chapter 9

• (1)
• Which demand curve when rivals match all price
  changes?
• D2 (steeper)
• (b) Which demand curve when rivals do not match
  all price changes?
• D1
• (c) Rivals match cuts but not increases. (1) What
  is P if Q20?
• 20
• (2) What is Q if P70?
• 0
• (3) For what range in MC will the firm continue
  to charge P60?
• D1 P70-Q, MR170-2Q
• D2 P100-4Q, MR2100-8Q
• D1D2 at Q10, P60. From this point onwards, D2
  and MR2 are relevant. When Q10, MR220. Before
  this point D1 and MR1 are relevant. When Q10,
  MR150. Answer 20-50

2

• 9.5
• 4 firms, identical product, MC100. Inverse
  demand 500-2Q
• Equilibrium Q?
• Set P MC to get 500 2Q 100. Solving yields
  Q 200 units.
• (b) Equilibrium price?
• P MC 100.
• (c) Equilibrium profits?
• Each firm earns zero economic profits.

3

• 9.6 Give example of
• (a) Cournot oligopoly
• Oil production. Each firm produces output
  independently and the market price is determined
  by the total amount produced
• (b) Stackelberg oligopoly
• Diamond production. DeBeers is the leader that
  sets diamond production, and smaller firms follow
  with their own levels of production. Gasoline in
  NL (Shell is price leader)
• (c) Bertrand competition
• Competitive bidding by identical contractors. In
  this case, the contractor bidding the lowest fee
  will win the contract. I.e. construction.

4
Questions chapter 9

• (8) Duopoly, each firm produces at MC100 and
  FC0. What happens if MC2 becomes 110 and MC1
  remains 100?
• (a) Cournot duopoly?
• Firm 1s output and profit would increase.
  Firm2s output and profits would decrease.
• (b) Sweezy oligopoly
• For small changes in costs, there would be no
  change in output or profits.

5
Questions chapter 9

• (10) 2 firms, Inv. Demand P5,100-0.5Q, MC750,
  Revenues PQi 6.38 mln, profits (net of fixed
  cost) (P-MC)Qi-750Q1mln. New method reduces MC
  to 500.
• How does this impact production and pricing?
• Since this is a homogeneous product Cournot
  oligopoly, Q can be found from 5,100Q-0.5Q26.38
  mln. Solving for Q gives Q 2900
• P can be found from P29006.38 mln, so 2,200
• Profit gross of fixed costs is (P MC)Qi
  (2200 - 750)(2900) 4,205,000.
• Profits net of fixed costs are 1 million, so it
  follows that BlackSpots fixed costs are 3.205
  million.

6
Questions chapter 9

• (10) continued
• Marginal cost for BlackSpot (only) falls to 500
• Reaction curvesQ1(a-c1)/2b-1/2Q2
• Q1(5100-500)/(1)-1/2(Q2)
• Q2(5100-750)/(1)-1/2(Q1).
• Q2(5100-750)/(1)-1/2((5100-500)/(1)-1/2(Q2) )
• (3/4)Q2(5100-750)-1/2((5100-500)2050
• Q22733 and Q14600-(0.5)27333233.3
• The market price falls to 5,100-0.5(2733.33233.3)
  2,116.67. BlackSpots new profits are
  PQ-MCQ-FC (2,117-500)3233-3.205mln by
  2,02mln.

7
Questions chapter 9

• (11) Homogeneous Bertrand Competition Q50-10P
• MC1.25. What happens?
• In a homogeneous product Bertrand oligopoly, the
  equilibrium price equals marginal cost of 1.25.
  The total market quantity sold is Q 50
  10(1.25) 37.5 units.
• What if one station is self service?
• If one station is self-serve while the other is
  full-service, the differentiated nature of the
  products may permit each firm to charge a price
  above 1.25. This will result in fewer units of
  gasoline being sold, but the firms will enjoy
  higher profits.

8
Questions chapter 9

• (13) What must OPEC do to keep the price of oil
  at its desired level when Russia etc. increase
  production?
• OPEC must reduce its output when rivals (such as
  Russia, Omar, Mexico, Norway, and other non-OPEC
  countries) increase their output. This reduction
  in output lowers their profits, making it
  difficult to accomplish.

9
Questions chapter 9

• (16) Composite box is Stackelberg leader.
  P800-4Q. MCc40c and MCf80. Should CB propose
  to merge?
• Your output Qc(80080-240)/(24)100 and Fs
  output is (800-80)/8-5040
• P800-4(10040)240
• Stackelberg profits are 100(240-40)20,000 and
  your rivals profits are 40(240-80)6,400.
• If you merge, you would not face any
  competition. In addition, would be able to
  produce all output at your own facilities (which
  have lower costs). Your post-merger monopoly
  profits would be based on your monopoly output,
  which occurs where MR MC 800 8Q 40, or Q
  95 units. The monopoly price is P800-4(95)
  420. Your monopoly profits are (420 - 40)(95)
  36,100, so you stand to gain 16,100 by
  merging. If you offer your rival 6,400.01 to
  merge, it is strictly better off and so are you