Managerial Economics Final Suggested answers

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Managerial Economics FinalSuggested answers

• MBS, Term 2, 2004
• Paul Kerin

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1a) Pay-off matrix M
Joint optimum
-0.125, 2.375
1.75, 1.75
H Retailer A L
0.5, 0.5
2.375, -0.125
L H Retailer B
Nash equilibrium
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1a) Pay-off matrix (cont)

• Pay-off calculationsLH -0.125
  0.25(10-2.50) 2 2.375 1.75(5-2.50)
  2HH 1.75 0.5(10-2.50) 2HL the
  converse of LHLL 0.5 1(5-2.5) 2

OutcomesNash equilibrium LL, as L is the
dominant strategy of each player at LL, neither
player has an incentive to move, given, the other
players choiceCo-operative outcome HH, as
this is the joint optimum that is, the sum of
the players pay-offs (1.751.75 3.5) is
greater than that in any other cell
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1a) Pay-off matrix (cont)

• Common mistakes
• Very few!
• Confusing Nash equilibrium with joint optimum
  they are not the same thing
• Calculation errors

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1b) Price-matching policy M
Joint optimum
The only payoff changes vs. a)
1.125, 0.5
1.75, 1.75
H Retailer A L
0.5, 0.5
2.375, -0.125
Now there is no Nash equilibrium
L H Retailer B
Ignores things such as cost of advertising
good answers worked out the maximum advertising
cost for which the policy would still create
value
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1b) Price-matching policy (cont)

• Pay-off calculations
• Only the LH pay-offs are affected
• 1.125 0.5(5-2.50) 0.25(10-2.50) 2
• 0.5 1(5-2.50) - 2

OutcomesNash equilibrium no longer
existsLikely outcome HHIf B believes that A
will always go high (ie, As commitment is
credible), then B will go H, as 1.75 gt
0.5 Should A introduce? YesAs pay-off will
increase by 1.25M (from 0.125 to 1.125). A will
be better-off as long as the advertising cost is
lt 1.25M
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1b) Price matching policy (cont)

• Common mistakes
• Incorrect calculation of how the payoffs change
• Lack of logic in determining how the payoff
  changes affect the likely outcome

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2a) Maximum profit

• P 823 4QD MR 823 8QD (same
  intercept, twice slope)
• MR MC 823 8QD 15 QD
  101 (check this is feasible, as
  
  101 lt capacity (275) )
• P 823 4101 (plugging QD 101 into demand
  curve)
• P 419
• Profit QD (P MC) 101(419 15)
  Maximum profit 40,804
• Explanation
• P/MC 419/15 27.9 a huge markup. Why?
  Elasticity of demand at profit
• maximising point is 1.037 eD (DQ/DP)P/Q
  (-1/4)(419/101) -1.037
• As the elasticity is very close to 1, the
  profit-maximising mark-up is very high (from
  the inverse elasticity rule P/MC 1/(11/eD)

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2a) Maximum profit (cont)

• Common mistakes
• Maximising revenue, rather than profit
• Forgetting to explain

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2b) Competitor profits

• It is not clear from the question whether this is
  Bertrand or Cournot fortunately,
• it doesnt matter as the capacity constraint
  becomes binding
• If assume Cournot
• P 1,223 4QD
• MRDEF 1,223 8QDEF 4QGHI (same
  intercept, twice slope on own
  output, same
  slope on competitor output)
• As this is symmetrical (same MC), each firms
  output (call it Q) will be the same, ie
  QQDEFQGHI. Therefore, MRDEF simplifies
  toMRDEF 1,223 12QMRDEF MC 1,223
  12Q 15 Q 100.67, but this is gt
  75 and therefore not feasible. While each firm
  would like to produce 100.67 units, they each
  face a 75 unit capacity constraint QDEF
  QGHI 75
• P 1,223 8(7575) (plugging QDEF QGHI 75
  into demand curve)
• P 623
• QDEF profit QDEF(P MC) 75(623 15)
  DEF profit 45,600 GHI profit
  45,600 (by symmetry) total profit 91,200
  (45,6002)

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2b) Competitor profits (cont)

• If assume Bertrand
• P MC 15 but, from demand curve, at P15,
  QD (1,223-15)/4 302, but this is gt 150 (
  total capacity)
• Therefore, capacity will determine quantity
  produced and price will be given
• by the demand curve at that quantity so we get
  the same result as when we
• assumed Cournot

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2b) Competitor profits (cont)

• Explanation
• Total industry profits have more than doubled,
  from 40,804 in a) to 91,200 in b). While a move
  from monopoly to a Bertrand or Cournot situation
  would normally reduce profits, this has been more
  than offset by 2 factors- increased demand
  (higher price at any quantity)- capacity
  constraint, which reduces the supply increase
  that would normally occur in moving from
  monopoly to Bertrand or Cournot and therefore
  stops price declining
• Common mistakes
• Ignoring the capacity constraint
• Assuming it is definitely Cournot or definitely
  Bertrand (we dont know so we need test what
  happens under each)
• Plugging only one competitors quantity (rather
  than total quantity) into the demand curve to
  determine price
• Forgetting to explain

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2c) Tough price competition

• It is now Bertrand, so PMC P 15
• P 423 4QD QD (423-P)/4
  (423-15)/4 102
• Total QD 102, which is feasible as it is lt
  total capacity of 150
• So each produces 51 units (102/2)
• Each firms profit is zero, as PMC
• Common mistake assuming Cournot, rather than
  Bertrand (tough price
• competition Bertrand)

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2d) Acquisition WTP P

• DEF has 2 options buy GHI or dont buy it (DEF
  could also be bought by GHI but, given
• symmetry, GHIs WTP for DEF will be the same as
  DEFs WTP for GHI)
• If DEF doesnt buy GHI, its profits (BATNA) will
  be zero (from d)
• If DEF does buy GHI, it will act as a
  monopolistP 423 4QD MR 423
  8QD (same intercept, twice the slope)MR MC
  423 8QD 15 QD 51
• P 423 451 (plugging QD 51 into the demand
  curve) P 219DEF profit QD (P
  MC) 51(219 15) 10,404
• Therefore, DEFs WTP for GHI 10,404 ( the
  profit difference between the 2 options)
• GHIs WTS 0 ( profit it earns if doesnt sell)
• Expected price (when they split the surplus
  50/50) 5,202 (10,404/2)

Ignoring a possible further gain could sell
one of the plants, as QD is now lt the capacity of
one plant
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2d) Acquisition WTP P (cont)

• Common mistakes
• Using the wrong model to calculate profit if no
  acquisition is made
• Using the wrong model to calculate profit if the
  acquisition is made
• Assuming that DEF will have to pay all of its WTP
  or only GHIs WTS, without explanation (rather
  than a 50/50 split of the surplus)

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3a) 3b) Minimum sell prices

• Minimum sell price WTS
• 3a) For EG /Mwh
• MC of electricity (if no breakdown) 20.00
• Breakdown cost (1.61M/1M) 1.60
• Total expected cost 21.60
• Therefore, WTS 21.60/Mwh
• 3b) For each of the competitors /Mwh
• MC of electricity (if no breakdown) 20.00
• Breakdown cost (3.71M/1M) 3.70
• Total expected cost 23.70
• Therefore, WTS 23.70/Mwh
• So competitors would be willing to provide a
  guarantee, but only for Pgt23.70/Mwh
• Common mistake ignoring breakdown cost

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3c) Which bids?
Bid Competitor Calculation profit if win
M (Q(P-MC)) A 0 1(20-20) B
0.6 1(20.60-20) C -3.1 1(20.6-23.70
) D -0.1 1(23.60-23.70)
Only bids A and B would not lose money, but only
B would make a positive economic profit
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3c) Which bids? (cont)
Bid EG profit Calculation if win
M (Q(P-MC)) A 0 1(20-20) B
0.6 1(20.60-20) C -1.0 1(20.60-21.6
0) D 2.0 1(23.60-21.60)
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3c) Which bids? (cont)

• EG should not bid C (as it would lose money) and
  there is no point in bidding A, as it wouldnt
  make any money so we are left with B and D
• If EG can only submit one bid, it should choose
  bid D - D is more profitable than B
• His competitors cannot afford to submit bid D,
  because they would lose money so they will bid
  B.
• AS prefers bid D to bid B, because they expect
  their costs to be 23.6 million instead of 24.30
  million, so he will win if he bids D.

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3d) Revise bid?
Bid GI profit Calculation if win
M (Q(P-MC)) A -0.5 1(20-20)
0.5 B 0.1 1(20.60-20) 0.5 C
-1.4 1(20.6-21.50) 0.5 D
1.6 1(23.60-21.50) 0.5
In contrast to in 3c) GI is now much more likely
to submit bid D, as it is now very profitable
21.50 20 (1.51M/1M)
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3d) Revise bid? (cont)
Payoff calculations You can write down a game
table and find the Nash equilibrium (when there
are two choices consideredbid B and bid D). But
its pretty clear that both have a dominant
strategy of bidding D its preferred by the
customer, and its more profitable for them. So
they each bid D, and each wins with 50
probability. You should not revise your bid.
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3d) Revise bid? pay-off matrixM
EG B D
0.3, 0.3
0, 2.0
B GI D
1.6, 0
0.8, 1.0
dominantstrategy for both is bid D