Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
9th Edition
ISBN: 9781259290619
Author: Michael Baye, Jeff Prince
Publisher: McGraw-Hill Education
Question
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Chapter 9, Problem 4CACQ

(A)

To determine

The reaction function of the follower is to be ascertained.

(A)

Expert Solution
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Explanation of Solution

  P=160004Q where Q=QL+QF

  P=160004QL4QF

  CL(QL)=4000QL

  CF(QF)=6000QF

Reaction function of follower

  MRF=MCF

  dTRFdQF=dCF(QF)dQF

  dP×QFdQF=d6000QFdQF

  d(160004QL4QF)QFdQF=6000

  d(16000QF4QLQF4QF2)dQF=6000

  160004QL8QF=6000

  QF=18(100004QL)

  QF= 125012QL

Therefore, reaction function of the follower is QF= 125012QL

(B)

To determine

The equilibrium level of output for both the leader and follower is to be calculated.

(B)

Expert Solution
Check Mark

Explanation of Solution

For finding the equilibrium output,putting the follower reaction function value of QF in P

  P= 160004QL4QF

  P=160004QL4(125012QL)

        P=160004QL5000+2QL

  P=110002QL

Now, TRL=P×QL

  =(110002QL)×QL

  =11000QL2QL2

Putting MRL= MCL

  110004QL=4000

   7000=4QL

  QL=1750 units

Now, put the value of QL in reaction function of follower.

  QF=125012QL

  QF=125012×1750

  QF= 375 units.

Therefore , QL = 1750 units and QF = 375 units.

(C)

To determine

The equilibrium market price is to be ascertained.

(C)

Expert Solution
Check Mark

Explanation of Solution

Equilibrium market price

  P=160004QL4QF

  P=160004×17504×375

  P=1600070001500

             P = $7500.

Therefore, equilibrium market price is $7500.

(D)

To determine

The profits of both leader and follower is to be calculated.

(D)

Expert Solution
Check Mark

Explanation of Solution

Profit of the leader is TRL TCL

  Profit=P×QL4000QL

  =7500×17504000×1750

  =131250007000000

  = $6125000

Profit of the follower is TRF TCF

  Profit=P×QF6000QF

  =7500×3756000×375

  =28125002250000

           = $562500 .

Therefore , profit of the leader is $6125000 and profit of the follower is $562500.

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