Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
Question
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Chapter 12, Problem 1E

a)

To determine

To calculate:

The long-run equilibrium output and the selling price for each firm.

a)

Expert Solution
Check Mark

Answer to Problem 1E

The long-run equilibrium output for firm Cis175 and for firm D is 150 and the selling price for each firm $275

Explanation of Solution

Profit for firm C

  P=600-QC-QDTotal Revenue=Price×Quantity

  =(600QCQD)QC......(1)=600QCQC2QCQD

The cost function for firm C

  TC=25,000+100Qc

Profit function is,

  =TotalRevenueTotalCost=600QCQC2QCQD25,000100QC=25,000+500QCQC2QCQD

Differentiating the total profit function and equating it with zero:

  Mπ=ddQC(25000+500QCQC2QCQD).......(2)=5002QCQD

Profit for the firm D is,

  P=6000QCQDTotalRevenue=Price×Quantity=(600QCQD)QD=600QDQD2QCQD

The cost function of the firm D is,

  TC=20,000+125QD

Profit function is,

  TotalRevenue=Price×Quantity=600QDQD2QCQD20,000125QD=20,000+475QDQD2QCQD

Differentiating the total profit function with respect to the QC and equating with zero:

Simultaneously by equating (2) and (3) ,

   2 Q D +4 Q C =1000 2 Q D + Q C =475_3QC=525QC=5253=175

By substituting the value of QC in equation (3),

  4752QDQC=04752QD175=02QD=3002=150

Substituting the output values of both firms:

  P=600QCQD=600175150=$275

Economics Concept Introduction

Introduction:

The long-run self-adjustment mechanism is one process that can bring the economy back to “normal” after a shock. The idea behind this assumption is that an economy will self-correct; shocks matter in the short run, but not the long run.

b)

To determine

To calculate:

The total profits for each firm at the equilibrium output

b)

Expert Solution
Check Mark

Answer to Problem 1E

The total profits for firm D and C at the equilibrium output is $2,500 and $5,625 respectively.

Explanation of Solution

The profit function of firm C is,

  =25000+500QcQC2QCQD

Substituting the value of output of both firms in above equation,

  =25000+500QcQC2QCQD =25000+500(175) (175) 2 (175)(150)=25000+87,50030,62526,250=$5,625

The profit function of firm D is,

  =20,000+475QDQD2QCQD

Substituting the value of output of both firms in profit function:

  =20,000+475QDQD2QCQD =20,000+475(150) (150) 2 (150)(175)=20,000+71,25022,50026,250=$2,500

Economics Concept Introduction

Introduction: The long-run self-adjustment mechanism is one process that can bring the economy back to “normal” after a shock. The idea behind this assumption is that an economy will self-correct; shocks matter in the short run, but not the long run.

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Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

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