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

Question

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Answer 1

Question

Chapter 12, Problem 1E

a)

To determine

To calculate:

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

a)

Expert Solution

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

=(600−QC−QD)QC......(1)=600QC−QC2−QCQD

The cost function for firm C

TC=25,000+100Qc

Profit function is,

=TotalRevenue−TotalCost=600QC−QC2−QCQD−25,000−100QC=−25,000+500QC−QC2−QCQD

Differentiating the total profit function and equating it with zero:

Mπ=ddQC(−25000+500QC−QC2−QCQD).......(2)=500−2QC−QD

Profit for the firm D is,

P=6000−QC−QDTotalRevenue=Price×Quantity=(600−QC−QD)QD=600QD−QD2−QCQD

The cost function of the firm D is,

TC=20,000+125QD

Profit function is,

TotalRevenue=Price×Quantity=600QD−QD2−QCQD−20,000−125QD=−20,000+475QD−QD2−QCQD

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),

475−2QD−QC=0475−2QD−175=02QD=3002=150

Substituting the output values of both firms:

P=600−QC−QD=600−175−150=$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

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+500Qc−QC2−QCQD

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

=−25000+500Qc−QC2−QCQD =−25000+500(175)− (175) 2 −(175)(150)=−25000+87,500−30,625−26,250=$5,625

The profit function of firm D is,

=−20,000+475QD−QD2−QCQD

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

=−20,000+475QD−QD2−QCQD =−20,000+475(150)− (150) 2 −(150)(175)=−20,000+71,250−22,500−26,250=$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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Answer 2

Question

Chapter 12, Problem 1E

a)

To determine

To calculate:

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

a)

Expert Solution

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

=(600−QC−QD)QC......(1)=600QC−QC2−QCQD

The cost function for firm C

TC=25,000+100Qc

Profit function is,

=TotalRevenue−TotalCost=600QC−QC2−QCQD−25,000−100QC=−25,000+500QC−QC2−QCQD

Differentiating the total profit function and equating it with zero:

Mπ=ddQC(−25000+500QC−QC2−QCQD).......(2)=500−2QC−QD

Profit for the firm D is,

P=6000−QC−QDTotalRevenue=Price×Quantity=(600−QC−QD)QD=600QD−QD2−QCQD

The cost function of the firm D is,

TC=20,000+125QD

Profit function is,

TotalRevenue=Price×Quantity=600QD−QD2−QCQD−20,000−125QD=−20,000+475QD−QD2−QCQD

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),

475−2QD−QC=0475−2QD−175=02QD=3002=150

Substituting the output values of both firms:

P=600−QC−QD=600−175−150=$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

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+500Qc−QC2−QCQD

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

=−25000+500Qc−QC2−QCQD =−25000+500(175)− (175) 2 −(175)(150)=−25000+87,500−30,625−26,250=$5,625

The profit function of firm D is,

=−20,000+475QD−QD2−QCQD

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

=−20,000+475QD−QD2−QCQD =−20,000+475(150)− (150) 2 −(150)(175)=−20,000+71,250−22,500−26,250=$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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Answer 3

Question

Chapter 12, Problem 1E

a)

To determine

To calculate:

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

a)

Expert Solution

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

=(600−QC−QD)QC......(1)=600QC−QC2−QCQD

The cost function for firm C

TC=25,000+100Qc

Profit function is,

=TotalRevenue−TotalCost=600QC−QC2−QCQD−25,000−100QC=−25,000+500QC−QC2−QCQD

Differentiating the total profit function and equating it with zero:

Mπ=ddQC(−25000+500QC−QC2−QCQD).......(2)=500−2QC−QD

Profit for the firm D is,

P=6000−QC−QDTotalRevenue=Price×Quantity=(600−QC−QD)QD=600QD−QD2−QCQD

The cost function of the firm D is,

TC=20,000+125QD

Profit function is,

TotalRevenue=Price×Quantity=600QD−QD2−QCQD−20,000−125QD=−20,000+475QD−QD2−QCQD

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),

475−2QD−QC=0475−2QD−175=02QD=3002=150

Substituting the output values of both firms:

P=600−QC−QD=600−175−150=$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

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+500Qc−QC2−QCQD

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

=−25000+500Qc−QC2−QCQD =−25000+500(175)− (175) 2 −(175)(150)=−25000+87,500−30,625−26,250=$5,625

The profit function of firm D is,

=−20,000+475QD−QD2−QCQD

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

=−20,000+475QD−QD2−QCQD =−20,000+475(150)− (150) 2 −(150)(175)=−20,000+71,250−22,500−26,250=$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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 12, Problem 1E

a)

To determine

To calculate:

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

a)

Expert Solution

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

=(600−QC−QD)QC......(1)=600QC−QC2−QCQD

The cost function for firm C

TC=25,000+100Qc

Profit function is,

=TotalRevenue−TotalCost=600QC−QC2−QCQD−25,000−100QC=−25,000+500QC−QC2−QCQD

Differentiating the total profit function and equating it with zero:

Mπ=ddQC(−25000+500QC−QC2−QCQD).......(2)=500−2QC−QD

Profit for the firm D is,

P=6000−QC−QDTotalRevenue=Price×Quantity=(600−QC−QD)QD=600QD−QD2−QCQD

The cost function of the firm D is,

TC=20,000+125QD

Profit function is,

TotalRevenue=Price×Quantity=600QD−QD2−QCQD−20,000−125QD=−20,000+475QD−QD2−QCQD

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),

475−2QD−QC=0475−2QD−175=02QD=3002=150

Substituting the output values of both firms:

P=600−QC−QD=600−175−150=$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

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+500Qc−QC2−QCQD

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

=−25000+500Qc−QC2−QCQD =−25000+500(175)− (175) 2 −(175)(150)=−25000+87,500−30,625−26,250=$5,625

The profit function of firm D is,

=−20,000+475QD−QD2−QCQD

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

=−20,000+475QD−QD2−QCQD =−20,000+475(150)− (150) 2 −(150)(175)=−20,000+71,250−22,500−26,250=$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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 12, Problem 1E

a)

To determine

To calculate:

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

a)

Expert Solution

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

=(600−QC−QD)QC......(1)=600QC−QC2−QCQD

The cost function for firm C

TC=25,000+100Qc

Profit function is,

=TotalRevenue−TotalCost=600QC−QC2−QCQD−25,000−100QC=−25,000+500QC−QC2−QCQD

Differentiating the total profit function and equating it with zero:

Mπ=ddQC(−25000+500QC−QC2−QCQD).......(2)=500−2QC−QD

Profit for the firm D is,

P=6000−QC−QDTotalRevenue=Price×Quantity=(600−QC−QD)QD=600QD−QD2−QCQD

The cost function of the firm D is,

TC=20,000+125QD

Profit function is,

TotalRevenue=Price×Quantity=600QD−QD2−QCQD−20,000−125QD=−20,000+475QD−QD2−QCQD

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),

475−2QD−QC=0475−2QD−175=02QD=3002=150

Substituting the output values of both firms:

P=600−QC−QD=600−175−150=$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

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+500Qc−QC2−QCQD

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

=−25000+500Qc−QC2−QCQD =−25000+500(175)− (175) 2 −(175)(150)=−25000+87,500−30,625−26,250=$5,625

The profit function of firm D is,

=−20,000+475QD−QD2−QCQD

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

=−20,000+475QD−QD2−QCQD =−20,000+475(150)− (150) 2 −(150)(175)=−20,000+71,250−22,500−26,250=$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.

Answer 6

Chapter 12, Problem 1E

a)

To determine

To calculate:

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

a)

Expert Solution

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

=(600−QC−QD)QC......(1)=600QC−QC2−QCQD

The cost function for firm C

TC=25,000+100Qc

Profit function is,

=TotalRevenue−TotalCost=600QC−QC2−QCQD−25,000−100QC=−25,000+500QC−QC2−QCQD

Differentiating the total profit function and equating it with zero:

Mπ=ddQC(−25000+500QC−QC2−QCQD).......(2)=500−2QC−QD

Profit for the firm D is,

P=6000−QC−QDTotalRevenue=Price×Quantity=(600−QC−QD)QD=600QD−QD2−QCQD

The cost function of the firm D is,

TC=20,000+125QD

Profit function is,

TotalRevenue=Price×Quantity=600QD−QD2−QCQD−20,000−125QD=−20,000+475QD−QD2−QCQD

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),

475−2QD−QC=0475−2QD−175=02QD=3002=150

Substituting the output values of both firms:

P=600−QC−QD=600−175−150=$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.

Answer 7

Chapter 12, Problem 1E

a)

To determine

To calculate:

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

Answer 8

a)

Expert Solution

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

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Profit for firm C

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

=(600−QC−QD)QC......(1)=600QC−QC2−QCQD

The cost function for firm C

TC=25,000+100Qc

Profit function is,

=TotalRevenue−TotalCost=600QC−QC2−QCQD−25,000−100QC=−25,000+500QC−QC2−QCQD

Differentiating the total profit function and equating it with zero:

Mπ=ddQC(−25000+500QC−QC2−QCQD).......(2)=500−2QC−QD

Profit for the firm D is,

P=6000−QC−QDTotalRevenue=Price×Quantity=(600−QC−QD)QD=600QD−QD2−QCQD

The cost function of the firm D is,

TC=20,000+125QD

Profit function is,

TotalRevenue=Price×Quantity=600QD−QD2−QCQD−20,000−125QD=−20,000+475QD−QD2−QCQD

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),

475−2QD−QC=0475−2QD−175=02QD=3002=150

Substituting the output values of both firms:

P=600−QC−QD=600−175−150=$275

Answer 13

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.

Answer 14

b)

To determine

To calculate:

The total profits for each firm at the equilibrium output

b)

Expert Solution

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+500Qc−QC2−QCQD

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

=−25000+500Qc−QC2−QCQD =−25000+500(175)− (175) 2 −(175)(150)=−25000+87,500−30,625−26,250=$5,625

The profit function of firm D is,

=−20,000+475QD−QD2−QCQD

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

=−20,000+475QD−QD2−QCQD =−20,000+475(150)− (150) 2 −(150)(175)=−20,000+71,250−22,500−26,250=$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.

Answer 15

b)

To determine

To calculate:

The total profits for each firm at the equilibrium output

Answer 16

b)

Expert Solution

Answer to Problem 1E

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

Answer 17

b)

Expert Solution

Answer 18

b)

Expert Solution

Answer 19

Expert Solution

Answer 20

Explanation of Solution

The profit function of firm C is,

=−25000+500Qc−QC2−QCQD

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

=−25000+500Qc−QC2−QCQD =−25000+500(175)− (175) 2 −(175)(150)=−25000+87,500−30,625−26,250=$5,625

The profit function of firm D is,

=−20,000+475QD−QD2−QCQD

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

=−20,000+475QD−QD2−QCQD =−20,000+475(150)− (150) 2 −(150)(175)=−20,000+71,250−22,500−26,250=$2,500

Answer 21

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.