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

Question

Want to see more full solutions like this?

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.

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!

Students have asked these similar questions

Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:P=1000−QC−QDwhere QC and QD are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCC=15,000+50QC TCD=10,000+75QD Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change). Please, find the equilibrium output of firm C.

Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P=200− Q A − Q B where Q A and Q B are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TC A =1,500+55 Q A + Q A 2 TC B =1,200+20 Q B +2 Q B 2 Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce units and sell at . Similarly, Company B will produce units and sell at . At the optimum output levels, Company A earns total profits of and Company B earns total profits of . Therefore, the total industry profits are . At the optimum output levels, the marginal cost of Company A is and the marginal cost of Company B is . The following table shows the long-run equilibrium if the firms act independently, as in the Cournot model…

Only typed answer Two firms both produce leather boots. The inverse demand equation is given by P = 340 - 2Q, where P is the price of boots in USD/pair and Q is quantity of boots in million pair. The cost function is given by: C(Q) = 40Q. If the two firms are Stackelberg oligopolists), the output of the leader is equal to: 1) 60 2) 80 3) 75 4) 900

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.

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 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.

Answer 22

Ch. 12 - Prob. 1E Ch. 12 - Prob. 2E Ch. 12 - Prob. 3E Ch. 12 - Prob. 4E Ch. 12 - Prob. 5E Ch. 12 - Prob. 6E Ch. 12 - Prob. 7E

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

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

Answer to Problem 1E

Explanation of Solution

To calculate: The total profits for each firm at the equilibrium output

Answer to Problem 1E

Explanation of Solution

Want to see more full solutions like this?

Chapter 12 Solutions

To calculate:

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

To calculate:

The total profits for each firm at the equilibrium output