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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Suppose that firms’ marginal and average costs are constant and equal to c and that inverse market demand is given by P = a – bQ, where a, b > 0 (a) Calculate the profit-maximizing quantity-price combination and for a monopolist. (b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities and for their identical products simultaneously. Also compute market output and market price. (c) Calculate the perfectly competitive equilibrium price and market output. (d) Suppose now that there are n identical firms in a Cournot model (oligopoly). Compute the Nash equilibrium quantities as functions of n. Also compute market output and market price. (e) Verify (i) that the monopoly outcome from part (a) can be reproduced in part (d) by setting n = 1; (ii) that the duopoly outcome from part (b) can be reproduced in part (d) by setting n = 2; (iii) that letting n approach infinity yields the same market price and output as…

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-Qa-Qb where QAQA and QBQB, are the quantities sold by the respective firms and P is the selling price. The total cost functions for the two companies are TCa=1,500+55Qa+Qa2 TCb=1,200+20Qb+2Qb2 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). For Company A, the long-run equilibrium output is and the selling price is $ . For Company B, the long-run equilibrium output is , and selling price is $ . At the equilibrium output, Company A earns total profits of $ and Company B earns total profits of $ . Therefore, the total industry profits are $ .

Additional Problem 3: Assume two companies (C and D) are Cournot duopolists that produce identical products. Demand for the products is given by the following linear demand function: ? = 600 − ?C − ?D where ?C and ?D are the quantities sold by the respective firms and P is the price. Total cost functions for the two companies are ??C= 25,000 +100?C 2 ??D = 20,000 + 125?D c. Determine the equilibrium price and quantities sold by each firm. d.Determine the profits for the market as well as eachfirm.

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.