To know: Whether $200 to be invested or not.

Question

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Answer 1

Question

Chapter 9, Problem 19PAA

To determine

To know:Whether $200 to be invested or not.

Expert Solution & Answer

Explanation of Solution

There are two firms: TT and ST

Following is the cost function of TT:

∂TRTT∂QTT = ∂CTT∂QTT∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

Following is the cost function of ST:

CST (QST) = 4QST

Following is the inverse demand function:

P = 160−2Q = 160−2(QTT+QST)

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCTT = MRTT

This implies:

∂TRTT∂QTT = ∂CTT∂QTT∂PQTT∂QTT = ∂4QTT∂QTT

∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

160−4QTT−2QST = 4

QTT =14(160−4−2QST)

QTT =39−12QST

Reaction function of TT firm is given as: QTT =39−12QST .

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCST = MRST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST0 = 4

160−2QTT−4QST = 4

QST = 14(160−4−2QTT)

In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.

This implies:

QTT = 39−12(39−12QTT)

QTT = 39−19.5+14QTTQTT = 26QST = 26

Solving both the equations,

Thus, equilibrium output of TT is 26 and of ST is26

The equilibrium market price is given by:

P = 160−2(QTT+QST)

P = 160−2(26+26)P = 56

Profit is calculated by subtracting total revenue and total cost. For TT firm,

π1 = TRTT − CTT = PQST − CST = 56× 26 − 4× 26 = 1352

Profit is calculated by subtracting total revenue and total cost. For ST firm,

π1 = TRST − CST = PQST − CST = 56× 26 − 4× 26 = 1352

Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.

Under stackelberg duopoly model, profit maximizing condition is as follows:

MRST = MCST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST = 4

160−2QTT−4QST = 4

QST = 39−12QTT

The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects Q_T_T_.

The profit of the leader firm is given by:

πTT = TRTT − CTT = PQTT − 4QTT = 82QTT−QTT2 − 4QL = 78QTTQTT2 −

The leader firm chooses Q_T_T that maximizes the given profit function.

Hence, Q_T_T that maximizes the profit function of the leader firm is:

∂πTT∂QTT = 02QTT = 78QTT = 39

Hence, the equilibrium output level for the leader firm is 39.

Calculation of equilibrium output:

QST = 39−12QTT = 39−1239 = 19.5

Firm St has 19.5 units of output.

Calculation of equilibrium price:

P = 160−2Q = 160−2(QTT+2QST) = 160−2(39+19.5) = 43

Calculation of profit of TT firm is as follows:

π = TRTT− CTT = PQTT− CTT = 43× 39−4×39 = 1521

Calculation of profit of ST firm is as follows:

π = TRST− CST = PQST− CST = 43× 19.5−4×19.5 = 760.5

Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.

The unrecoverable fixed investment is $200, greater than $169.

That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.

Economics Concept Introduction

Introduction:

Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.

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Answer 2

Question

Chapter 9, Problem 19PAA

To determine

To know:Whether $200 to be invested or not.

Expert Solution & Answer

Explanation of Solution

There are two firms: TT and ST

Following is the cost function of TT:

∂TRTT∂QTT = ∂CTT∂QTT∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

Following is the cost function of ST:

CST (QST) = 4QST

Following is the inverse demand function:

P = 160−2Q = 160−2(QTT+QST)

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCTT = MRTT

This implies:

∂TRTT∂QTT = ∂CTT∂QTT∂PQTT∂QTT = ∂4QTT∂QTT

∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

160−4QTT−2QST = 4

QTT =14(160−4−2QST)

QTT =39−12QST

Reaction function of TT firm is given as: QTT =39−12QST .

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCST = MRST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST0 = 4

160−2QTT−4QST = 4

QST = 14(160−4−2QTT)

In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.

This implies:

QTT = 39−12(39−12QTT)

QTT = 39−19.5+14QTTQTT = 26QST = 26

Solving both the equations,

Thus, equilibrium output of TT is 26 and of ST is26

The equilibrium market price is given by:

P = 160−2(QTT+QST)

P = 160−2(26+26)P = 56

Profit is calculated by subtracting total revenue and total cost. For TT firm,

π1 = TRTT − CTT = PQST − CST = 56× 26 − 4× 26 = 1352

Profit is calculated by subtracting total revenue and total cost. For ST firm,

π1 = TRST − CST = PQST − CST = 56× 26 − 4× 26 = 1352

Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.

Under stackelberg duopoly model, profit maximizing condition is as follows:

MRST = MCST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST = 4

160−2QTT−4QST = 4

QST = 39−12QTT

The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects Q_T_T_.

The profit of the leader firm is given by:

πTT = TRTT − CTT = PQTT − 4QTT = 82QTT−QTT2 − 4QL = 78QTTQTT2 −

The leader firm chooses Q_T_T that maximizes the given profit function.

Hence, Q_T_T that maximizes the profit function of the leader firm is:

∂πTT∂QTT = 02QTT = 78QTT = 39

Hence, the equilibrium output level for the leader firm is 39.

Calculation of equilibrium output:

QST = 39−12QTT = 39−1239 = 19.5

Firm St has 19.5 units of output.

Calculation of equilibrium price:

P = 160−2Q = 160−2(QTT+2QST) = 160−2(39+19.5) = 43

Calculation of profit of TT firm is as follows:

π = TRTT− CTT = PQTT− CTT = 43× 39−4×39 = 1521

Calculation of profit of ST firm is as follows:

π = TRST− CST = PQST− CST = 43× 19.5−4×19.5 = 760.5

Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.

The unrecoverable fixed investment is $200, greater than $169.

That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.

Economics Concept Introduction

Introduction:

Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.

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

Answer 3

Question

Chapter 9, Problem 19PAA

To determine

To know:Whether $200 to be invested or not.

Expert Solution & Answer

Explanation of Solution

There are two firms: TT and ST

Following is the cost function of TT:

∂TRTT∂QTT = ∂CTT∂QTT∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

Following is the cost function of ST:

CST (QST) = 4QST

Following is the inverse demand function:

P = 160−2Q = 160−2(QTT+QST)

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCTT = MRTT

This implies:

∂TRTT∂QTT = ∂CTT∂QTT∂PQTT∂QTT = ∂4QTT∂QTT

∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

160−4QTT−2QST = 4

QTT =14(160−4−2QST)

QTT =39−12QST

Reaction function of TT firm is given as: QTT =39−12QST .

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCST = MRST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST0 = 4

160−2QTT−4QST = 4

QST = 14(160−4−2QTT)

In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.

This implies:

QTT = 39−12(39−12QTT)

QTT = 39−19.5+14QTTQTT = 26QST = 26

Solving both the equations,

Thus, equilibrium output of TT is 26 and of ST is26

The equilibrium market price is given by:

P = 160−2(QTT+QST)

P = 160−2(26+26)P = 56

Profit is calculated by subtracting total revenue and total cost. For TT firm,

π1 = TRTT − CTT = PQST − CST = 56× 26 − 4× 26 = 1352

Profit is calculated by subtracting total revenue and total cost. For ST firm,

π1 = TRST − CST = PQST − CST = 56× 26 − 4× 26 = 1352

Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.

Under stackelberg duopoly model, profit maximizing condition is as follows:

MRST = MCST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST = 4

160−2QTT−4QST = 4

QST = 39−12QTT

The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects Q_T_T_.

The profit of the leader firm is given by:

πTT = TRTT − CTT = PQTT − 4QTT = 82QTT−QTT2 − 4QL = 78QTTQTT2 −

The leader firm chooses Q_T_T that maximizes the given profit function.

Hence, Q_T_T that maximizes the profit function of the leader firm is:

∂πTT∂QTT = 02QTT = 78QTT = 39

Hence, the equilibrium output level for the leader firm is 39.

Calculation of equilibrium output:

QST = 39−12QTT = 39−1239 = 19.5

Firm St has 19.5 units of output.

Calculation of equilibrium price:

P = 160−2Q = 160−2(QTT+2QST) = 160−2(39+19.5) = 43

Calculation of profit of TT firm is as follows:

π = TRTT− CTT = PQTT− CTT = 43× 39−4×39 = 1521

Calculation of profit of ST firm is as follows:

π = TRST− CST = PQST− CST = 43× 19.5−4×19.5 = 760.5

Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.

The unrecoverable fixed investment is $200, greater than $169.

That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.

Economics Concept Introduction

Introduction:

Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.

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 9, Problem 19PAA

To determine

To know:Whether $200 to be invested or not.

Expert Solution & Answer

Explanation of Solution

There are two firms: TT and ST

Following is the cost function of TT:

∂TRTT∂QTT = ∂CTT∂QTT∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

Following is the cost function of ST:

CST (QST) = 4QST

Following is the inverse demand function:

P = 160−2Q = 160−2(QTT+QST)

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCTT = MRTT

This implies:

∂TRTT∂QTT = ∂CTT∂QTT∂PQTT∂QTT = ∂4QTT∂QTT

∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

160−4QTT−2QST = 4

QTT =14(160−4−2QST)

QTT =39−12QST

Reaction function of TT firm is given as: QTT =39−12QST .

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCST = MRST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST0 = 4

160−2QTT−4QST = 4

QST = 14(160−4−2QTT)

In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.

This implies:

QTT = 39−12(39−12QTT)

QTT = 39−19.5+14QTTQTT = 26QST = 26

Solving both the equations,

Thus, equilibrium output of TT is 26 and of ST is26

The equilibrium market price is given by:

P = 160−2(QTT+QST)

P = 160−2(26+26)P = 56

Profit is calculated by subtracting total revenue and total cost. For TT firm,

π1 = TRTT − CTT = PQST − CST = 56× 26 − 4× 26 = 1352

Profit is calculated by subtracting total revenue and total cost. For ST firm,

π1 = TRST − CST = PQST − CST = 56× 26 − 4× 26 = 1352

Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.

Under stackelberg duopoly model, profit maximizing condition is as follows:

MRST = MCST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST = 4

160−2QTT−4QST = 4

QST = 39−12QTT

The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects Q_T_T_.

The profit of the leader firm is given by:

πTT = TRTT − CTT = PQTT − 4QTT = 82QTT−QTT2 − 4QL = 78QTTQTT2 −

The leader firm chooses Q_T_T that maximizes the given profit function.

Hence, Q_T_T that maximizes the profit function of the leader firm is:

∂πTT∂QTT = 02QTT = 78QTT = 39

Hence, the equilibrium output level for the leader firm is 39.

Calculation of equilibrium output:

QST = 39−12QTT = 39−1239 = 19.5

Firm St has 19.5 units of output.

Calculation of equilibrium price:

P = 160−2Q = 160−2(QTT+2QST) = 160−2(39+19.5) = 43

Calculation of profit of TT firm is as follows:

π = TRTT− CTT = PQTT− CTT = 43× 39−4×39 = 1521

Calculation of profit of ST firm is as follows:

π = TRST− CST = PQST− CST = 43× 19.5−4×19.5 = 760.5

Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.

The unrecoverable fixed investment is $200, greater than $169.

That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.

Economics Concept Introduction

Introduction:

Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.

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 9, Problem 19PAA

To determine

To know:Whether $200 to be invested or not.

Expert Solution & Answer

Explanation of Solution

There are two firms: TT and ST

Following is the cost function of TT:

∂TRTT∂QTT = ∂CTT∂QTT∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

Following is the cost function of ST:

CST (QST) = 4QST

Following is the inverse demand function:

P = 160−2Q = 160−2(QTT+QST)

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCTT = MRTT

This implies:

∂TRTT∂QTT = ∂CTT∂QTT∂PQTT∂QTT = ∂4QTT∂QTT

∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

160−4QTT−2QST = 4

QTT =14(160−4−2QST)

QTT =39−12QST

Reaction function of TT firm is given as: QTT =39−12QST .

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCST = MRST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST0 = 4

160−2QTT−4QST = 4

QST = 14(160−4−2QTT)

In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.

This implies:

QTT = 39−12(39−12QTT)

QTT = 39−19.5+14QTTQTT = 26QST = 26

Solving both the equations,

Thus, equilibrium output of TT is 26 and of ST is26

The equilibrium market price is given by:

P = 160−2(QTT+QST)

P = 160−2(26+26)P = 56

Profit is calculated by subtracting total revenue and total cost. For TT firm,

π1 = TRTT − CTT = PQST − CST = 56× 26 − 4× 26 = 1352

Profit is calculated by subtracting total revenue and total cost. For ST firm,

π1 = TRST − CST = PQST − CST = 56× 26 − 4× 26 = 1352

Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.

Under stackelberg duopoly model, profit maximizing condition is as follows:

MRST = MCST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST = 4

160−2QTT−4QST = 4

QST = 39−12QTT

The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects Q_T_T_.

The profit of the leader firm is given by:

πTT = TRTT − CTT = PQTT − 4QTT = 82QTT−QTT2 − 4QL = 78QTTQTT2 −

The leader firm chooses Q_T_T that maximizes the given profit function.

Hence, Q_T_T that maximizes the profit function of the leader firm is:

∂πTT∂QTT = 02QTT = 78QTT = 39

Hence, the equilibrium output level for the leader firm is 39.

Calculation of equilibrium output:

QST = 39−12QTT = 39−1239 = 19.5

Firm St has 19.5 units of output.

Calculation of equilibrium price:

P = 160−2Q = 160−2(QTT+2QST) = 160−2(39+19.5) = 43

Calculation of profit of TT firm is as follows:

π = TRTT− CTT = PQTT− CTT = 43× 39−4×39 = 1521

Calculation of profit of ST firm is as follows:

π = TRST− CST = PQST− CST = 43× 19.5−4×19.5 = 760.5

Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.

The unrecoverable fixed investment is $200, greater than $169.

That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.

Economics Concept Introduction

Introduction:

Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.

Answer 6

Chapter 9, Problem 19PAA

To determine

To know:Whether $200 to be invested or not.

Expert Solution & Answer

Explanation of Solution

There are two firms: TT and ST

Following is the cost function of TT:

∂TRTT∂QTT = ∂CTT∂QTT∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

Following is the cost function of ST:

CST (QST) = 4QST

Following is the inverse demand function:

P = 160−2Q = 160−2(QTT+QST)

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCTT = MRTT

This implies:

∂TRTT∂QTT = ∂CTT∂QTT∂PQTT∂QTT = ∂4QTT∂QTT

∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

160−4QTT−2QST = 4

QTT =14(160−4−2QST)

QTT =39−12QST

Reaction function of TT firm is given as: QTT =39−12QST .

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCST = MRST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST0 = 4

160−2QTT−4QST = 4

QST = 14(160−4−2QTT)

In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.

This implies:

QTT = 39−12(39−12QTT)

QTT = 39−19.5+14QTTQTT = 26QST = 26

Solving both the equations,

Thus, equilibrium output of TT is 26 and of ST is26

The equilibrium market price is given by:

P = 160−2(QTT+QST)

P = 160−2(26+26)P = 56

Profit is calculated by subtracting total revenue and total cost. For TT firm,

π1 = TRTT − CTT = PQST − CST = 56× 26 − 4× 26 = 1352

Profit is calculated by subtracting total revenue and total cost. For ST firm,

π1 = TRST − CST = PQST − CST = 56× 26 − 4× 26 = 1352

Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.

Under stackelberg duopoly model, profit maximizing condition is as follows:

MRST = MCST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST = 4

160−2QTT−4QST = 4

QST = 39−12QTT

The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects Q_T_T_.

The profit of the leader firm is given by:

πTT = TRTT − CTT = PQTT − 4QTT = 82QTT−QTT2 − 4QL = 78QTTQTT2 −

The leader firm chooses Q_T_T that maximizes the given profit function.

Hence, Q_T_T that maximizes the profit function of the leader firm is:

∂πTT∂QTT = 02QTT = 78QTT = 39

Hence, the equilibrium output level for the leader firm is 39.

Calculation of equilibrium output:

QST = 39−12QTT = 39−1239 = 19.5

Firm St has 19.5 units of output.

Calculation of equilibrium price:

P = 160−2Q = 160−2(QTT+2QST) = 160−2(39+19.5) = 43

Calculation of profit of TT firm is as follows:

π = TRTT− CTT = PQTT− CTT = 43× 39−4×39 = 1521

Calculation of profit of ST firm is as follows:

π = TRST− CST = PQST− CST = 43× 19.5−4×19.5 = 760.5

Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.

The unrecoverable fixed investment is $200, greater than $169.

That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.

Economics Concept Introduction

Introduction:

Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.

Answer 7

Chapter 9, Problem 19PAA

To determine

To know:Whether $200 to be invested or not.

Answer 8

Expert Solution & Answer

Explanation of Solution

There are two firms: TT and ST

Following is the cost function of TT:

∂TRTT∂QTT = ∂CTT∂QTT∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

Following is the cost function of ST:

CST (QST) = 4QST

Following is the inverse demand function:

P = 160−2Q = 160−2(QTT+QST)

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCTT = MRTT

This implies:

∂TRTT∂QTT = ∂CTT∂QTT∂PQTT∂QTT = ∂4QTT∂QTT

∂(160QTT−2QTT2−2QTTQST)∂QTT = 4

160−4QTT−2QST = 4

QTT =14(160−4−2QST)

QTT =39−12QST

Reaction function of TT firm is given as: QTT =39−12QST .

There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:

MCST = MRST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST0 = 4

160−2QTT−4QST = 4

QST = 14(160−4−2QTT)

In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.

This implies:

QTT = 39−12(39−12QTT)

QTT = 39−19.5+14QTTQTT = 26QST = 26

Solving both the equations,

Thus, equilibrium output of TT is 26 and of ST is26

The equilibrium market price is given by:

P = 160−2(QTT+QST)

P = 160−2(26+26)P = 56

Profit is calculated by subtracting total revenue and total cost. For TT firm,

π1 = TRTT − CTT = PQST − CST = 56× 26 − 4× 26 = 1352

Profit is calculated by subtracting total revenue and total cost. For ST firm,

π1 = TRST − CST = PQST − CST = 56× 26 − 4× 26 = 1352

Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.

Under stackelberg duopoly model, profit maximizing condition is as follows:

MRST = MCST

This implies:

∂TRST∂QST = ∂CST∂QST

∂PQST∂QST = ∂4QST∂QST

∂(160QST−2QTTQST−2QST2)∂QST = 4

160−2QTT−4QST = 4

QST = 39−12QTT

The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects Q_T_T_.

The profit of the leader firm is given by:

πTT = TRTT − CTT = PQTT − 4QTT = 82QTT−QTT2 − 4QL = 78QTTQTT2 −

The leader firm chooses Q_T_T that maximizes the given profit function.

Hence, Q_T_T that maximizes the profit function of the leader firm is:

∂πTT∂QTT = 02QTT = 78QTT = 39

Hence, the equilibrium output level for the leader firm is 39.

Calculation of equilibrium output:

QST = 39−12QTT = 39−1239 = 19.5

Firm St has 19.5 units of output.

Calculation of equilibrium price:

P = 160−2Q = 160−2(QTT+2QST) = 160−2(39+19.5) = 43

Calculation of profit of TT firm is as follows:

π = TRTT− CTT = PQTT− CTT = 43× 39−4×39 = 1521

Calculation of profit of ST firm is as follows:

π = TRST− CST = PQST− CST = 43× 19.5−4×19.5 = 760.5

Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.

The unrecoverable fixed investment is $200, greater than $169.

That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Economics Concept Introduction

Introduction:

Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.

Answer 12

Ch. 9 - Prob. 1CACQ Ch. 9 - Prob. 2CACQ Ch. 9 - Prob. 3CACQ Ch. 9 - Prob. 4CACQ Ch. 9 - Prob. 5CACQ Ch. 9 - Prob. 6CACQ Ch. 9 - Prob. 7CACQ Ch. 9 - Prob. 8CACQ Ch. 9 - Prob. 9CACQ Ch. 9 - Prob. 10CACQ

To know: Whether $200 to be invested or not.

To know:Whether $200 to be invested or not.

Explanation of Solution

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