Question

SCENARIO 3: Consider an industry consisting of two firms producing an identical product. The inverse market demand equation is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1 = 4Q1 and TC2 = 4Q2, respectively.

Refer to SCENARIO 3. Firm 1 is the Stackelberg leader and firm 2 is the Stackelberg

follower. The profit of the Stackelberg leader is:

a. $288.

b. $432.

c. $486.

d. $576.

e. None of the above.

Answer #1

Ans. Option e

Inverse market demand function, P = 100 - 2q1 - 2q2

Total revenue of firm 2, TR2 = 100q2 - 2q2^2 - 2q2*q1

=> Marginal revenue of firm 2, MR2 = dTR2/dq2 = 100 - 4q2 - 2q1

Marginal Cost of firm 2, MC2 = dTC2/dq2 = 4

At equilibrium,

MR2 = MC2

=> 100 - 4q2 -2q1 = 4

=> q2 = 25 - 0.5q1 ---> Eq1

Substituting Eq1 in inverse market demand function, we get,

P = 100 - 2(25 - 0.5q1) - 2q1

=> P = 50 - q1

=> Total revenue of firm 1, TR1 = P*q1 = 50q1 - q1^2

=> Marginal revenue, MR1 = dTR1/dq1 = 50 - 2q1

and marginal cost, MC1 = dTC1/dq1 = 4

At equilibrium,

MR1 = MC1

=> 50 - 2q1= 4

=> q1 = 23 units

Profit = P*q1 - TC1

=> Profit = (50 - 23) * 23 - 4*23

=> Profit = $529

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Consider an industry consisting of two firms producing
an identical product. The inverse market demand equation is P = 100
− 2Q. The total cost equations for firms 1 and 2 are TC1 = 4Q1 and
TC2 = 4Q2, respectively. Firm 1 is the Stackelberg leader and firm
2 is the Stackelberg follower. The profit of the Stackelberg
follower is:
$864.
$576.
$432.
$288.
$1,152.

Consider an industry consisting of two firms producing an
identical product. The inverse market demand equation is P = 100 −
2Q. The total cost equations for firms 1 and 2 are TC1 = 4Q1 and
TC2 = 4Q2, respectively.
Firm 1 is the Stackelberg leader and firm 2 is the Stackelberg
follower. The output of the Stackelberg follower is:
6.
12.
24.
48.
None of the above.

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse market demand equation
is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1
= 4Q1 and TC2 = 4Q2, respectively.
Refer to SCENARIO 3. Suppose that the two firms are Bertrand
rivals. The equilibrium level
of output for firm 1 is:
a. 8.
b. 10.
c. 12.
d. 24.
e. None of the above.

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse
market demand equation is P = 100 − 2Q. The total cost equations
for firms 1 and 2 are TC1 = 4Q1 and
TC2 = 4Q2, respectively.
Refer to SCENARIO 3. Suppose that the two firms are Cournot
rivals. Firm 1 will earn a
profit of:
a. $512.
b. $732.
c. $836.
d. $1,014.
e. None of the above.

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse market demand equation
is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1
= 4Q1 and TC2 = 4Q2, respectively.
Refer to SCENARIO 3. Suppose that the two firms are Cournot
rivals. The equilibrium level
of output for firm 1 is:
a. 8.
b. 16.
c. 24.
d. 32.
e. None of the above.

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse market demand equation
is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1
= 4Q1 and TC2 = 4Q2, respectively.
9. Refer to SCENARIO 3. Suppose that the two firms are Cournot
rivals. Firm 1’s reaction function is:
a. Q1 = 12 − Q2.
b. Q1 = 12 − 0.25Q2.
c. Q1 = 24 − 0.5Q2.
d. Q1...

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse market demand equation
is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1
= 4Q1 and TC2 = 4Q2, respectively.
9. Refer to SCENARIO 3. Suppose that the two firms are Cournot
rivals. Firm 1’s reaction function is: a. Q1 = 12 − Q2. b. Q1 = 12
− 0.25Q2. c. Q1 = 24 − 0.5Q2. d. Q1...

Consider an industry consisting of two firms producing an
identical product. The inverse market demand equation is P = 100 −
2Q. The total cost equations for firms 1 and 2 are TC1 = 4Q1 and
TC2 = 4Q2, respectively. Suppose that the two firms are Cournot
rivals. Firm 2 will earn a profit of:
$512.
$732.
$836.
$1,014.
None of the above.

Suppose that two firms compete in the same market producing
homogenous products with the following inverse demand function:
P=1,000-(Q1+Q2)
The cost function of each firm is given by:
C1=4Q1
C2=4Q2
Suppose that the two firms engage in Bertrand price
competition. What price should firm 1 set in equilibrium? What
price should firm 2 set? What are the profits for each firm in
equilibrium? What is the total market output?
Suppose that the two firms collude in quantity, i.e.,
acting together...

The geegaw industry consists of two Cournot competitors
producing an identical product. The inverse demand equation is
P=591-4Q.
The total cost equations of the two firms are:
TC_1=15Q_1
TC_2=31Q_2.
a. Determine the total revenue equation for each firm.
b. What is the reaction function of each firm?
c. What is the Cournot-Nash equilibrium level of output?
d. What is the market-determined price of geegaws?
e. Calculate each firm’s total profit.

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