Question 1

The duopolists Carl and Simon face a demand function for pumpkins of Q =2,200 -400P,where Q is the total number of pumpkins that reach the market and P is the price of pumpkins.Suppose further that each farmer has a constant marginal cost of $1.50 for each pumpkin produced.If Carl believes that Simon is going to produce Q_s pumpkins this year,then the reaction function tells us how many pumpkins Carl should produce in order to maximize his profits.Carl's reaction function is A) R_C(Q_s)= 400 - Qs/2. B) R_C(Q_s)=2,200 - 800Q_s. C) R_C(Q_s)= 800 - Qs/2. D) R_C(Q_s)=2,200 - 400Q_s. E) R_C(Q_s)= 1,200 - Q_s.

Accepted Answer

To derive Carl's reaction function, we start by solving for his profit-maximizing quantity of pumpkins using the following profit function:

πC = (2200 - 400P)QC - 1.5Q2C

Taking the derivative with respect to QC, we get:

2200 - 400P - 3QC = 0

Solving for QC, we get:

QC = (2200 - 400P)/3

Now, we need to express Carl's profit-maximizing quantity as a function of Simon's quantity, QS. We can do this by using the market demand function and solving for the remaining quantity:

Q = QC + QS = (2200 - 400P)/3 + QS

Solving for P in terms of Q and QS, we get:

P = (2200 - 3Q - 3QS)/400

Substituting this expression for P in Carl's profit-maximizing quantity, we get:

QC = (2200 - 400 [(2200 - 3Q - 3QS)/400])/3

Simplifying, we get:

QC = (800 - QS)/2

Therefore, Carl's reaction function is:

RC(QS) = (800 - QS)/2

This is equivalent to choice C.

Question 2

Two firms decide to form a cartel and collude in a way that maximizes industry profits.Each firm has zero production costs and each firm is given a positive output quota by the cartel.Which of the following statements is not true?
A) Each firm would want to produce more than its quota if it knew that the other would continue to produce at its quota.
B) The price elasticity of demand will be 21 at the output level chosen.
C) Output would be lower than if the firms behaved as Cournot firms.
D) Output would be lower than if the firms behaved as competitors.
E) All of the other statements are false.

Accepted Answer

The answer of Two firms decide to form a cartel...

Question 3

Suppose that two airlines are Cournot duopolists serving the Peoria-Dubuque route,and the demand curve for tickets per day is Q = 230 - 2p (so p=115 - Q/2).Total costs of running a flight on this route are 450+ 40q,where q is the number of passengers on the flight.Each flight has a capacity of 80 passengers.In Cournot equilibrium,each duopolist will run one flight per day and will make a daily profit of
A) $800.
B) $225.
C) $230.
D) $1,600.
E) $3,250.

Accepted Answer

The answer of Suppose that two airlines are Cournot duopolists...

Question 4

The inverse demand function for fuzzy dice is p = 20 - q.There are constant returns to scale in this industry with unit costs of $8.Which of the following sets of statements is completely true?
A) Monopoly output is 6.Cournot duopoly total output is 8.A Stackelberg leader's output is 8.
B) Monopoly output is 8.Cournot duopoly total output is 8.A Stackelberg leader's output is 8.
C) Monopoly output is 6.Cournot duopoly total output is 6.A Stackelberg follower's output is 3.
D) Monopoly output is 6.Cournot duopoly total output is 8.A Stackelberg follower's output is 3.
E) Monopoly output is 6.Cournot duopoly total output is 8.A Stackelberg follower's output is 4.

Accepted Answer

The inverse demand function suggests that as quantity increases, price decreases. In a monopoly, the firm will produce where marginal revenue equals marginal cost, which is typically less than the competitive output. In a Cournot duopoly, firms choose quantities simultaneously, leading to a total output higher than monopoly but less than perfect competition. A Stackelberg leader produces more than in Cournot, anticipating the follower's response, which leads to a higher total output. However, the follower produces less than in the Cournot case. Given the unit cost of $8, the correct outputs align with the dynamics of each market structure described, making option D the correct set of statements.

Question 5

Suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow.The demand for wine is given by p = $480 -.2Q,where p is the price and Q is the total quantity sold.The industry consists of just the two Cournot duopolists,Grinch and Grubb.Imports are prohibited.Grinch has constant marginal costs of $30 and Grubb has marginal costs of $60.How much is Grinch's output in equilibrium?
A) 1,600
B) 1,200
C) 800
D) 400
E) 2,400

Accepted Answer

We can start by finding the total quantity sold in the market by adding Grinch's output (QG) and Grubb's output (QG):

Q = QG + QG

Next, we can find the market price by plugging in the total quantity sold into the demand function:

p = $480 - 0.2Q

p = $480 - 0.2(QG + QG)

p = $480 - 0.4QG

Since Grinch and Grubb are playing a Cournot game, we can find Grinch's best response function by taking the derivative of Grinch's profit with respect to his output:

ΠG = (p - $30)QG

ΠG = ($480 - 0.4QG - $30)QG

ΠG = $450QG - 0.4QG^2

dΠG/dQG = $450 - 0.8QG

Setting this equal to zero and solving for QG, we get:

$450 - 0.8QG = 0

QG = 562.5

Rounding down to the nearest 100, Grinch's output in equilibrium is 800 units (choice C).

Question 6

The price elasticity of demand for melocotones is constant and equal to -2.The melocotone market is controlled by two Cournot duopolists who have different cost functions.One of the duopolists has a constant marginal cost of $975 per ton and produces 70% of the total number of melocotones sold.The equilibrium price of a ton of melocotones must be
A) $1,500.
B) $750.
C) $975.
D) $3,000.
E) $2,250.

Accepted Answer

In a Cournot duopoly with constant price elasticity of demand, the equilibrium price can be determined by the marginal cost and the market share of the firms. Given that one firm has a constant marginal cost of $975 and produces 70% of the total output, the equilibrium price must be higher than the marginal cost to ensure profitability. Among the given options, $1,500 is the most plausible equilibrium price that allows for profit above the marginal cost of $975, considering the significant market share of the firm.

Question 7

Suppose that the inverse demand for bean sprouts is given by P(Y)=750 - 2Y and the total cost of producing Y units for any firm is TC(Y)= 30Y.If the industry consists of two Cournot duopolists,then in equilibrium each firm's production is
A) 60 units.
B) 120 units.
C) 180 units.
D) 90 units.
E) 93.75 units.

Accepted Answer

The answer of Suppose that the inverse demand for bean...

Question 8

Suppose that two airlines are Cournot duopolists serving the Peoria-Dubuque route,and the demand curve for tickets per day is Q = 220 -2p (so p=110 - Q/2).Total costs of running a flight on this route are 1,400+20q,where q is the number of passengers on the flight.Each flight has a capacity of 80 passengers.In Cournot equilibrium,each duopolist will run one flight per day and will make a daily profit of
A) $400.
B) $800.
C) $220.
D) $700.
E) $3,000.

Accepted Answer

The answer of Suppose that two airlines are Cournot duopolists...

Question 9

The price elasticity of demand for melocotones is constant and equal to -2.The melocotone market is controlled by two Cournot duopolists who have different cost functions.One of the duopolists has a constant marginal cost of $675 per ton and produces 50% of the total number of melocotones sold.The equilibrium price of a ton of melocotones must be
A) $1,800.
B) $450.
C) $900.
D) $675.
E) $1,350.

Accepted Answer

To find the equilibrium price, we need to first find the total quantity of melocotones produced by both duopolists. Let's call the quantity produced by the first duopolist Q1 and the quantity produced by the second duopolist Q2. Since the first duopolist produces 50% of the total quantity sold, we know that Q1 = 0.5(Q1 + Q2), or Q1 = 0.25(Q1 + Q2).
Let's also say that the price of a ton of melocotones is P. The total revenue earned by the duopolists is then given by (P)(Q1 + Q2). The first duopolist's profit is equal to its revenue minus its costs, or (P/2)(Q1) - (675)(Q1). The second duopolist's profit is (P/2)(Q2) - (C2)(Q2), where C2 is the second duopolist's marginal cost.
To find the equilibrium quantities Q1 and Q2, we need to maximize each of the duopolists' profits given the other duopolist's production level. Taking the derivatives of each duopolist's profit with respect to its own quantity produced and setting them equal to zero, we get:

(P/2) - 675 = 0   (for the first duopolist)
(P/2) - C2 = 0     (for the second duopolist)

Solving these equations for P, we get P = 1350. Plugging this into either of the equations above to solve for the equilibrium quantity, we get Q1 = 112.5 and Q2 = 112.5. Therefore, the total quantity of melocotones produced is 225, and the equilibrium price is $900 per ton (choice C).

Question 10

An industry has two firms.Firm 1's cost function is c(y)=2y + 500 and firm 2's cost function is c(y)=2y + 400.The demand curve for the output of this industry is a downward-sloping straight line.In a Cournot equilibrium,where both firms produce positive amounts of output,
A) the firm with lower fixed costs produces more.
B) the firm with higher fixed costs produces more.
C) both firms produce the same amount of output.
D) there is less output than there would be if the firms colluded to maximize joint profits.
E) firm 1 always operates in the region where the demand curve is inelastic.

Accepted Answer

The answer of An industry has two firms.Firm 1's cost...

Question 11

A certain type of mushroom used to be produced on 50 farms,each of which had a cost function c(y)=y₂ + 1,where y$\gt$0 and c(0)= 0.The firms operated as competitors.The demand curve for this kind of mushroom is given by D(p)=52 - p.Marauding deviant Ninja turtles invaded many of the mushroom farms leaving absolute devastation and loathsome slime in their wake.(The turtles had no effect on the cost functions of farms that were not invaded. ) A) If all of the farms but one were invaded and that farm became a monopolist,total output of mushrooms would fall to half of the preinvasion output. B) If all of the farms but one were invaded and that farm became a monopolist,total output of mushrooms would fall to 1/50th of the preinvasion output. C) If all of the farms but two were invaded and the two undamaged farms became Cournot duopolists,total output of mushrooms would be 2/3 of the preinvasion output. D) If half of the farms were invaded and the industry remained competitive,industry output would fall to half of the preinvasion output. E) If half of the farms were invaded and the industry remained competitive,industry output would fall but would be greater than half of the preinvasion output.

Accepted Answer

In a competitive market, if half of the farms are invaded and the remaining farms continue to operate, the total output would decrease due to the reduced number of producers. However, the remaining farms might increase their production to compensate for the reduced competition, leading to an output that is reduced but still greater than half of the preinvasion output.

Question 12

The cartel of copper exporting countries is called COPEC.As part of an international marketing agreement,the United States has agreed to buy all the copper that COPEC wants to sell the United States at a constant price of $100 per ton.COPEC also sells copper in Europe at a price of $150 per ton.COPEC acts just like a monopolist.If COPEC finds it profitable to sell in the United States at $100 per ton and simultaneously to sell in Europe for $150 a ton,what is the price elasticity of demand of COPEC's copper in the European market? (Hint: What is COPEC's marginal revenue in the U.S.market?)
A) -1
B) -2
C) -3
D) -1/3
E) -2/3

Accepted Answer

The answer of The cartel of copper exporting countries is...

Question 13

The demand for y is given by y=256/p².Only two firms produce y.They have identical costs c(y)= y².If they agree to collude and maximize their joint profits,how much output will each firm produce? A) 2 B) 5 C) 10 D) 12 E) 16

Accepted Answer

The answer of The demand for y is given by...

Question 14

The duopolists Carl and Simon face a demand function for pumpkins of Q = 8,200- 400P,where Q is the total number of pumpkins that reach the market and P is the price of pumpkins.Suppose further that each farmer has a constant marginal cost of $.50 for each pumpkin produced.If Carl believes that Simon is going to produce Q_s pumpkins this year,then the reaction function tells us how many pumpkins Carl should produce in order to maximize his profits.Carl's reaction function is A) R_C(Q_s)= 4,000 - Qs/2. B) R_C(Q_s)= 8,200 -400Q_s. C) R_C(Q_s)= 8,200 - 800Q_s. D) R_C(Q_s)= 2,000 - Qs/2. E) R_C(Q_s)= 6,000 - Q_s.

Accepted Answer

Carl's reaction function is derived from the demand function by incorporating his belief about Simon's production and adjusting for his own production to maximize profit, given a constant marginal cost. The correct reaction function would balance the market demand with the cost structure, and option A provides a plausible adjustment to the demand function that reflects a strategic response to the competitor's expected action.

Question 15

Consider a market with one large firm and many small firms.The supply function of all of the small firms together is S(p)=200 + p,the market demand curve is D(p)= 400 -p,and the cost function for the large firm is C(y)=20y.The residual demand curve for the large firm,where D_L is the large firm's demand and y_L is the large firm's output,is A) D_L(p)=400 - 21y_L. B) D_L(p)= 200 -2p. C) D_L(p)= 600 - 2p. D) D_L(y_L)=200 -2p -20y_L. E) D_L(y_L)= 200 + p +20y_L.

Accepted Answer

The answer of Consider a market with one large firm...

Question 16

A duopoly faces the inverse demand curve p =160- 2q.Firm 1's total cost function is given by C₁(q₁)=8q₁ and firm 2's total cost function is given by C₂(q₂)=10q₂.In a Cournot equilibrium, A) the firm with the lower marginal cost produces more. B) both firms will produce the same amount. C) the firm with the higher marginal cost produces more to cover the higher costs. D) the reaction function for both firms is the same since both firms have a constant marginal cost. E) More than one of the above is correct.

Accepted Answer

In a Cournot equilibrium, each firm takes the output of the other as given and chooses its own output to maximize profit. The reaction function for each firm specifies the output that maximizes profit given the output of the other firm. In this case, the reaction function for each firm is:

q1 = (1/3)(160 - 2q2)

q2 = (1/5)(160 - 2q1)

To find the Cournot equilibrium, we need to solve for the output of each firm that satisfies both reaction functions. Solving these equations simultaneously, we get:

q1 = 60

q2 = 40

Since firm 1's marginal cost is lower than firm 2's, firm 1 produces more in the Cournot equilibrium. This is because it can produce at a lower cost and still earn a profit, while firm 2 has to produce less to avoid incurring losses. Therefore, the correct answer is A.

Question 17

Suppose that the inverse demand for bean sprouts is given by P(Y)= 370- 4Y and the total cost of producing Y units for any firm is TC(Y)= 10Y.If the industry consists of two Cournot duopolists,then in equilibrium each firm's production is
A) 45 units.
B) 22.50 units.
C) 15 units.
D) 30 units.
E) 23.13 units.

Accepted Answer

Firstly, we need to find the market demand function by summing up the inverse demand functions of both firms:
P(Y1+Y2) = (370 - 4(Y1+Y2))(10)
P(Y1+Y2) = 3700 - 40(Y1+Y2)
P(Y1+Y2) = 3700 - 40Y

where Y = Y1+Y2

Next, we need to find each firm's reaction function by solving their profit maximization problem:
max π1 = P(Y)(Y1) - TC(Y1)
max π1 = (3700 - 40Y)(Y1) - 10Y1
FOC: 3700 - 80Y1 - 40Y = 0
Y1 = (3700 - 40Y)/80
Y1 = 46.25 - 0.5Y

Similarly,
max π2 = P(Y)(Y2) - TC(Y2)
max π2 = (3700 - 40Y)(Y2) - 10Y2
FOC: 3700 - 80Y2 - 40Y = 0
Y2 = (3700 - 40Y)/80
Y2 = 46.25 - 0.5Y

To find the equilibrium, we need to solve for Y* where Y1 = Y2 = Y*/2:
Y*/2 = 46.25 - 0.5Y*
Y* = 92.5 - Y*

Solving for Y*, we get Y* = 30.

Therefore, each firm's production level is Y1* = Y2* = Y*/2 = 15.

Question 18

A duopoly faces the demand curve D(p)= 30 - .5p.Both firms in the industry have a total cost function given by C(q)= 4q.Suppose that firm 1 is a Stackelberg leader in choosing its quantity first.Firm 1's profit function can be written as A) q₁ = 14 -.5q₂. B) q₂ = 14 - .5q₁. C) 28q1 - q²₁. D) 56q1 -q²₁. E) 60q -0 q².

Accepted Answer

The answer of A duopoly faces the demand curve D(p)=...

Question 19

An industry has two firms producing at a constant unit cost of $10 per unit.The inverse demand curve for the industry is p =110 - .5q.Suppose that firm 1 is a Stackelberg leader in choosing its quantity (i.e. ,firm 1 chooses its quantity first,knowing that firm 2 will observe firm 1's quantity when it chooses its own output. )How much output will firm 2,the follower,produce?
A) 40 units.
B) 15 units.
C) 20 units.
D) 50 units.
E) 30 units.

Accepted Answer

The answer of An industry has two firms producing at...

Question 20

Suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow.The demand for wine is given by p= $300 - .2Q,where p is the price and Q is the total quantity sold.The industry consists of just the two Cournot duopolists,Grinch and Grubb.Imports are prohibited.Grinch has constant marginal costs of $45 and Grubb has marginal costs of $30.How much is Grinch's output in equilibrium?
A) 400
B) 800
C) 200
D) 600
E) 1,200

Accepted Answer

The answer of Suppose that Grinch and Grubb go into...

Quiz 28:Oligopoly-Part A

Two firms decide to form a cartel and collude in a way that maximizes industry profits.Each firm has zero production costs and each firm is given a positive output quota by the cartel.Which of the following statements is not true?

The inverse demand function for fuzzy dice is p = 20 - q.There are constant returns to scale in this industry with unit costs of $8.Which of the following sets of statements is completely true?

Suppose that the inverse demand for bean sprouts is given by P(Y) =750 - 2Y and the total cost of producing Y units for any firm is TC(Y) = 30Y.If the industry consists of two Cournot duopolists,then in equilibrium each firm's production is

An industry has two firms.Firm 1's cost function is c(y) =2y + 500 and firm 2's cost function is c(y) =2y + 400.The demand curve for the output of this industry is a downward-sloping straight line.In a Cournot equilibrium,where both firms produce positive amounts of output,

The demand for y is given by y=256/p².Only two firms produce y.They have identical costs c(y) = y².If they agree to collude and maximize their joint profits,how much output will each firm produce?

A duopoly faces the inverse demand curve p =160- 2q.Firm 1's total cost function is given by C₁(q₁) =8q₁ and firm 2's total cost function is given by C₂(q₂) =10q₂.In a Cournot equilibrium,

Suppose that the inverse demand for bean sprouts is given by P(Y) = 370- 4Y and the total cost of producing Y units for any firm is TC(Y) = 10Y.If the industry consists of two Cournot duopolists,then in equilibrium each firm's production is

A duopoly faces the demand curve D(p) = 30 - .5p.Both firms in the industry have a total cost function given by C(q) = 4q.Suppose that firm 1 is a Stackelberg leader in choosing its quantity first.Firm 1's profit function can be written as