Question 1

Suppose that the market demand curve for bean sprouts is given by P = 880 - 4Q, where P is the price and Q is the total industry output. Suppose that the industry has two firms, a Stackelberg leader and a follower. Each firm has a constant marginal cost of $80 per unit of output. In equilibrium, total output by the two firms will be

Accepted Answer

In Stackelberg duopoly, the leader firm first chooses its output level, and then the follower firm chooses its output level accordingly. To find the leader's output, we set the follower's best response to the leader's output equal to the leader's output.

The follower's best response is to maximize profit given the leader's output, which is: 
Q_f = (880 - P)/8 = (880 - 4Q_l)/8 = 110 - 0.5Q_l

Setting Q_f = Q_l, we get: 
Q_l = 110 - 0.5Q_l 
1.5Q_l = 110 
Q_l = 73.33

So, the leader firm's output is 73.33 units, and the follower's output is: 
Q_f = 110 - 0.5Q_l = 110 - 0.5(73.33) = 150

Therefore, the total industry output is 73.33 + 150 = 223.33 or approximately 150 units, which is answer choice C.

Question 2

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_Lis the large firm's demand and y_Lis the large firm's output, is

Accepted Answer

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

Question 3

The demand for y is given by . 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?

Accepted Answer

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

Question 4

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

Accepted Answer

The answer of The duopolists Carl and Simon face a...

Question 5

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 -  ). 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

Accepted Answer

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

Question 6

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,

Accepted Answer

In a Cournot equilibrium, each firm assumes the other firm's output level and maximizes profit given that assumption. Firm 1's profit-maximizing output level is q1 = (88 - q2)/4, where q2 is firm 2's output level. Firm 2's profit-maximizing output level is q2 = (80 - q1)/5, where q1 is firm 1's output level. Thus, the output levels of both firms depend on each other's output level. 
To find out which firm produces more, we compare their marginal costs. Firm 1's marginal cost is MC1 = 8, and firm 2's marginal cost is MC2 = 10. Since firm 1 has a lower marginal cost, it can produce more than firm 2 and still earn a profit. Therefore, the correct choice is A.

Question 7

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?

Accepted Answer

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

Question 8

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 -  ). 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

Accepted Answer

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

Question 9

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

Accepted Answer

The answer of The duopolists Carl and Simon face a...

Question 10

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?

Accepted Answer

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

Question 11

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,

Accepted Answer

In a Cournot equilibrium, each firm produces the quantity that maximizes its profits given the quantity produced by the other firm. Given the cost functions and the demand curve, the industry's equilibrium quantity is the one that equates the total quantity supplied to the market to the quantity demanded by consumers. Since the cost functions are identical except for the fixed costs, the equilibrium quantity is split evenly between the two firms. Therefore, both firms produce the same amount of output. Choices A and B are incorrect because they imply that fixed costs affect the optimal quantity, but in Cournot competition, only marginal costs matter. Choice D is incorrect because Cournot competition leads to a lower level of output than joint profit maximization, which corresponds to the socially optimal level of output. Choice E is incorrect because it is not necessarily true that firm 1 operates in the region where the demand curve is inelastic.

Question 12

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?

Accepted Answer

The answer of The inverse demand function for fuzzy dice...

Question 13

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 > 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.)

Accepted Answer

The answer of A certain type of mushroom used to...

Question 14

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?

Accepted Answer

In the Cournot duopoly, each firm chooses its quantity based on the assumption that the other firm's quantity remains constant. Grinch's profit-maximizing output level can be found by setting his marginal revenue equal to his marginal cost:

MR = p + (dQ/dx)Q = $480 - .4Q - .2Q = $480 - .6Q 
MC = $30

Setting MR = MC, we get:

$480 - .6Q = $30 
.6Q = $450 
Q = 750

Therefore, Grinch's equilibrium output level is 750.

Question 15

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

Accepted Answer

Since the price elasticity of demand for melocotones is constant (-2), the demand curve is linear. Each firm will choose its output by assuming the rival's output is constant. The total quantity demanded will be divided by the two duopolists according to their market shares. If one duopolist has a 50% market share, then the other must also have a 50% market share. The total quantity sold will be twice the quantity sold by each duopolist. So the market demand function can be written as:
Q = (P/2) x (-2)
Q = -P
Each duopolist's profit is π = (P - MC) x Q, where P is the price, MC is the marginal cost, and Q is the quantity sold by that duopolist. To maximize profit, each duopolist will choose its output to maximize its own profit given the other's output. The best response function for the duopolist with the constant MC of $675 can be found as follows:
π = (P - 675) x (0.5P)
dπ/dP = 0.5P - 675 - (P - 675)
dπ/dP = -0.5P
-0.5P = 0
P = 0
This is not a valid price, so we must look for another extreme point. Since the best response function is linear, it must be either increasing or decreasing. To determine which, we can check the endpoints of the range of possible prices, which is determined by the lowest MC (belonging to the duopolist with the constant MC) and the highest possible price that the market will bear. This highest possible price is the price at which one duopolist would sell no melocotones, so the other's quantity sold would be the entire market demand of 0.5P. Setting this quantity equal to the other duopolist's output and solving for P:
0.5P = -P
P = 0
This is not a valid price, so we must look for another extreme point:
0.5P = P/2 - 675
1.5P/2 = 675
P = $900
So the best response function for the duopolist with the constant MC of $675 is P = 1800 - Q/2. The best response function for the other duopolist (with some other cost function) can be found in the same way. The equilibrium price and quantity can be found by solving for the intersection of the two best response functions. Alternatively, we can use the fact that each duopolist sells half the total quantity at the equilibrium price, so we can simply add up their profits and set the sum equal to zero. At the equilibrium:
P = $900
Q = 900
Revenue for each duopolist is: TR = P x Q/2 = $450,000
Cost for each duopolist is: TC = 675 x Q/2 = $303,750
Profit for each duopolist is: $146,250
The equilibrium quantity is 900, so the total revenue is $810,000, which is divided equally between the duopolists. Therefore, each duopolist's profit is $146,250.

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

In a Cournot duopoly with constant price elasticity of demand, the equilibrium price can be found using the Lerner index formula: (P - MC) / P = -1/E, where E is the elasticity of demand. Given E = -2 and MC = $975, solving gives P = $1,500.

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

Accepted Answer

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

Question 19

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

Accepted Answer

To find the Cournot equilibrium, we need to calculate each firm's reaction function. Firm 1's reaction function is given by:

Q1 = (1/2)*(370 - 4Q2 - 10)

where Q2 is the quantity produced by the other firm. Similarly, Firm 2's reaction function is:

Q2 = (1/2)*(370 - 4Q1 - 10)

To find the equilibrium, we need to solve for Q1 and Q2 such that they are simultaneously satisfied. Substituting Firm 1's reaction function into Firm 2's gives:

Q2 = (1/2)*(370 - 4*((1/2)*(370 - 4Q2 - 10)) - 10)

Simplifying this expression gives:

Q2 = 23.125

Substituting this value of Q2 into Firm 1's reaction function gives:

Q1 = (1/2)*(370 - 4(23.125) - 10) = 30

Therefore, each firm's production in equilibrium is 30 units.

Question 20

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?)

Accepted Answer

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

Quiz 26: Oligopoly

The demand for y is given by . 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,