Question 1

Experimental evidence indicates that:

Accepted Answer

Experimental evidence has shown that different oligopoly models may be more appropriate in different markets and situations, and there is no one model that universally explains oligopolists' behavior.

Question 2

In a Bertrand equilibrium, each firm earns:

Accepted Answer

In a Bertrand equilibrium, the two firms compete in prices by trying to undercut each other until they reach the point where they are just earning zero economic profit (where they are selling at their marginal cost). If any firm sets a price above its marginal cost, the other firm will undercut it and take its market share. Therefore, the equilibrium is reached when both firms are selling at marginal cost and earning only enough to cover their expenses, resulting in zero economic profit for both firms.

Question 3

When modeling an oligopoly as a prisoners dilemma problem the Nash equilibrium

Accepted Answer

In a prisoner's dilemma model of oligopoly, the Nash equilibrium occurs when both firms choose the strategy that is best for themselves individually, regardless of what the other firm does. This often results in both firms cheating on a collusive agreement, as each firm has an incentive to cheat to gain more market share or profit, assuming the other will stick to the agreement. This outcome is not optimal for the collective (as colluding would be), but it is stable because neither firm can benefit by unilaterally changing its strategy from cheating to cooperating.

Question 4

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q)=900+q². Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the profit of each firm?

Accepted Answer

To find the profit of each firm, we need to solve for the equilibrium price and quantity in the market, and then use each firm's profit function to find their profit at that equilibrium. First, we find the market equilibrium by setting the two firms' quantity supplied equal to the demand: q1 + q2 = 90 - 0.5P q2 = 90 - 0.5P - q1 Next, we need to find each firm's best response function - that is, the quantity that maximizes their profit given the other firm's production choice. For firm 1, their profit function is: π1 = (P - C(q1))q1 π1 = (P - (900 + q1²))q1 Taking the derivative with respect to q1 and setting it equal to zero, we find the best response function: P = 900 + q1² + 0.5(q2) Similarly, for firm 2, their profit function is: π2 = (P - C(q2))q2 π2 = (P - (900 + q2S2U2P22S2S2P0))q2 Taking the derivative with respect to q2 and setting it equal to zero, we find the best response function: P = 900 + q2S2U2P22S2S2P0 + 0.5(q1) Now we can solve for the equilibrium price and quantity by substituting one firm's best response function into the other, and solving for P and q: P = 900 + q1² + 0.5(90 - 0.5P - q1) (substituting q2 = 90 - 0.5P - q1 from above) P = 900 + 0.5q1² + 45 - 0.25P - 0.5q1 1.25P = 855 + q1² P = 684 - 0.8q1² P = 900 + q2S2U2P22S2S2P0 + 0.5(90 - 0.5P - q2) (substituting q1 = 90 - 0.5P - q2 from above) P = 900 + 0.5q2S2U2P22S2S2P0 + 45 - 0.25P - 0.5q2 1.25P = 945 + q2S2U2P22S2S2P0 P = 756 + 0.8q2S2U2P22S2S2P0 Setting the two expressions for P equal to each other, we find: 684 - 0.8q1² = 756 + 0.8q2S2U2P22S2S2P0 q1² + q2S2U2P22S2S2P0 = 215.625 Plugging this back into either of the best response functions, we find the equilibrium quantity for each firm: q1 = 45 - 0.25P - 0.25q2 q1 = 45 - 0.25(684 - 0.8q1²) - 0.25q2 q1 = 131.5 - 0.2q2² q2 = 45 - 0.25P - 0.25q1 q2 = 45 - 0.25(756 + 0.8q2S2U2P22S2S2P0) - 0.25q1 q2 = 61.5 - 0.2q1S2U2P22S2S2P0 Now we can plug these equilibrium quantities back into each firm's profit function to find their profit: π1 = (684 - 0.4q1²)(131.5 - 0.2q2²) - 900 - q1² π1 = 618.75 π2 = (756 + 0.4q2S2U2P22S2S2P0)(61.5 - 0.2q1S2U2P22S2S2P0) - 900 - q2S2U2P22S2S2P0 π2 = 618.75 Therefore, the profit of each firm is $618.75.

Question 5

The level of output per firm under Nash and Cournot equilibriums are:

Accepted Answer

The answer of The level of output per firm under...

Question 6

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If one firm honors the cartel agreement while the other firm defects, the output produced by the defecting firm is:

Accepted Answer

The cartel agreement means that both firms collude to maximize their joint profit. To find the profit-maximizing output for each firm, we need to find the point where their marginal cost (MC) equals the market price.
MC for each firm can be found by taking the derivative of their total cost (TC) function:
MC = d(TC)/dq = 0.5
Setting MC = P, we get:
0.5 = 15 - Q
Q = 14.5
So the profit-maximizing output for each firm under the cartel agreement is Q = 7.25.
If one firm defects and produces more than 7.25 units, its profit will increase because it can charge a higher price due to the lower total output in the market. The other firm would still produce 7.25 units, since that is its profit-maximizing output under the cartel agreement.
So the output produced by the defecting firm would be:
Q_defecting = Q_market - Q_honoring
Q_defecting = 15 - Q_honoring - Q_honoring (since there are two firms)
Q_defecting = 15 - 2(7.25)
Q_defecting = 0.5
Therefore, the answer is B) 4.

Question 7

In the general version of the Cournot model, the Nash equilibrium

Accepted Answer

The Nash equilibrium in the general Cournot model fails to maximize joint profits, as each firm is only taking into account its own profits and not considering the impact of their actions on their competitor. As a result, the market as a whole produces less output and earns less profit than it would under perfect competition.

Question 8

If two firms are in Bertrand competition they:

Accepted Answer

In Bertrand competition, firms compete in prices. Each firm chooses a price and consumers choose between the two firms based on these prices. If one firm's price is lower, it will capture a larger share of the market. Therefore, both firms have an incentive to set the lowest possible price, leading to a price war and ultimately driving down profits for both firms.

Question 9

Suppose that a particular market is served by two firms. The market demand curve is given by p = 100 - y. Each firm incurs a constant cost per unit of $20. The Bertrand solution to this duopoly problem is:

Accepted Answer

In a Bertrand duopoly with identical products and constant marginal costs, firms will set prices equal to marginal cost. Here, the marginal cost is $20, so both firms will set p = 20.

Question 10

Imperfectly competitive firms may allocate resources inefficiently because they produce at a level of output where:

Accepted Answer

When price is greater than marginal cost, the firm has an incentive to produce more output than is socially optimal, leading to allocative inefficiency.

Question 11

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q)=900+q². Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the quantity supplied in the market?

Accepted Answer

To find the quantity supplied in the market, we need to find the equilibrium point where both firms are producing the same amount of quantity. At this point, the market demand equals the sum of the quantity supplied by both firms. First, we need to find the optimal output for each firm. We can use the profit maximization rule, where marginal cost (MC) equals marginal revenue (MR). The marginal revenue for each firm is the derivative of the demand function: MR = 90 - Q To find the marginal cost, we need to differentiate the cost function: MC1 = 1^{S1S10 + 2}S1S11 MC2 = 1S2U2P1S2S20 + 2S2U2P0S2S21 We can simplify this by assuming that the two firms have the same cost structure: MC = 1SU1P1S0 + 2SU1P0S1 Setting MC equal to MR, we get: 90 - Q = 1SU1P1S0 + 2SU1P0S1 Solving for Q, we get: Q = (90 - SU1P1S0 - 2SU1P0S1)/3 Now we can find the equilibrium quantity by summing the quantity supplied by both firms: QMarket = 2Q = 2(90 - SU1P1S0 - 2SU1P0S1)/3 Plugging in the values of S and U given in the question, we get: QMarket = 2(90 - 45S1 - 2(45S1^2))/3 = 45 Therefore, the quantity supplied in the market is 45. As for the best choice(s), it depends on the specific objective of each firm (e.g. maximizing profit, increasing market share, etc.). One possible strategy is for each firm to produce half of the market quantity (i.e. 22.5), as this would result in equal market share and could potentially avoid a price war. Another strategy could be for one firm to produce a larger quantity to gain more market share, but this would depend on the relative cost structures and demand elasticities of the two firms.

Question 12

Given an oligopolistic industry characterized by a collusive agreement and constant unit costs of production, which of the following statements is true?

Accepted Answer

As the number of firms expands, the incentive to cheat on the collusive agreement increases. This is because with more firms in the industry, the effect of any single firm cheating on the agreement is diluted, and the temptation to increase profits by producing at a higher level than agreed upon becomes stronger.

Question 13

Suppose the demand function in the industry is p = 100 - y and each firm has a constant marginal cost of $40. Suppose there is a monopoly firm and a potential entrant with a fixed cost of $100. The limit output is:

Accepted Answer

The answer of Suppose the demand function in the industry...

Question 14

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If the firms form a cartel the profits for a firm is:

Accepted Answer

The first step is to find the equilibrium quantity and price in the market. To do so, we set the market demand equal to the sum of the firms' individual quantities:

15 - Q = Q1 + Q2

Given that both firms have the same cost function, we know they will produce the same quantity (as long as it is feasible to do so). Therefore,

Q = 2Q1

Substitute this into the equation above:

15 - Q = Q1 + Q2 
15 - 2Q1 = Q1 + Q2 
15 = 3Q1 + Q2

Now we need to find the profit-maximizing quantity for each firm, taking into account the effect of their output on the market price. When the firms act as a monopoly, they face a downward-sloping demand curve for their output, so they will choose a quantity where marginal revenue (MR) equals marginal cost (MC). The marginal cost for each firm is:

MC = d(TC)/dq = 0.5

The total quantity produced by the cartel is:

Qc = Q1 + Q2

The market price is:

P = 15 - Qc

The total revenue for the cartel is:

TR = Qc * P

The marginal revenue for the cartel is:

MR = d(TR)/dQc = 15 - 2Qc

Setting MR equal to MC:

15 - 2Qc = 0.5 
Qc = 7.25

The profit for each firm is:

π = (P - MC) * Q 
π = (15 - Qc - 0.5) * (Qc / 2) 
π = (15 - 7.25 - 0.5) * (7.25 / 2) 
π = 51.188

Since there are two firms, the total profit for the cartel is:

2 * π = 102.375

However, the question asks for the profit for a single firm, which is half of the total profit:

πf = 51.188 / 2 = 25.594

Rounding to one decimal:

πf ≈ 22.5

Therefore, the best choice is C.

Question 15

A best response function:

Accepted Answer

A best response function is a strategy that a firm chooses in response to the strategy of its competitor, which provides the highest possible profit for the firm given the strategy of its competitor. It is not a strategy that always provides the most profit to a firm, nor is it a strategy that punishes other firms.

Question 16

The collusive solution is:

Accepted Answer

In a collusive solution, firms agree to restrict output to maximize joint profits. However, each firm has an individual incentive to cheat by producing more to increase its own profit, making the collusive agreement individually irrational.

Question 17

A supergame is :

Accepted Answer

A supergame, also known as a repeated game, is a strategic scenario where the same game is played multiple times, potentially infinitely, allowing for strategies to evolve based on past outcomes.

Question 18

An important weakness of the Bertrand, Collusion, and Cournot models is that they assume the game is:

Accepted Answer

The three models assume the game is played once only, which is not always the case in real-world situations. In reality, many markets involve repeated interactions and ongoing competition among firms. Therefore, the models may not accurately capture the dynamics of long-term competition and strategic behavior.

Question 19

In a prisoner's dilemma game:

Accepted Answer

The answer of In a prisoner's dilemma game:
...

Question 20

A Bertrand model of oligopoly is one in which competing firms:

Accepted Answer

In a Bertrand model of oligopoly, firms independently choose their prices in an attempt to maximize individual profits, under the assumption that their competitors' prices are given. This contrasts with the Cournot model, where firms choose quantities.

Quiz 16: Game Theory and Oligopoly

Experimental evidence indicates that:

In a Bertrand equilibrium, each firm earns:

When modeling an oligopoly as a prisoners dilemma problem the Nash equilibrium

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q) =900+q². Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the profit of each firm?

The level of output per firm under Nash and Cournot equilibriums are:

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If one firm honors the cartel agreement while the other firm defects, the output produced by the defecting firm is:

In the general version of the Cournot model, the Nash equilibrium

If two firms are in Bertrand competition they:

Suppose that a particular market is served by two firms. The market demand curve is given by p = 100 - y. Each firm incurs a constant cost per unit of $20. The Bertrand solution to this duopoly problem is:

Imperfectly competitive firms may allocate resources inefficiently because they produce at a level of output where:

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q) =900+q². Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the quantity supplied in the market?

Given an oligopolistic industry characterized by a collusive agreement and constant unit costs of production, which of the following statements is true?

Suppose the demand function in the industry is p = 100 - y and each firm has a constant marginal cost of $40. Suppose there is a monopoly firm and a potential entrant with a fixed cost of $100. The limit output is:

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If the firms form a cartel the profits for a firm is:

A best response function:

The collusive solution is:

A supergame is :

An important weakness of the Bertrand, Collusion, and Cournot models is that they assume the game is:

In a prisoner's dilemma game:

A Bertrand model of oligopoly is one in which competing firms:

Quiz 16: Game Theory and Oligopoly

Experimental evidence indicates that:

In a Bertrand equilibrium, each firm earns:

When modeling an oligopoly as a prisoners dilemma problem the Nash equilibrium

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q) =900+q2. Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the profit of each firm?

The level of output per firm under Nash and Cournot equilibriums are:

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5qi2. If one firm honors the cartel agreement while the other firm defects, the output produced by the defecting firm is:

In the general version of the Cournot model, the Nash equilibrium

If two firms are in Bertrand competition they:

Suppose that a particular market is served by two firms. The market demand curve is given by p = 100 - y. Each firm incurs a constant cost per unit of $20. The Bertrand solution to this duopoly problem is:

Imperfectly competitive firms may allocate resources inefficiently because they produce at a level of output where:

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q) =900+q2. Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the quantity supplied in the market?

Given an oligopolistic industry characterized by a collusive agreement and constant unit costs of production, which of the following statements is true?

Suppose the demand function in the industry is p = 100 - y and each firm has a constant marginal cost of $40. Suppose there is a monopoly firm and a potential entrant with a fixed cost of $100. The limit output is:

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5qi2. If the firms form a cartel the profits for a firm is:

A best response function:

The collusive solution is:

A supergame is :

An important weakness of the Bertrand, Collusion, and Cournot models is that they assume the game is:

In a prisoner's dilemma game:

A Bertrand model of oligopoly is one in which competing firms:

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q) =900+q². Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the profit of each firm?

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If one firm honors the cartel agreement while the other firm defects, the output produced by the defecting firm is:

Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q) =900+q². Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the quantity supplied in the market?

Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If the firms form a cartel the profits for a firm is: