8. Game Theory; Property Rights, Externalities & Coase

Question 1

Define Nash Equilibrium

Answer 1

The Nash Equilibrium is a concept in game theory where the optimal outcome is one where there is no incentive for players to deviate from their initial strategy. Here are some key points:

Optimal Strategy: In the Nash equilibrium, each player’s strategy is optimal when considering the decisions of other players. Every player wins because everyone gets the outcome that they desire.

No Incremental Benefit: An individual can receive no incremental benefit from changing actions, assuming that other players remain constant in their strategies.

Knowledge of Opponent’s Strategy: The players have knowledge of their opponent’s strategy and still will not deviate from their initial chosen strategies because it remains the optimal strategy for each player.

Multiple or No Nash Equilibria: A game may have multiple Nash equilibria or none at all.

Nash Equilibrium vs. Dominant Strategy: Nash equilibrium is often compared alongside dominant strategy, both being strategies of game theory. The Nash equilibrium states that the optimal strategy for an actor is to stay the course of their initial strategy while knowing the opponent’s strategy and that all players maintain the same strategy. Dominant strategy asserts that the chosen strategy of an actor will lead to better results out of all the possible strategies that can be used, regardless of the strategy that the opponent uses.

Question 2

What are the steps to calculate the Nash Equilibrium?

Answer 2

1. Identify the Players and Strategies: First, you need to identify the players in the game and the strategies available to each player.

2. Create the Payoff Matrix: Next, create a matrix that represents the payoffs for each player for each combination of strategies.

3. Find the Best Responses: For each player, identify the best response(s) to each strategy of the other player(s). The best response is the strategy that maximizes a player’s payoff given the strategies of the other player(s).

4. Identify the Nash Equilibria: The Nash equilibria are the strategy profiles where each player is playing their best response to the other players’ strategies. In other words, no player can unilaterally improve their payoff by deviating from their strategy.

Question 3

Define Dominant Strategy in Game Theory.

Answer 3

Dominant Strategy is the best action for an individual to take, regardless of what other players do. In other words, a player’s dominant strategy is the one that maximizes their payoff, no matter what strategies the other players choose. The dominant strategy is static and doesn’t change when conditions change.
It’s important to note that a game’s dominant strategy could also be its Nash equilibrium.

Question 4

Battle of the Sexes
(Nash Equilibrium)

Answer 4

In this game, there is no dominant strategy, and everything is rationalizable. Suppose
Alice plays opera. Then, the best thing Bob can do is to play opera, too. Thus opera is a best response for Bob against Alice playing opera. Similarly, opera is a best response
for Alice against opera. Thus, at (opera, opera), neither party wants to take a different action. This is a Nash Equilibrium.

In other words, no player would have an incentive to deviate, if he correctly guesses the other players’ strategies. If one views a strategy profile as a social convention, then being a Nash equilibrium is tied to being self-enforcing, that is, nobody wants to deviate when they think that the others will follow the convention.

Likewise, (football, football) is also a Nash equilibrium. On the other hand, (opera, football) is not a Nash equilibrium because Bob would like to go to opera instead.

Question 5

Single Nash Equilibrium
(Advertising Campaign)

Answer 5

Imagine two competing companies: Company A and Company B. Both companies want to determine whether they should launch a new advertising campaign for their products.

If both companies start advertising, each company will attract 100 new customers. If only one company decides to advertise, it will attract 200 new customers, while the other company will not attract any new customers. If both companies decide not to advertise, neither company will engage new customers. (See the payoff table.)

Company A should advertise its products because the strategy provides a better payoff than the option of not advertising. The same situation exists for Company B. Thus, the scenario when both companies advertise their products is a Nash equilibrium.

Question 6

Multiple Nash Equilibrium
(Class Registration)

Answer 6

John and Sam are registering for the new semester. They both have the option to choose either a finance course or a psychology course. They only have 30 seconds before the registration deadline, so they do not have time to communicate with each other.

If John and Sam register for the same class, they will benefit from the opportunity to study for the exams together. However, if they choose different classes, neither of them will get any benefit.

In the example (see table), there are multiple Nash equilibria. If John and Sam both register for the same course, they will benefit from studying together for the exams. Thus, the outcomes finance/finance and psychology/psychology are Nash equilibria in this scenario.

Question 7

What strategy results in a Nash Equilibrium?

Answer 7

Protect, Protect (4,4)

Question 8

What is the Prisoner’s Dilemma?

Answer 8

The Prisoner’s Dilemma is a paradox in decision analysis where two individuals acting in their own self-interests do not produce the optimal outcome.

Here’s how it typically works:

Two individuals, say, Elizabeth and Henry, are arrested and interrogated in separate rooms. They can either cooperate with each other by remaining silent or betray the other by testifying. The outcomes are:

If both cooperate and remain silent, they each get one year in jail (1 year for Elizabeth + 1 year for Henry = 2 years total jail time).
If one testifies and the other remains silent, the one who testifies will go free, and the other will get five years (0 years for the one who defects + 5 for the one convicted = 5 years total).
If both testify against each other, they each get two years in jail.

The dilemma is that while the best outcome for the group is for both to cooperate and remain silent, individual logic tempts each prisoner to betray the other. This scenario illustrates how decisions made under individual rationality may differ from those made under collective rationality.

Question 9

Example of Prisoner Dilemma
(Price War)

Answer 9

If both keep prices high, profits for each company increase by $500 million (because of normal growth in demand).
If one drops prices (i.e., defects) but the other does not (cooperates), profits increase by $750 million for the former because of greater market share and are unchanged for the latter.
If both companies reduce prices, the increase in soft drink consumption offsets the lower price, and profits for each company increase by $250 million.

Thus, a price drop by either company may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if Coca-Cola drops its price but Pepsi continues to keep prices high, the former is defecting, while the latter is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, Coca-Cola may win market share and earn incremental profits by selling more colas.

Question 10

Matt Murdoch has the choice between receiving $100 now or receiving $140 in two years. Which of the following statements are true?
a. If the interest rate is 20%, he should take the $100 now.
b. If the interest rate is 10%, he should take the $100 now.
c. He should not take the $100 now if the interest rate is anything below
20%.
d. None of the above

Answer 10

a. If the interest rate is 20%, he should take the $100 now.
To solve this problem, we need to calculate the future value of $100 at the given interest rates and compare it with the $140 that Matt would receive in two years. The future value (FV) of an investment can be calculated using the formula:

FV=PV∗(1+r)n

where:

PV is the present value of the investment (in this case, $100)
r is the interest rate
n is the number of periods (in this case, 2 years)

Let’s calculate:

a. If the interest rate is 20%, the future value of $100 after two years would be:

FV=$100∗(1+0.20)2=$144

Since $144 > $140, Matt should take the $100 now.

Question 11

An example of an “externality” is
a. the pollution generated from a power plant which the firm fully pays
for after an agreement with the local community.
b. the pollution generated from a power plant regardless of whether the
firm is paying for the marginal damage from the pollution or not.
c. the marginal damage generated from a power plant that the firm
does not internalize when making decisions.
d. an input that increases the private cost to a firm.

Answer 11

c. the marginal damage generated from a power plant that the firm
does not internalize when making decisions.
An “externality” is a cost or benefit that affects a party who did not choose to incur that cost or benefit. It’s often used in the context of negative externalities, which are costs that are not directly accounted for by the producer or consumer.

Let’s evaluate each option:

a. This is not an example of an externality because the firm is fully paying for the pollution, meaning the cost of the pollution is internalized.

b. This could be an example of an externality, but it’s not specific enough. It doesn’t clarify whether the firm is internalizing the cost of pollution or not.

c. This is a clear example of an externality. The firm is generating marginal damage (in this case, pollution) that it does not account for when making decisions, thus creating a negative externality.

d. This is not an example of an externality. An input that increases the private cost to a firm is an internal cost, not an external one.

So, the correct answer is c. the marginal damage generated from a power plant that the firm does not internalize when making decisions. This statement accurately describes a negative externality.

Question 12

Suppose that marginal cost is zero and a monopolist faces
a downward-sloping, linear demand curve. The profit maximizing quantity
occurs where
a. MR < MC.
b. MR > MC.
c. P = MR.
d. MR = MC, which, in this case, is also the midpoint price and
quantity.
e. MR = MC, which, in this case, is at a price higher than the midpoint
price and a quantity lower than the midpoint quantity.

Answer 12

d. MR = MC, which, in this case, is also the midpoint price and quantity.
The profit-maximizing quantity in a monopoly occurs when the marginal revenue (MR) equals the marginal cost (MC). In other words, a monopolist will choose to produce up to the point where the cost of producing an additional unit (marginal cost) is equal to what they earn from selling that additional unit (marginal revenue). This rule applies to all firms, not just monopolies. However, because a monopoly faces no competition, its marginal revenue curve is different from that of a competitive firm.

Question 13

Suppose that marginal cost is now constant and greater
than zero. Again, the monopolist faces a downward-sloping, linear demand curve. The profit maximizing quantity occurs where
a. MR < MC.
b. MR > MC.
c. P = MR.
d. MR = MC, which, in this case, is also the midpoint price and quantity.
e. MR = MC, which, in this case, is at a price higher than the midpoint
price and a quantity lower than the midpoint quantity

Answer 13

e. MR = MC, which, in this case, is at a price higher than the midpoint
price and a quantity lower than the midpoint quantity
The profit-maximizing quantity for a monopolist occurs where the marginal revenue (MR) equals the marginal cost (MC). This is because the monopolist will produce up to the point where the cost of producing an additional unit (marginal cost) is equal to what they earn from selling that additional unit (marginal revenue).
So, the correct answer is e. MR = MC, with the understanding that the price and quantity do not necessarily correspond to the midpoint of the demand curve. The monopolist will set a price on the demand curve where the quantity corresponds to MR = MC. The price will be higher than the price at the midpoint of the demand curve, and the quantity will be lower than the quantity at the midpoint of the demand curve. This is because the demand curve is downward sloping, so the price decreases as quantity increases.

Question 14

A perfect price discriminating monopolist will
end up with ___ of the gains from trade.
a. all
b. half
c. none
d. more than half but less than all
e. less than half but more than none

Answer 14

a. all
A perfect price discriminating monopolist is a theoretical market structure where a monopolist can charge each buyer their exact willingness to pay. This means the monopolist captures all consumer surplus, turning it into producer surplus.

In terms of gains from trade, this means that a perfect price discriminating monopolist ends up with all of the gains from trade. So, the correct answer is a. all.

Question 15

Ignatius makes $20 an hour as a carpenter. He must take two hours off from work (unpaid) to go to the dentist to have his toothpulled. The dentist charges Ignatius $100. The opportunity cost of Ignatius’s visit to the dentist is
a. $20.
b. $40.
c. $120.
d. $140

Answer 15

d. $140
Opportunity cost is the cost of forgoing the next best alternative when making a decision. In this case, Ignatius’s opportunity cost for visiting the dentist includes both the cost of the dentist visit and the income he loses by taking time off work.

The dentist charges Ignatius $100. He also has to take two hours off from work, during which he could have earned $20 per hour, totaling $40. Therefore, the total opportunity cost of the visit is the sum of these two amounts.

So, the opportunity cost of Ignatius’s visit to the dentist is $100 (dentist’s charge) + $40 (lost wages) = $140.

Question 16

Which of the following is an example of a normative statement?
a. If the price of a product decreases, quantity demanded increases.
b. If the price of a product decreases, a price floor should be imposed.
c. Reducing tax rates on the wealthy would lower unemployment.
d. If the national saving rate were to increase, so would the rate of
economic growth.

Answer 16

b. If the price of a product decreases, a price floor should be imposed.
A normative statement is one that makes a value judgment, a claim that something is good or bad, right or wrong, better or worse, desirable or undesirable. It’s a statement that cannot be tested or verified, it’s based on an opinion.

Let’s analyze the options:

a. “If the price of a product decreases, quantity demanded increases.” - This is a positive statement, as it describes a factual relationship between two economic variables, price and quantity demanded, which can be tested or verified.

b. “If the price of a product decreases, a price floor should be imposed.” - This is a normative statement. It’s making a value judgment that a price floor is desirable when the price of a product decreases.

c. “Reducing tax rates on the wealthy would lower unemployment.” - This is a positive statement, as it describes a cause-and-effect relationship between tax rates and unemployment that can be tested or verified.

d. “If the national saving rate were to increase, so would the rate of economic growth.” - This is a positive statement, as it describes a cause-and-effect relationship between the national saving rate and economic growth that can be tested or verified.

So, the answer is option b. It’s the only statement that makes a value judgment, hence it’s a normative statement.

Question 17

Under perfect competition, in the long-run, …
a. profits can be positive, negative, or zero.
b. profits can only be positive.
c. profits are equal to zero.
d. profits cover variable costs but not fixed costs.

Answer 17

c. profits are equal to zero.
In the long run under perfect competition, firms will enter or exit the market until they are making zero economic profit. This is because if firms in the market are making a positive economic profit, new firms have an incentive to enter the market. This will increase the supply of the product, which leads to a decrease in the market price and a decrease in each firm’s profit. Conversely, if firms in the market are making a negative economic profit, some firms will exit the market, decreasing the supply of the product, increasing the market price, and increasing each remaining firm’s profit. This process continues until firms in the market are making zero economic profit.

So, the answer is option c, profits are equal to zero. This is a characteristic of long-run equilibrium in a perfectly competitive market.

Question 18

Under perfect competition, in the short-run, …
a. profits can be positive, negative, or zero.
b. profits can only be positive.
c. profits are always equal to zero.
d. a firm maximizes revenue but not profits.

Answer 18

a. profits can be positive, negative, or zero.
In the short run under perfect competition, a firm’s profits can be positive, negative, or zero. This is because in the short run, there are fixed costs that the firm cannot recover. Therefore, even if the firm is not profitable, it might choose to continue production as long as it can cover its variable costs.

Let’s analyze the options:

a. “Profits can be positive, negative, or zero.” - This is correct. In the short run, a firm can make a profit if its average revenue is greater than its average total cost, incur a loss if its average revenue is less than its average total cost, or break even if its average revenue equals its average total cost.

b. “Profits can only be positive.” - This is incorrect. As explained above, a firm can also incur losses or break even in the short run.

c. “Profits are always equal to zero.” - This is incorrect. While profits tend to be zero in the long run under perfect competition, in the short run, profits can be positive, negative, or zero.

d. “A firm maximizes revenue but not profits.” - This is incorrect. A firm’s goal is to maximize profits, not revenue. A firm maximizes its profits by producing the quantity of output where marginal cost equals marginal revenue.

So, the answer is option a, profits can be positive, negative, or zero. This is a characteristic of short-run equilibrium in a perfectly competitive market.

Question 19

Under perfect competition, in the short-run, when a firm is earning negative profits, …
a. the firm should always exit.
b. the firm should exit if it meets all its variable and fixed costs.
c. the firm should exit if it cannot cover all of its variable costs—let
alone its fixed costs.
d. the firm should exit if it can cover all its variable costs but can only
cover half of its fixed costs.

Answer 19

c. the firm should exit if it cannot cover all of its variable costs—let
alone its fixed costs.
In the short run under perfect competition, a firm’s decision to continue operating or exit the market is based on its ability to cover its variable costs.

Let’s analyze the options:

a. “The firm should always exit.” - This is incorrect. A firm should not always exit when it’s earning negative profits. If it can cover its variable costs, it should continue operating in the short run.

b. “The firm should exit if it meets all its variable and fixed costs.” - This is incorrect. If a firm can cover all its variable and fixed costs, it’s breaking even, not making a loss. In this case, there’s no need for the firm to exit the market.

c. “The firm should exit if it cannot cover all of its variable costs—let alone its fixed costs.” - This is correct. If a firm cannot cover its variable costs, it should exit the market. This is because the firm would be able to reduce its losses by stopping production and only having to pay fixed costs.

d. “The firm should exit if it can cover all its variable costs but can only cover half of its fixed costs.” - This is incorrect. If a firm can cover all its variable costs, it should continue operating in the short run, even if it can’t cover all its fixed costs. This is because by continuing to operate, the firm can offset some of its fixed costs and reduce its losses.

So, the answer is option c, the firm should exit if it cannot cover all of its variable costs—let alone its fixed costs. This is a characteristic of short-run decision making in a perfectly competitive market.

Question 20

If a firm who charges a single-price faces
a downward-sloping demand for its product, then the firm can
a. price above marginal cost.
b. price at marginal cost.
c. price in a way to extract all the consumer surplus from each consumer.
d. price below marginal cost.

Answer 20

a. price above marginal cost.
A firm that faces a downward-sloping demand curve for its product is a price maker, meaning it has some degree of market power to set its own price. This is in contrast to a firm in perfect competition, which is a price taker.

Let’s analyze the options:

a. “Price above marginal cost.” - This is correct. A firm with market power can set its price above marginal cost. This is because the firm’s downward-sloping demand curve means that it can increase its price without losing all of its customers.

b. “Price at marginal cost.” - This is incorrect. While firms in perfect competition price at marginal cost, a firm with market power can price above marginal cost.

c. “Price in a way to extract all the consumer surplus from each consumer.” - This is incorrect. While a firm with market power can capture some consumer surplus, it cannot capture all of it unless it perfectly price discriminates, which is not the case here as the firm charges a single price.

d. “Price below marginal cost.” - This is incorrect. A firm would not want to price below its marginal cost, as this would mean it is making a loss on each additional unit of output it sells.

So, the answer is option a, the firm can price above marginal cost. This is a characteristic of firms with market power facing a downward-sloping demand curve.

Question 21

Define Coase Theorem

Answer 21

The Coase Theorem is a legal and economic theory developed by economist Ronald Coase. It states that where there are complete competitive markets with no transaction costs and an efficient set of inputs and outputs, an optimal decision will be selected.

The theorem asserts that bargaining between individuals or groups related to property rights will lead to an optimal and efficient outcome, no matter what that outcome is. It argues that under the right conditions, parties to a dispute over property rights will be able to negotiate an economically optimal solution, regardless of the initial distribution of the property rights.

However, for the Coase Theorem to apply fully, the conditions of efficient, competitive markets, and most importantly zero transaction costs, must occur. In the real world, it is rare that perfect economic conditions exist, making the Coase Theorem better suited to explaining why inefficiencies exist as opposed to a way to resolve disputes.

The Coase Theorem is applied when there are conflicting property rights. It states that under ideal economic conditions, where there is a conflict of property rights, the involved parties can bargain or negotiate terms that will accurately reflect the full costs and underlying values of the property rights at issue, resulting in the most efficient outcome.

In order for this to occur, the conditions conventionally assumed in the analysis of efficient, competitive markets must be in place, particularly the absence of transaction costs. The information must be free, perfect, and symmetrical. One of the tenets of the Coase Theorem is that bargaining must be costless; if there are costs associated with bargaining, such as those relating to meetings or enforcement, it affects the outcome.