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A fair bet is
- one whose expected value is zero. The expected value is the value of each possible outcome times the probability of that outcome.
- (0.25 ´400) + (0.75 ´ 200) = 250.
How do you calculate variance?
- The expected value of the
- stock is (0.25 ´ 400) + (0.75 ´ 200) = 250.
The variance is
0.25(400 - 250)2 + 0.75(200 - 250)2
A measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set.
A Pareto improvement is
- a change, such as a reallocation of goods or productive inputs,
- that helps at least one person without harming anyone else. A change that is a
- Pareto improvement necessarily passes the cost-benefit test because at least
- one person benefits but there are no costs.
The cost-benefit principle states that
- change is desirable if benefits exceed the costs. Because there may be costs, a
- change that satisfies the cost-benefit principle may not be a Pareto
- improvement, which is a change that helps at least one person without harming
- anyone else
A perfectly competative market achieves
- economic efficiency: It maximizes total surplus, which is the sum
- of consumer and producer surplus. However, most markets fall short of perfect
- competition, and some exhibit a significant market failure, which substantially
- reduces economic efficiency and deadweight loss. Types of market failures
- include monopoly pricing, where price is set above marginal cost, adverse
- selection, when one party to a transaction possesses information about a hidden
- characteristic that is unknown to other parties and takes economic advantage of
- this information, and moral hazard, which occurs when an informed party
- takes an action that the other party cannot observe and that hurts the
- less-informed party.
A firm shuts down...
- only if it can reduce its loss by doing so. That is, the firm shuts down only if its revenue is less than its avoidable variable cost. This is because if the firm shuts down, it does not incur the variable cost, so its only loss is its unavoidable fixed cost.
- In the first case, revenue is greater than variable cost, so the firm should not shut down to minimize losses.
A monopoly maximizes profit by
producing the quantity where marginal cost (MC) equals marginal revenue (MR). Price is then set according to the demand curve (D).
In a monopoly, MR is...
half of the demand curve, always. Twice a steep.
I.e. if demand was P = 10 and Q = 30, the MR would be P=10 and Q=15
In order for a firm to be a natural monopoly...
, its production must exhibit economies of scale; that is, firm’s average cost curve must be downward sloping. If the firm operates in the upward-sloping region of its average cost curve, it is possible that two or more firms could produce in the same industry more efficiently than one firm.
A natural monopoly is a situation where for technical or social reasons there cannot be more than one efficient provider of a good. Public utilities are usually considered to be natural monopolies. Examples include water services and electricity.Natural monopolies tend to occur in cases where capital costs predominate. It is very expensive to build transmission networks (water/gas pipelines, electricity and telephone lines); therefore, it is unlikely that a potential competitor would be willing to make the capital investment needed to even enter the monopolist's market.
in order to price discriminate....
the company must have market power and the ability to set prices.
In order to price discriminate, Alexx must have market power—the ability to set prices. Consumers must have varying price sensitivities, and Alexx must be able to identify individual consumers or groups of individuals based on willingness to pay. Alexx must also be able to prevent reselling after the initial sale.
The monopoly, when maximizing profit at a single price...
produces Q* units (where marginal cost equals marginal revenue) and charges the price indicated by the demand curve at the profit-maximizing quantity (p*).
a two-part price is...
where a firm charges a consumer a lump-sum fee for the right to buy as many units of the good as the consumer wants at a specified price.
A two-part tariff is a price discrimination technique in which the price of a product or service is composed of two parts - a lump-sum fee as well as a per-unit charge. In general, price discrimination techniques only occur in partially or fullymonopolistic markets. It is designed to enable the firm to capture more consumer surplus than it otherwise would in a non-discriminating pricing environment. Two-part tariffs may also exist in competitive markets when consumers are uncertain about their ultimate demand. Health club consumers, for example, may be uncertain about their level of future commitment to an exercise regimen.
Examples of two-part tariffs
membership discount retailers" such as shopping clubs that charge an annual fee for admission to the point of sale and also charge for your purchasesamusement parks where there are admission fees and also per-ride feescover charge for bars combined with per drink feescredit cards which charge an annual fee plus a per-transaction feeloyalty cards or clubslandline telephones where there is a fee to use the service ('line rental') and also a fee per call. The line rental covers the cost of providing the service, the per minute charge covers the cost of placing the call on the network.personal seat licenses in professional sports, in which fans of a team pay an up-front lump sum fee for the right to purchase tickets at face value
An oligopoly is
a market form in which a market or industry is dominated by a small number of sellers (oligopolists). Oligopolies can result from various forms of collusion which reduce competition and lead to higher prices for consumers.
A Nash-Bertrand equilibrium is
a set of prices such that no firm can obtain a higher profit by choosing a different price if the other firms continue to charge these prices. If the products are identical, in any Nash-Bertrand equilibrium, the firms must charge the same price, or no one will buy from the high-price firm. This holds regardless of the number of firms because consumers will always purchase from the firm with the lowest price and the other firms will receive no sales. The result of this is that the Nash-Bertrand equilibrium price equals the marginal cost, as in the price-taking equilibrium. Knowing that rivals will set price equal to marginal cost, a firm would receive no sales if it charged a price above marginal cost. Firms have no incentive to charge less than marginal cost because they would incur losses.
is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.
Key elements of a game
- ◦The players
- ◦Timing of a game: Simultaneous or Sequential.
- ◦Information Availability: Perfect or Imperfect.
- ◦The list of possible strategies/actions for each player.
- ◦The payoffs associated with each combination of strategies.
- ◦The decision rule.
a strategy that produces a higher payoff than any other strategy the player can use no matter what its rivals do.
If a dominant strategy is available, a rational player always chooses such strategy over all other strategies.
Game theory: Best Responses
- the strategy that maximizes a player’s payoff given its beliefs about its rivals’ strategies.
- A dominant strategy is a special case where the dominant strategy is a best response to all possible strategies that a rival might use.
Strategy and Nash Equilibrium
- A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy.
- A Nash equilibrium is self-enforcing: no player wants to follow a different strategy.
Cheap Talk to Coordinate Which Nash Equilibrium
- Firms can engage in credible cheap talk if they communicate before the game and both have an incentive to be truthful (higher profits from coordination).
- If Network 1 announces in advance that it will broadcast on Wed, Network 2 will choose Thu and both networks will benefit. The game becomes a coordination game.
Pareto Criterion to Coordinate Which Nash Equilibria
- If cheap talk is not allowed or is not credible, it may be that one of the Nash equilibria provides a higher payoff to all players than the other Nash equilibria.
- If so, we expect firms acting independently to select a solution that is better for all parties (Pareto Criterion), even without communicating.
Unique Nash Equilibrium
Unique Nash equilibrium: only one combination of strategies is each firm’s strategy a best response to its rival’s strategy.
Multiple Nash Equilibria
- Many games have more than one Nash equilibrium.
- Game 2 has 2 Nash-equilibria.
- Nash Equilibrium #1: Network 1 chooses to air its show on Wednesday and Network 2 chooses to air its show on Thursday.
- Nash Equilibrium #2: Network 1 chooses to air its show on Thursday and Network 2 chooses to air its show on Wednesday.
- To predict the likely outcome of multiple equilibria (which one) we may use additional criteria.
- Mixed Strategy Nash Equilibria
- In the games we played so far, players were certain about what action to take at each rival’s decision (pure strategy).
- When players are not certain they use a mixed strategy: a rule telling the player how to randomly choose among possible pure strategies.
a rule telling the player how to randomly choose among possible pure strategies
game thoery: incomplete information
- We have assumed so far firms have complete information: know all strategies and payoffs. However, in more complex games firms have incomplete information.
- Incomplete information may occur because of private information or high transaction costs.
any situation in which two or more parties with different interests or objectives negotiate voluntarily over the terms of some interaction, such as the transfer of a good from one party to another,
- Bargaining Game Solution
- The solution for bargaining games is called Nash Bargaining Solution.
- Nash Bargaining Solution is not a Nash Equilibrium.
- The Nash Equilibrium is for non-cooperative games where players do not negotiate quantities or prices.
- Cournot Model
- Small number of firms and no entry
- Identical products.
- Market price is given by P(Q) = a – bQ where Q = Q1 + Q2.
- Q1 = Q – Q2 is the residual demand for firm 1.
- Q2 = Q – Q1 is the residual demand for firm 2.
- Each firm maximizes profit by setting quantity such that MR1 = MC1. This results in a firm’s “best responses” to another firm’s choice of quantity.
- The equilibrium is a set of quantities chosen by firms such that, holding the quantities of all other firms constant, no firm can obtain a higher profit by choosing a different quantity. This is defined as the Nash equilibrium.
- The equilibrium quantity must be on the best response curve for all firms
- Small number of firms and no entry
- Identical products.
- Market price is given by P(Q) = a – bQ
- Each firm maximizes profit by setting prices. This results in a firm’s “best responses” to another firm’s choice of price.
- The equilibrium is a set of prices chosen by firms such that, holding the prices of all other firms constant, no firm can obtain a higher profit by choosing a different price. This is defined as the Nash equilibrium.
What can firms do to increase profit?
- Mergers could be vertical or horizontal and both want to increase profit.
- Vertical mergers may lower cost with a more efficient supply chain organization.
- If the merger results in even a modest cost advantage, the merger may be worthwhile.
- Horizontal mergers may increase market power and reduce competition.
- In general, the reduction in the number of firms may raise price insufficiently to make a merger profitable unless there is cost reduction.
- Cartel Basic Functioning
- Typically, each member of a cartel agrees to reduce its output from the level it would produce if it acted independently. As a result, the market price rises and the firms earn higher profits. If the firms reduce market output to the monopoly level, they achieve the highest possible collective profit.
- Why Cartels Fail: External Reasons
- Cartels are generally illegal. High fines and jail terms may prevent collusion.
- Some cartels fail because they do not control enough of the market to significantly raise the price.
- Why Cartels Fail: Internal Reasons
- Cartel members have incentives to cheat if a member thinks its firm is just one of many firms so its extra output hardly affects the market price and the other firms in the cartel can’t tell who is producing more.
- For a firm’s announced strategy to be a credible threat, rivals must believe that the firm’s strategy is rational (works in the firm’s best interest).
- In the simultaneous-move game, is a threat of choosing 96,000 capacity made by American Airline credible?
- However, in the sequential game because American makes the 1st move, its commitment to produce 96 is credible. This is called the First Mover Advantage.
probability, assessing risk..
- Probability: number between 0 and 1 that indicates the likelihood that a particular outcome will occur.
- If an outcome cannot occur, probability = 0. If the outcome is sure to happen, probability = 1. If it rains one time in four on July 4th, probability = ¼ or 25%.
- Important criteria:
- So probabilities must add up to 100% under these assumptions
- Mutually exclusive. In this case, it either rains or doesn’t.
- Exhaustive. No other outcome is possible.
- = Pr1(V1 – EV)2 + Pr2(V2 – EV)2 + … + Prn(Vn – EV)2
- Variance, 2: measures the spread of the probability distribution; probability-weighted average of the squares of the differences between the observed outcome and the expected value.
- Example: Back to the concert and rain example. Suppose.
- Outcome #1 – Sunny. Probability, Pr1 = ½ and Value (Profit), V1 = 15.
- Outcome #2 – Rainy. Probability, Pr2 = ½ and Value (Profit), V2 = -5.
- EV = 5
Levels of risk preference
- Risk averse person: Someone who is unwilling to make a fair bet.
- Risk neutral person: Someone who is indifferent about making a fair bet.
- Risk preferring person: Someone who will make a fair bet.
- A bet where expected value equals to zero.
- Which one of the two scenarios below reflect a fair bet?
- Scenario 1: You pay $2 to flip a coin. If it is head, you win $3, if it is tail, you get nothing.
- Scenario 2: You pay $2 to flip a coin. If it is head, you win $4, if it is tail, you get nothing.
- Risk averse person, will not choose scenario 2.
- Risk neutral person, will be indifferent between taking scenario 2 and not taking scenario 2.
- Risk preferring person, will be happy to take scenario 2. He might even consider taking scenario 1.
- The risk premium is the maximum (minimum) amount that a decision-maker would pay (accept) to avoid taking (take) a risk.
- Risk Premium Calculation
- Risk premium: the difference between the expected value of the uncertain prospect and the certainty equivalent
- Example: Suppose Irma is currently under option 1. Now, there is a change and she might have to be under option 2. What is the max amount of money is she willing to pay to remain in option 1?
What are some strategies to reduce risk?
- - obtaining information
- - diversification
How much diversification reduces risk depends on...
- the degree to which the payoffs of various investments are correlated (move in the same direction).
- Possible Correlation Direction.
- Independent or uncorrelated.
- a change that benefits some people without harming anyone else.
- A government policy that eliminates a market failure is a Pareto improvement if the reallocation of goods helps at least one person without harming anyone else.
- Because there is possible gains from trade.
- Gain from trade comes from at least two sources:
- Comparative Advantage.
- Increasing Return to Scale.
factors that may affect international trade
- Exchange Rate.
- Transportation Cost.
- Language & Cultural Difference.
- Trade Policies
- Allow free trade: No trade restrictions.
- Ban all imports: The government sets a quota of zero on imports.
- Set a tariff: The government imposes a tariff on imported goods.
- Set a positive quota: The government limits imports to a determined QM level.
Why trade barriers?
- Rent Seeking.
- Creating Market Power.
- Contingent protection: trade policy that protects domestic producers from certain actions by foreign firms (anti-dumping).
Adverse selection is when....
In order to fight adverse selection, insurance companies try to reduce exposure to large claims by limiting coverage or raising premiums.
- 1. The tendency of those in dangerous jobs or high risk lifestyles to get life insurance.
- 2. A situation where sellers have information that buyers don't (or vice versa) about some aspect of product quality.
How do you reduce adverse selection?
- Different ways:
- Healthy seniors provide proof that they are healthy. Note: signal must be credible and costly to acquire. Why would healthy senior choose costly signal as a sound strategy?
- Insurance company makes seniors to go through health test.
- Insurance: everyone must buy.
What is a moral hazard?
In economics, moral hazard occurs when one person takes more risks because someone else has agreed to bear the burden of those risks. A moral hazard may occur where the actions of one party may change to the detriment of another after a financial transaction has taken place.Moral hazard occurs under a type of information asymmetry where the risk-taking party to a transaction knows more about its intentions than the party paying the consequences of the risk. More broadly, moral hazard occurs when the party with more information about its actions or intentions has a tendency or incentive to behave inappropriately from the perspective of the party with less information.
How do you reduce moral hazards?
- Fixed-fee contract
- Contingent contracts.
- Payoffs that are contingent on some other observable variables.
- When monitoring is possible, contingency may be the action itself (case 1).
- When monitoring is not possible, payoff may be contingent to the state of nature, profit sharing, bonuses & options, piece rates and commissions.