Summary Managerial Economics: Complete
Managerial Economics (EBC2023)
Maastricht University
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Managerial Economics EBC 2023 Summary
Author: Dominik Betz
Tutorial 1
13 Segmentation of market structures: Number of firms Barriers to entry Ability to differentiate the products from rivals
Market failure: whenever p > MR p > MC
13 Non-cooperative oligopoly There are many models of non-cooperative oligopolies even though there is only one model for competition and monopoly structures. Which model to choose depends on the actions firms take, such as setting price or quantity and the sequence of actions, whether they act simultaneously or sequentially. Cournot model: firms simultaneously choose quantities without colluding Stackelberg model: leader firm chooses a quantity and then the follower firms independently choose their quantities
Monopoly Oligopoly Monop. Competition Competition
- Profit-maximization condition
- Ability to set price
- Market power
- Entry conditions
- Number of firms
- Long-run profit
- Strategy dependent?
- Products
- Example
MR = MC
Price Setter p > MC No entry 1 ≥ 0 No (no rivals) Single product Gas market
MR = MC
Price Setter p > MC Limited entry Few ≥ 0 Yes Differentiated Car manuf.
MR = MC
Price Setter p > MC Free entry Few or many 0 Yes Differentiated Plumbers in town
MR = MC = p Price Taker p = MC Free entry Many 0 No (just mkt. price) Undifferentiated Apple farmers
Bertrand model: firms simultaneously and independently choose prices Assumptions:
- Firms are identical: same cost functions, undifferentiated and identical products
- Duopoly with only two firms, where no entry is possible
- Market lasts for only one period (only one choice) Nash Equilibrium: No firm can obtain a higher profit by choosing a different action, holding all the other firms actions’ constant
13 Cournot Model Simultaneous and independent actions (output choices) by firms in a market that lasts only for one period Imperfect information (each firm must choose its output level before knowing what the other firms will choose) each firm takes into account its beliefs about the output its rivals will set
Nash-Cournot equilibrium: 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.
The important concept in this context is the one of the residual demand curve, which is the market demand that is not met by other sellers at any given price. The residual demand determines their best response, which is the output level that maximizes profit, given the beliefs about how much the rival company will produce. The strategy that each firm uses depends on the demand curve it faces and its marginal costs.
That means in a duopoly that if firm A produces qA units regardless of the price, firm B produces only the residual demand qB = Q - qA. Firm B can think of itself as having a monopoly with respect to the people who do not buy from firm A. To maximize profits, firm B sets its output so that its marginal revenue, corresponding to this residual demand, equals its marginal cost. By shifting its residual demand curve appropriately, firm B can calculate its best response to any given qA using this type of analysis. The negative slope of the best- response curve shows that firm B sells less output, the more people firm B thinks that firm A will serve.
If consumers think products differ, the Cournot quantities and prices will differ across firms. Each firm faces a different inverse demand function and hence charges a different price.
13 Bertrand model Nash-Bertrand equilibrium: A set of prices such that no firm can obtain a higher profit by choosing a different price of the other firms continue to charge these prices.
In this case, if firms start at a price higher than the competitive one, they immediately start undercutting each other by a small amount ε in order to capture the entire market (remember that products are identical undercutting firm captures the whole market). In the end, firms split the market and make zero profit.
The two best-response curves intersect only at the intersection of the marginal cost. Thus, the Bertrand equilibrium when firms produce identical products is the same as the price- taking, competitive equilibrium.
Observations
- When firms produce identical products and have a constant marginal cost, the Cournot model is more plausible than the Bertrand. Reason: Bertrand is insensitive to demand conditions and the number of firms and only cares about costs (Cournot depends on all three)
- When firms produce differentiated products, firms set prices above marginal cost and prices are sensitive to demand conditions, and the Bertrand model is more appropriate, since then firms set prices and the consumers determine the quantities.
The Bertrand best-response curves, which plot relationships between prices, slope upward, indicating that a firm charges a higher price the higher the price its rival charges.
Because differentiation makes demand curves less elastic, prices are likely to be higher when products are differentiated than when they are identical. Differentiation leads to higher prices, but has the desirable characteristic of giving consumers more choices.
14 An overview of game theory General terms A game is any competition between players or firms in which strategic behavior plays a major role An action is a move that a player makes at a specified stage of a game, such as how much output to produce in the current period A strategy is a battle plan that specifies the action that a player will make conditional on the information available at each move and for any possible contingency, such as producing the cooperative output as long as the other one does that and producing the competitive outcome if the other firm cheats. A payoff is a player’s valuation of the outcome of the game, such as profits for firms or utilities for individuals Common knowledge is what all players know about the rules of the game, that each player’s payoff depends on actions taken by all players, that all players want to maximize their payoffs, that all players know the payoffs and that their opponents want to maximize their payoffs and so on. Complete information is a situation where the payoff function is common knowledge among all players Perfect information is a situation where the player who is about to move knows the full history of the play of the game to this point and that information is updated with each subsequent action. A static game is a game in which each player acts only once and the players act simultaneously (complete information about the payoff function but imperfect information about rivals’ move) A dynamic game is a game in which players move either sequentially (complete information about the payoff function and perfect information about previous moves) or repeatedly (perfect information about previous moves but imperfect information about simultaneous moves in current period).
14 Static games Simultaneous actions
Pure strategy: Each player chooses a single action (probability assigned: 1) Mixed strategy: A firm chooses among possible actions according to probabilities it assigns A pure strategy is a rule telling a player what action to take, whereas a mixed strategy is a rule telling the player which dice to throw to choose an action
Cooperation Whether players cooperate in a static game depends on the payoff function. The reason why there is no cooperation in a prisoner’s dilemma game is a lack of trust. The reason they do not trust each other is that each firm knows it is in the other firm’s best interest to deviate from the actions that would maximize joint profits (only a binding, enforceable agreement could make the players choose the cooperative outcome). However, if the dominant strategies of both players result in the same NE as the collusive outcome would, then cooperation is effectively attained.
Tutorial 2
14 Dynamic games players move sequentially or simultaneously repeatedly over time A player as perfect information about other player’s previous moves and complete information about the payoff function Extensive form, which specifies the n players, the sequence in which they make their moves, the actions hey can take at each move, the information that each player has about players’ previous moves, and the payoff function over all the possible strategies Solved by backward induction
Action: A move that a player makes at a specified point Strategy: A battle plan that specifies the action that a player will make conditional on the information available at each move.
Sequential game Each box is a point of decision by one of the firms, called a decision node. The lines or branches extending out of the box represent a complete list of the possible actions that a player can make at that point of the game. Within this game are sub games. At a given stage, a sub game consists of all the subsequent decisions that players may make given the actions already taken and corresponding payoffs.
A set of strategies forms sub game perfect NE if the players’ strategies is a NE in every sub game (so they do not want to change their strategy). As the entire dynamic game is a sub game, a sub game perfect NE is also a NE. This game is solved for the sub game perfect NE using backward induction, where we first determine the best response by the last player to move, next determine the best response for the player who made the next-to-last move, and then repeat the process until we reach the move at the beginning of the game. To predict what the first mover does, the first mover first determines how the second mover will react to any of its actions at the first stage.
The outcome differs from the simultaneous-move outcome because one firm has a first mover advantage. As it moves first, it makes a commitment to produce a certain quantity (by limiting its options, it makes itself stronger). This is a credible threat, an announcement that a firm will use a strategy harmful to its rival and that the rival believes because the firm’s strategy is rational in the sense that it is in the firm’s best interest to use it. Typically, for a threat to succeed, a firm must have an advantage that allows it to harm the other firm before
Tutorial 3
13 Stackelberg Model sequential output decisions: leader sets its output before the follower sets its output decision (e. if one firm enters a market before another)
In this game, the leader realizes that once it sets its output, the rival firm will use its Cournot best-response curve to pick a best-response output. Thus, the leader predicts what the follower will do before the follower acts.
In this case, if firm B is the leader and firm A the follower, firm B uses its residual demand curve to determine its profit-maximizing output. Firm B knows that when it sets qB, firm A will use its Cournot best-response function to pick its best-response output qA (all the possible output decisions firm A may produce are summarized there). In the Stackelberg equilibrium a higher quantity is produced, as the leaders increase in output more than offsets the follower’s reduction in output. Therefore, consumers prefer the Stackelberg equilibrium to the Cournot equilibrium.
Moving sequentially is essential When firms move simultaneously, none of them has a credible threat with which it could announce the Stackelberg output (as it is not in their best interest to produce this output profits would decline if they would do so). In contrast, when one firm moves first, its threat to produce a large quantity is credible because it has already committed to producing the larger quantity, thereby carrying out its threat.
Strategic trade policy A government may be tempted to intervene to make its firm a Stackelberg leader. A government may give a subsidy to its country’s firm, thereby reducing its marginal cost to a lower level. Since this firm’s marginal costs would decline, compared to the other one (no matter which output is produced), the threat is credible. This policy might be effective if the government is interested in maximizing its domestic firm’s profit net of the government’s subsidy.
Problems with intervention In theory, a government may want to subsidize its domestic firm to make it produce the same output as if it would if it were a Stackelberg leader. If such subsidies are to work as desired, five conditions must hold:
- the government must be able to set its subsidy before the firms choose their output levels (as one firm cannot act before the other, but its government can)
- the other government must not retaliate (otherwise both countries may loose)
- the government’s actions must be credible
- the government must know enough about how firms behave to intervene appropriately: demand function, costs etc.
- the government must know which game the firms are playing beggar thy neighbor policies, which are undesirable since protection results in an overall welfare loss
13 Comparison of Collusive, Cournot, Stackelberg and Competitive Equilibriums The Cournot and Stackelberg equilibrium quantities, prices and profits lie between those for the competitive (price taking) and collusive equilibriums.
The profit possibility frontier (see figure 13, p. 458), which corresponds to the contract curve, shows this relationship as well.
Payoffs from the book
Monopoly Cartel Cournot Stackelberg Price-taking qA qB
96
0
48
48
64
64
96
48
96
96
Tutorial 4
13 Cartels A cartel forms if members of the cartel believe that they can raise their profits by coordinating their actions. Although cartels usually involve oligopolies, cartels may form in a market that would otherwise be competitive. A cartel takes into account how changes in any one firm’s output affect the profits of all members of the cartel, which is in sharp contrast to the competitive firm, which only considers its own profit. If a competitive firm lowers its output, it raises the market price only slightly, so slightly that other firms ignore this effect. As long as the marginal cost of the cartel is higher than the marginal revenue, the cartel can raise its profit by lowering output. The less elastic the market demand the potential cartel faces, the higher the price the cartel sets and the greater the benefit from cartelizing.
Laws against cartels The Sherman Act in 1890 and the Federal Trade Commission Act of 1914 prohibit firms from explicitly agreeing to take actions that reduce competition. These antitrust laws (competition policies) limit or forbid cartels and impose penalties in case of detected violation. Also leniency programs encourage the defection of one cartel member. Cartels, however, still persist for three important reasons:
- international cartels and cartels within certain countries operate legally, e. OPEC
- some illegal cartels operate believing that they can avoid detection or that punishment will be insignificant (low fines)
- some firms are able to coordinate their behavior without explicitly colluding
An important point is that antitrust laws usually use evidence of conspiracy (such as explicit agreements) rather than the economic effect of monopoly to determine guilt. That implies that monopolies are not necessarily illegal and that tactic collusion by signaling is not by itself illegal.
Why Cartels fail Cartels fail if non-cartel members can supply consumers with large quantities of goods, as then cartels cannot sustain high prices and low quantities Cartels fail because they are internally instable (if a firm can be made better of cheating than remaining part of the cartel): Each cartel member has an incentive to cheat to the agreement. If enough firms quit the cartel, it collapses
Maintaining cartels Detection o Right to inspect each other’s books o If bids are reported, e. on government contracts, cartel members see whether one underbid the others o Divide the market, so that it can easily be seen whether one intervenes in another one’s market o Price matching or beating guarantees Enforcement o “most-favored-nation clauses”: Statement that the seller would not offer a lower price to any other current or future buyer without offering the same price decrease to that buyer if cheating cut prices for all previous buyers as well o threats of violence Government support o To prevent competition Barriers to entry o The fewer the firms in a market, the more likely it is that other firms will know if a given firm cheats and the easier it is to impose costs on that firm (average number in a cartel 7,25) o When other firms enter the market cartels fail frequently
Mergers If antitrust or competition laws prevent firms from colluding, they may try to merge instead. Recognizing this problem, laws usually restrict the ability of firms to merge if the effect would be anticompetitive. However, not all mergers are banned since some result in more efficient production and superior outcomes for all participants.
16 Comparing Money Today to Money in the Future interest rate: The percentage more that must be repaid to borrow money for a fixed period of time discount rate: a rate reflecting the relative value an individual places on future consumption compared to current consumption A person’s willingness to lend or borrow depends on whether his or her discount rate is greater or less than the market rate The accumulation of interest on interest is called compounding
Tutorial 5
17 Degree of risk To describe how risk an activity is, we need to quantify the likelihood that all possible outcomes occur. A probability is a number between 0 and 1 that indicates the likelihood that a particular outcome will occur. If we have a history of the outcomes for an event, we can use the frequency with which a particular outcome occurred as our estimate of the probabilities. Let n be the number of times one particular outcome occurred during the N total number of times an event occurred: θ = n/N If no history allows us to calculate the frequency, we use whatever information we have to form a subjective probability, which is our best estimate of the likelihood that an outcome will occur (e. a friend’s recommendation or disapproval). A probability distribution relates the probability of occurrence to each possible outcome. E. weather outcomes (as listed in figure 17 on page 574) are mutually exclusive, meaning that only one of these outcomes can occur at a given time, and exhaustive, meaning that no other outcomes than those listed are possible. Where outcomes are mutually exclusive and exhaustive, exactly one of the outcomes will occur with certainty and the probabilities must add up to 100%.
The expected value, EV, is the value of each possible outcome times the probability of that outcome: EV = (Probability x Value) for each value. In terms of payoffs, this is the value one would get on average if the event were repeated many times.
One approach to measure the risk involved in the EV calculation is to look at the degree by which actual outcomes vary from the expected value, EV. The variance measures the spread of the probability distribution. Formally, the variance is the probability-weighted average of the squares of the differences between the observed outcomes and the expected value: Variance = (Probability x (Value – EV)) 2 for each value. The standard deviation is the square root of the variance and is more often used than the variance as it is in the same units as the EV. Holding the expected value constant, the smaller the standard deviation or variance, the smaller the risk.
17 Decision making under uncertainty If people made choices to maximize EV, they would always choose the option with the highest EV regardless of the risks involved. However, most people care about risk and dislike it – they are risk averse – and would choose a bundle with higher risk only if its EV is
substantially higher than that of a less-risky bundle. Expected utility is the probability- weighted average of the utility from each possible outcome: EU = (Probability x U (Value)) for each value, where U is the utility function that may depend on the earnings. Both, the expected utility and expected value calculation are weighted averages in which the weights are the probability that the state of nature will occur. The difference is that the expected value is the probability-weighted average of the monetary value, whereas the expected utility is the probability-weighted average of the utility from the monetary value.
A fair bet is a wager with an EV of 0. A risk averse person is not willing to make this bet, a risk neutral person is indifferent about making it or not and a risk preferring person is willing to make the bet.
Risk Aversion In this case there is a diminishing marginal utility of wealth for example. A person whose utility function is concave picks the less risky choice if both choices have the same EV. The expected utility is the midpoint of the line, called a chord. The risk premium is the amount that a risk-averse person would pay to avoid taking a risk (and still have the same utility as in the case of making the bet).
Risk-neutrality Someone who is risk-neutral has a constant marginal utility of wealth for example: Each extra dollar of wealth raises utility by the same amount as the previous dollar. In general, a risk-neutral person chooses the option with the highest EV, because maximizing EV maximizes utility. A risk-neutral person chooses the riskier option if it has even a slightly higher EV than the less risky option. Equivalently, the risk premium is zero.
Risk preference An individual with an increasing marginal utility of wealth is risk preferring, willing to take a fair bet. A risk-preferring person is willing to pay for the right to make a fair bet. E. many people play lottery (or gamble) even though it is an unfair bet, but they expect such a high utility if the unlikely even of winning occurs that they are willing to make this unfair bet (alternatively: they might enjoy playing the game or people make mistakes and do not realize that they participate in an unfair bet) Snake-formed utility curve
Prospect Theory Properties: the curve passes through the reference point at the origin because gains and losses are determined relative to the initial situation (changes in wealth instead of the level of wealth as in expected utility theory) both sections of the curve are concave to the horizontal, outcome axis people treat gains and losses differently, which is in contrast to expected utility theory. The S-curve shows a bigger impact to a loss than to a comparable size gain. That is, the value function reflects loss aversion: people hate making losses more than they like making gains (decision weights are different, people may assign disproportionately high weights to rare events) People take on unfair lotteries because they put heavier weight on rare events than the true probability used in expected utility theory.
Prospect theory therefore differs from expected utility theory in both the valuation of the outcomes and how they are weighted.
Tutorial 6
Chapter 18 Externalities An externality occurs when a person’s well being or a firm’s production capability is directly affected by the actions of other consumers or firms rather than indirectly through changes in prices. An externality that harms someone is called a negative externality (e. a chemical plant that spoils a lake when dumping its waste products and in doing so harms a firm that rents boats, SUV driving), a positive externality is one that benefits others (e. national defense, Michael Jordan’s presence in away matches). A single action may confer positive externalities on some people and negative externalities on others (e. smell of a pipe).
18 The inefficiency of competition with externalities Competitive firms and consumers do not have to pay for the harms of their negative externalities, so they create excessive amounts. Similarly, because producers are not compensated for the benefits of a positive personality, too little of these is produced. A firm’s private cost, which is the cost of production only, excluding externalities, includes its direct costs of labor, energy etc. but not the indirect cost of the harm from the externality. The true social cost is the private cost plus the cost of the harms from externalities.
Supply-and-Demand Analysis In the competitive equilibrium, firms consider only their private costs in making decisions and ignore the harms of the pollution externality they inflict on others. The market supply curve is the aggregate private marginal cost curve, which is the horizontal sum of the private marginal cost curves of each of the suppliers. The Producer Surplus (PS) is the area between the marginal cost curve (Supply) and the competitive price, P1. The competitive equilibrium maximizes the sum of Consumer Surplus (CS) and private PS. Because of the negative externality (e. pollution), however, the competitive equilibrium does not maximize welfare. Competitive firms produce too much of the negative externality, resulting in a market failure, as competitive forces equalize price and private marginal cost rather than social marginal cost. The full cost is the marginal cost of producing the extra unit plus the harm generated by the negative externality. The height of the social marginal cost curve is the height of the marginal cost curve (Supply) plus the height of the marginal cost of the externality, due to the damage. The social marginal cost curve intersects the demand curve at the socially optimal quantity Q2. At smaller quantities, the price (the value consumers place on the last unit of the good sold) is higher than the full social marginal cost. There the gain of producing one unit exceeds the cost of producing this unit (plus the damage due to the externality). Welfare is the sum of CS and social PS, which
Summary Managerial Economics: Complete
Vak: Managerial Economics (EBC2023)
Universiteit: Maastricht University
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