101 ECON REVIEW SESSION
By Hiro Miyamoto December 16, 2007
Outline
Monopoly Game Theory Monopolistic Competition Externality Public Goods Risk and Uncertainty
Monopoly
A monopoly is a market that has only one seller but many buyers. In other words, when there is only a single firm in an industry, we say that it is a monopoly. Unlike a competitive firm, the monopolist gets to choose its price. Thus, it is a price maker. Market power: the ability of a producer to raise prices.
Monopolist's problem
The purpose of a monopolist is to maximize its profit. The monopolist determines not only the level of output q but also the level of price p.
Solving the monopolist's problem
Step 1: By using the profit maximizing condition, MR = MC, we can obtain the optimal output level. Step 2: By using the demand curve and the optimal level of output, we can get the optimal price.
Marginal Revenue
Marginal revenue: the change in revenue that results from a unit change in output.
Marginal Revenue
How can we get the MR curve?
Step 1: Draw a demand-curve in the space where quantity is in horizontal. Step 2: Find the half point of Q-intercept. Step 3: Connect the half-point and Pintercept.
MR Quantity Half-point Q-intercept Price, MR P-intercept
Demand Curve
Solving the monopolist's problem
P X
P* PC V W
Y MC Z MR D
Q*
Step 1: By using the optimal condition MR=MC, we can find the optimal output. In the above picture, at the point W, MR crosses MC. Thus, Q* is optimal output. Step2: to find the monopoly price, you have to go up vertically from the point W to the demand curve. Thus, you find the point Y. The monopoly price is P*.
Welfare Effects of Monopoly
Price CSm DWL A B D PSm MC
Pm PC
C E
MR Qm QC CS PS Welfare (W=CS+PS) Q/2
Demand Q Monopoly A B+D A+B+D Quantity Change -B-C B-E -C-E=DWL
Competition A+B+C D+E A+B+C+D+E
Price Discrimination
When a firm charges different prices to different groups, they price discriminate.
Perfect price discrimination
In the extreme, the firm may be able to charge exactly the highest price each customer is willing to pay (reservation price). If so, the firm is able to perfectly price discriminate.
P = WTP
The perfectly discriminating firm maximizes profits by producing where demand equals marginal cost. As with perfect competition, the efficient level of output results. Unlike perfect competition, each customer pays exactly what he or she is willing to pay, and so there is no consumer surplus.
Perfect price discrimination
P MC A Pm B Pc D C CE E ME
MR Qm
Competition A+B+C D+E A+B+C+D+E 0
Demand Q
Monopoly Perfect price discrimination 0 A+B+C+D+E A+B+C+D+E 0
Qc
Single-price A B+D A+B+D C+E
CS PS Welfare DWL
Game Theory
A game consists of
Players Strategies available to those players Payoffs (the reward received by a player in a game) for each combination of strategies. A payoff matrix: a payoff matrix shows how the payoff to each of the participants in a two player game depends on the actions of both.
Nash Equilibrium
A combination of strategies where no player would unilaterally alter its behavior. The result when each player in a game chooses the action that maximizes his or her payoff given the action of other players, ignoring the effects of his or her action on the payoffs received by those other players.
How to find Nash Equilibria
"NE is combination of best responses". Best Responses: Given the opponent's strategy, the strategy that yields the highest payoff is best response.
Find Nash equilibrium
P2 L P1 U D (5, 5) (4, 8)
R (7, 4) (8, 9)
Dominant strategy
An action is a dominant strategy when it is a player's best action regardless of the action taken by the other player.
Prisoner 2 Confess Confess -1, -1 Prisoner 1 Not confess 0, -9 -6, -6 -9, 0 not confess
Monopolistic Competition
Monopolistic competition:
Many competing producers Differentiated products Free entry and exit in the long-run
The industry structure is monopolistic in that each firm faces a downward-sloping demand curve for its product. It therefore has some market power in the sense that it can set its own price.
Monopolistic Competition
Short-run equilibrium: an industry takes the number of firms as given. Long-run equilibrium: it is reached only after enough time has elapsed for firms to enter or exit the industry. Notice that in the long-run, a profit of a firm is zero!!
Solving monopolistically competitive firm's problem
Similar to the monopolist's problem. The monopolistically competitive firm tries to maximize its profit. The monopolistically competitive firm chooses output and price. Solving Procedure:
Step 1: By using the profit maximizing condition, MR = MC, we can obtain the optimal output level. Step 2: By using the demand curve and the optimal level of output, we can get the optimal price.
Monopolistic Competition
Price, Cost, MR MC ATC
P* Profit MR Q* D Quantity
Monopolistic competition in the long run
In the long run, a monopolistically industry competitive ends up in zero-profit equilibrium. Thus, each firm makes zero profit at its profit-maximizing quantity. This result comes from the free entry and free exit condition. Thus, in the long run equilibrium, we have
p = ATC (Q )
* *
and
MR (Q*) = MC (Q*)
Monopolistic competition in the long run
Price, Cost, MR
MC
ATC
P*
MR Q*
D
Quantity
Externalities
Externalities: actions of an agent affect other agents. Positive externality:
an action of an agent increases the benefits of other agents. (demand side) an action of an agent reduces the cost of other agents. (supply side)
Negative externality:
an action of an agent decreases the benefits of other agents. (demand side) an action of an agent increases the cost of other agents. (supply side)
MSB and MSC
Marginal social benefit (MSB): the additional gain to society caused by an additional unit of the externality. MSB=marginal benefit (MB) + external benefit Marginal social costs (MSC): the additional cost to society caused by an additional unit of the externality. MSC=marginal cost (MC) + external benefit
External cost and benefit
External cost: an uncompensated cost that an individual or firm imposes on others. External benefit: a benefit that an individual or firm confers on others without receiving compensation.
society optimal quantity
The society optimal quantity is the quantity level that society would choose if all the costs and benefits were fully accounted for. At the optimal q*, we have
MSB(q*)=MSC(q*).
Negative externality on supply-side
MSB, MSC MSC
A E B F C D GH
MC
MSB=Demand Quantity Qp
Private A+B+C+D F+G+H C+D+E+G+H F-C-D-E A+B+F-E Change B+C+D H-B-C D+E+H -B-C-D-E -E=DWL
Qs
Social Optimum Consumer surplus Private producer surplus Externality cost Social producer surplus Welfare A B+C+F+G C+G B+F A+B+F
Solutions to Externalities
Pigouvian taxe is the tax designed to reduce external costs. Pigouvian subsidy is a payment designed to encourage activities that yields external benefits. Tax per unit = MSC(q*) - MC(q*) Subsidy = MSB(q*) MB(q*)
Negative externality and Optimal Pigouvian tax
MSB, MSC MSC Socially Optimal Price to consumers after tax Optimal Pigouvian tax Demand Price to producers after tax Q* Quantity Marginal external cost Supply
Public Goods
Public goods: a commodity or services whose consumption by one person does not preclude others from also consuming it. Demand for public goods: the demand for a public good is different from that for a private good. The social marginal benefit of a public good is the sum of the marginal benefit to each person who consumes the good. The social demand curve or willingness to pay curve for a public good is the vertical sum of the demand curves of each individual.
Public Goods
Price Social demand for the public goods
Social optimum Supply, MC Market equilibrium Individual 2's demand curve Individual 1's demand curve
Quantity
Risk and Uncertainty
Uncertainty: a situation in which more than one event can occur, but we cannot tell which event will occur. Probability: a number between 0 and 1 that indicates the likelihood that a particular outcome will occur. A random variable: a variable with an uncertain future value.
Expected Value
The expected value: the value of each possible outcome times the probability of that outcome. If there are n possible outcomes, the value of outcome i is Vi, and the probability of that outcome is Pi, then
EV = P1 V1 + P2 V2 + + Pn Vn .
Example
If it rains, you can get $100. If not, you can get $200. The probability of rain is 30% and probability of no rain fine is 70%. Then your expected value is
EV = 0.3 100 + 0.7 200 = 170.
Expected Utility
The expected utility: the probability-weighted average of the utility from each possible outcome. If there are n possible outcomes, the value of outcome i is Vi, and the probability of that outcome is Pi, then
EU = P1 U (V1 ) + P2 U (V2 ) + + Pn U (Vn ).
Risk Aversion, Neutral and Lover
Risk averse: the expected utility of wealth < the utility of expected wealth Risk neutral: the expected utility of wealth = the utility of expected wealth
EU (W ) < U ( EW )
EU (W ) = U ( EW ) EU (W ) > U ( EW )
Risk lover: the expected utility of wealth > the utility of expected wealth
Marginal utility of wealth and risk aversion
Utility of wealth: the amount of utility a person attaches to a given amount of wealth Diminishing marginal utility of wealth: the more wealth you have, the less you value each additional dollar of wealth Important Results:
A person with a diminishing marginal utility of wealth is risk averse. A person with a constant marginal utility is risk neutral
Example
Utility function is
u= w
A person has wealth $10000. There is possibility that he loses his wealth and wealth becomes $100 with probability 0.25. The expected wealth is
E ( w) = 0.25 100 + 0.75 10000.
The expected utility is
EU = 0.25 100 + 0.75 10000.