Microeconomics Lecture summary supplement Erasmus Universiteit Rotterdam

AthenaSummary Erasmus University Rotterdam Erasmus School of Economics – Bachelor 1 Microeconomics Lecture summary supplement

Table of contents Week 6 Chapter 13 - Market with a Few Firms and Inter-Agent Strategic Interactions Chapter 2 – Theory of demand and supply Chapter 14 + 15 – Capital and labour Chapter 16 –Externalities, the Coase Theorem and Government Intervention

page 2 page 8 page 12 page 13

Chapter 13 Market with a Few Firms and Inter-Agent Strategic Interactions The central concept in this chapter is Game Theory, which is used to study the interaction between rational and strategically behaving agents. Games (an analytical simulation of the decision process) can be either static or dynamic. The static game is utilized when matters such as reputation and credibility are not important (this usually implies that the game one takes place once). In every game, all the players know what the game looks like and they are aware of the other party’s preferences. The game, with all the options that are available to the party’s involved as well as the payoffs, are displayed in a matrix, and usually looks like this (the first number in every cell is the payoff for player 1, the second number the payoff for player 2):

A Dynamic game is usually depicted in the form of a tree that shows all the players involved, their possible strategies, the time at which the players can make their move and the eventual payoffs. (A dynamic tree of two people who are wondering whether they should go to the beach or go hiking, and whether they should go alone or together):

We call the number of times a player may be asked to play the number of contingencies per player. In this part of the course numerous famous Game theory model were presented in class. Below, the games will be shown and explained briefly. Prisoner’s Dilemma The police has arrested two individuals and suspect that they committed an atrocious murder. However, there is no real evidence and suspects remain mute. The police officers make them an offer, which will result in a shorter sentence if they confess.

2

The Stag Hunt (A cooperation game) Two friends go hunting, and they would love to hunt a stag. However, because stags are strong animals, they can only be killed when the two friends work together. If one abandons his friend and catches a hare instead, then the first player will be slightly injured by the stag.

Strictly Dominated Strategies A strategy is strictly dominated if and only if a player can always do better by playing another strategy, and this for any possible play by the other players. For example in the example of the prisoner’s dilemma, this is the option to deny (no matter what the other party does, confessing will always result in a higher utility). The Nash Equilibrium We look for Nash equilibria when eliminating strictly dominated strategies is not sufficient to come to a conclusive outcome. This denotes the best strategy as a response to a certain choice of the other party. When this analysis conducted for both players, you will have end up with a set of best responses.

3

4

Cournot Model of Duopoly Competition The Cournot. The Betrand and the Stackelberg model analyse the behaviour of two firms that are in the same market and are competing against each other. The products of the two firms are perfect substitutes. The demand curve of both firms is given by: The profit of the firms is computing by using the following formula: The Cournot Model assumes that the firms compete against each other by setting the production quantity. By setting the formula of the of the marginal revenue equal to zero, and rewriting the result, one can find the reaction function of both firms. The optimal production level as well as the price can be found by substituting the one reaction function into the other. Betrand Model of Duopoly Competition In the Betrand Model firms are competing against each other by setting the price. The outcome of this model will be that both firms offer their products to the market for a price that is equal to the marginal cost of production. If a company charges a price that is higher than the marginal cost, the other firm will make sure that it’s price is slightly lower in order to capture the entire market (remember: the products of the firms are perfect substitutes)

5

Stackelberg Model of Duopoly Competition The Stackelberg Model is a Cournot Model in which one of the firms gets to move first (the leader). After the leader has determined it’s optimal production level, the second firm (the follower) can determine its production level (keeping the production level of the leader in mind). The optimal level for the leader is calculated by inserting the reaction function into the demand function of firm 1, and using this formula to determine the maximal profits (again by setting the marginal revenue equal to the marginal costs). The production level of firm 2 is calculated by inserting the optimal production level of firm one in the demand function of firm 2. Hotelling’s Line Imagine a linear line of a length 1 that represents a market, and the consumers in this market are uniformly distributed along the line. When there is only one firm in the market, its position does not matter, since it will capture the entire market anyway. However, when there are two firms in the market, both will position themselves in the middle, to capture 50% of the market, even though this might not be the optimal point for the consumers. Government Shop Regulation in Circular City This theory concerns the issuing of licenses by the government for certain commercial activities. Suppose the mayor of a town is wondering how many licenses he should issue (for e.g. chemist shops). The town has the shape of a circle and its inhabitants are uniformly distributed on the circumference of 1 km. When each citizen buys one unit of drugs The total population is referred to as L), t denotes the travel costs per kilometre and d the distance from the consumers home to the shop, then on average the traveling costs for each consumer are: The total costs of each chemist shop is given by the formula

The government would want to minimize the travel costs of the consumers and to minimize the prouction costs. All the shops will be located on the edge of the circle. When there are 4 shops (N = 4), this means that the customer who lives furthest away from the shop will have to travel 1/(2N) = 1/8 km to get to a chemist shop. The total transportion costs for the entire population are given by: Whereas the total production costs can be calculated using the formula

(When assume that the sales are equally distributed among the shops, hence each shop sells B = L/N)

Ultimately the true problem that has to be solved is

6

7

Chapter 2 Theory of Demand and Supply A market is a place where two types of entities meet, buyers and sellers. The general characteristic of buyers is that they would like to buy goods for the lowest price possible. A demand curve indicates how much items buyers are willing to purchase for a specific price. The sellers, on the other hand, like to sell their products for the highest price possible. A supply curve exhibits the amount of products the producers are willing to sell to the market given a certain price. In general, the demand curve is downward-sloping and the supply curve is upward-sloping. The point where those two lines intersect is called the equilibrium, this is the price on which buyers and sellers agree. When the market is not in equilibrium, this will either result in an excess demand (so the buyers request more units of a specific good than the buyers are offering) or an excess supply (buyers request less units of the good than the buyers are offering). If there are not restrictions imposed by for example the government, the market will adjust prices so that the equilibrium is restored (this principle is often referred to as Adam Smith’s Invisible Hand). A relative increase in supply will lead to a lower equilibrium price, while a relative increase in demand will drive prices up. In this process, prices serve two goals: -

Rationing (not all bids can be satisfied) Allocative (the people that actually receive the good are the ones that ascribe the most value to the transaction)

The general characteristic of well-functioning markets is that moving from a disequilibrium to an equilibrium makes some agents better off and not one agent worse off. Determinants of Demand: -

Income (effect varies, depends whether the good is a normal good or an inferior good) Tastes Prices of substitutes and complements Expectations Number of buyers

Determinants of Supply: -

Technology Prices of production factors Number of suppliers Expectations Other (e.g. weather)

8

Taxation and Demand and Supply A unit tax t levied on suppliers shifts supply upwards by t units, whereas a unit tax t levied on buyers shifts demand downwards by t units. Yet, the question who really pays for the tax depends on the elasticity of supply and demand. Note that we are referring to the economic incidence (the surplus of whom is affected the most) and not about the legal definition. A general equilibrium is found by the quantity and price at which demand = supply.

The equilibrium price is found by plugging Q* In either the demand or the supply curve. When the unit tax t is levied on the buyers this will result in the following transformation of the demand curve (resulting in a downward shift of the demand curve):

9

An introduction of a unit tax t levied on suppliers will result in an upward shift of the supply curve:

Ultimately one can calculate the share of tax that is levied on buyers and sellers, respectively, by using the following formulas:

The sum of the result of those two equations should equals 1.The surplus that is lost as a result of the implementation of the taxations is referred to as the deadweight loss. The impact of taxation is shown in the following graph.

10

11

Chapter 14 and 15 Labour and Capital When you consider a firm that needs only one input for its production process, labour, the profit function for this firm will look like:

In this situation, the company has to decide how many workers it wants to hire. In order to find the optimal L, one takes the derivative of the profit function with respect to L.

The result is very significant, and asserts that a firm will hire workers as long as their marginal productivity exceeds the cost related to hiring an additional worker. When firms are not price takers, they will hire labour until the point at which the marginal revenue product of labour equals the marginal cost of labour

The Price of Capital The capital interest rate consists of three parts: 1. usual market interest rate i 2. maintenance costs m 3. depreciation rate

12

Chapter 16 Externalities, the Coase Theorem and Government Intervention In economics, people talk about externalities when they are discussing costs or benefits that are not incorporated in the price. If the externality involves a cost, we call this a negative externality, when it concerns a benefit, it is called a positive externality. Because the property rights of externalities are not clearly defined, this is a type of issue that leads to market failures. This means the government may have to intervene, at some occasions. The tragedy of the commons This concept is related to over-using property or resources that are shared among individuals, rather than strictly one individuals’ property. Each will try to maximize his own utility, and all will act individually. However, had the individuals coordinated together, the overall welfare (utility) would have been higher. The formal definition of this concept is: the depletion of a shared resource by individuals, acting independently and rationally according to each one’s self-interest, despite their understanding that depleting the common resource is contrary to their long-term best interests. The Coase Theorem This theorem states that if the agents involved in an externality can trade with each other at no cost and that their agreements are binding, then the outcome of negotiations on externalities will always result in an efficient outcome (so the laws or property rights do not matter). People/governments often try to internalize externalities (by incorporating them into the price), for example by levying taxes (in case of negative externalities) or offering subsidies (in case of positive externalities).

13