6 Competitive equilibrium: Introduction

Transcription

1 6 Competitive equilibrium: Introduction 6.1 Assumptions of perfect competition Assumptions. Perfect competition will always mean that 1. Goods are private and thus ownership can and is enforced (goods like corn but not national defense). 2. Goods are homogeneous (like corn, but not necessarily cars) 3. Goods are traded on common markets and prices are known. There is a single price for a given good - law of one price. No transaction costs like search cost, legal fees, transportation etc. 4. No market power (such as monopoly, oligopoly or cartel); we say that all agents are price-takers. 5. No externalities (like pollution, congestion, or making discoveries that benefit others) 6. No asymmetric information (i.e. qualities and abilities are known etc.) 7. Equal access to resources and markets, at least in the long-run. Consequently, entry to an industry and exit from it is free in the long-run. Assumptions made below for simplicity: all firms are identical and all input prices and technology are constant, even if the entire industry expands or contracts. Note that: Strictly speaking I do not assume that there are many firms and individuals. But since many assumptions above are justified only if there are many agents, we may as well make that de facto assumption (some books start with this assumption and derive the above as consequences). 47

2 6 Competitive equilibrium: Introduction Optimal behavior Price, p Quantity demanded D(p), quantity supplied S(p) Market clearing Figure 6.1: Price becomes endogenous We do not automatically assume that entry to an industry and exit from it is free in the short-run. In our presentation, we will assume free entry/exit in the long-run, but not in the short-run. Relaxing some of these assumptions lead to a market that looks like competitive market and thus some of our analysis below can be applied to an extent (say, if externalities exist or there is no free entry). We could call it a competitive market, but not perfectly competitive. Relaxing other assumptions may trip the logic of competition completely, so that our model below is useless we would need a different approach (say, when goods are public or firms are not price takers). 6.2 Definition of competitive equilibrium So far we proposed a theory of individual decision making. The society, if it existed at all, was something outside, affecting the decision maker, like weather, earthquakes or meteorites. We did not investigate how individual actions affect the society back. This will change now. That is why we call this part of the module social interactions. We showed that an external factor, e.g. the price of corn, affects buying and selling intentions of corn consumers and producers. We will now hypothesize that causality also goes in the other direction: collective behavior affects the price. This new relationship is symbolized by the lower arrow on Fig. 6.1 To investigate how the price is determined, draw supply and demand on one picture, like Fig. 6.2 If price is, say, 10 then quantity demanded is much larger than quantity sup- 48

3 6.2 Definition of competitive equilibrium Figure 6.2: Competitive equilibrium plied. There is excess demand. Imagine a queue of potential buyers chasing sellers. We expect that buyers bid up price, i.e. this price cannot be a part of equilibrium. If price is 13 then there is excess supply, sellers chase few buyers, and price is pushed down. If price is 12, then quantity demanded is equal to quantity supplied. Neither sellers nor buyers have an advantage; there is no pressure on price. Thus, in a competitive equilibrium, optimal behavior of consumers (demand) and optimal behavior of firms (supply) interact in a process determining the prices which is called market clearing. Competitive equilibrium is a price and quantity such that: 1. Given prices, every decision maker is behaving optimally and 2. Prices are such that markets clear (quantity supplied is equal quantity demanded) Remark: Remark: The story motivating this definition refers to a dynamic process of price adjustments and bargaining, but strictly speaking the concept is static (price & quantity such that...). Price is endogenous (for the first time) but it is not a decision variable (i.e. nobody actually selects it) Types There are many versions of competitive equilibrium, e.g. 49

4 6 Competitive equilibrium: Introduction 1. Long-run versus short-run. In our presentation below the difference is the following: a) In the long-run all inputs can be changed. In the short-run, some may be fixed. b) In long-run, firms can enter and exit from the market. In the short-run entry/exit is not possible. 2. Partial equilibrium versus general equilibrium. a) Partial equilibrium examine one market in isolation if it affects and is affected by other markets in a negligible way. b) General equilibrium if interactions between markets are non-negligible then one has to join a few partial equilibrium models together to capture these cross-market effects. Microeconomics versus macroeconomics traditional and contemporary sense. 6.3 Why we study competitive equilibria? For the same reason as any other type of equilibrium. Equilibrium is our prediction as to what will happen. Two types of questions are usually asked: 1. How does the equilibrium prediction change when exogenous parameters change? This is a positive question that leads us to a comparative statics exercises. Comparative statics is a technique of a theoretical analysis: calculate an equilibrium prediction for one set of exogenous parameters (one static situation), then calculate another one for another set of parameters (another static situation), then interpret the difference as the effect of the change of those exogenous parameters (compare two statics situations). 2. What are the welfare properties of equilibria; are outcomes good and can they be imporved? This is a normative question. Right now we focus on positive questions. 6.4 Some examples Simple comparative statics Suppose the market demand is D (p) = Y 10p (if income of the consumers is some Y ) and the market supply is S (p) =1+2p. Suppose that income happens 50

5 6.4 Some examples p Supply w/ tax p c tax Supply p s Demand Q Figure 6.3: Unit tax paid by producers to be Y = 21. We are looking for two objects p e,q e that characterize competitive equilibrium. Solution: Market clearing condition tells us that quantity demanded and quantity supplied are equal D (p) =S (p). If income is Y = 21, then we conclude that price that clears the market is p e = 10 and the quantity traded is Q e = S (p e )=D (p e )= 21. What happens if income goes up to Y =33? Unit tax Suppose the government imposes a tax of t pounds per unit of the product. The tax is paid by the producers. This essentially ads t to all average and marginal taxes, thus shifting them upward by t. Thus the supply function shifts upwards by t precisely. Demand is not affected. Changes of the equilibrium are: 1. The market price consumers pay, p c, is higher. The price suppliers get, p s,is lower, the difference being the tax t = p c p s. The original no tax price is in between, p s p t=0 p d. Read at home about tax incidence. 2. Quantity traded is lower, but how much depends on the shape of demand and supply curves. Notice, that if the consumers pay the unit tax, then nothing really changes Price control Consider housing market represented on Figure 6.4. If market is unregulated, then r 0 is equilibrium rent and q 0 is the quantity of flats rented in equilibrium. Suppose that 51

6 6 Competitive equilibrium: Introduction Figure 6.4: Rent control Figure 6.5: Shape of behavioral functions the gov introduces rent control: the maximum rent is r 1. Under this regulation the rent would like to go above r 1 to eliminate the excess demand, but it cannot. Excess demand of q 1 q 2 is a permanent feature on this market (if black market can be eliminated). However, the actual drop in number flats rented is smaller, q 0 q Elasticity Suppose that the army builds a new base in a town. Hundreds of new families move in. This shock is depicted on Fig 6.5 as a demand shift. 1. Short-run: it is impossible to add new flats and houses right away (no capital change); supply is fixed at q 0, and initial rent is r 0. Higher demand changes only prices as shown on the left panel on Figure

7 6.5 Elasticity Figure 6.6: Elasticity 2. Long-run: this is a town where land and permits for new developments are waiting for investors, so any number of new flats can and will be built as long as the rent just covers costs equal r 0. Higher demand triggers more investments only quantity changes as shown on the right panel. Conclusion: the same change (the army moves in) can have different effects depending on the shape of the demand and supply curves (supply in this case) Definition It is important to know how much quantity responds to a change of price for both demand and supply. Thus we need a measure of responsiveness of demand and supply. Consider Figure 6.6. The slope of the (inverse of) demand could be one measure, Δq/Δp. But much better measure is price elasticity of demand the percentage change of quantity demanded related to the percentage change of price, ɛ = %Δq %Δp = Δq/q Δp/p = Δq/Δp q/p slope of the tangent = slope of the secant (of the inverse) Example: suppose that if the price goes up from 1000 to 1010, then the quantity demanded falls from 50 to Then %Δp = 10/1000 = 1%, while %Δq = 2.5/50 = 5%. Therefore, the elasticity is 5%/1% = 5. Observation: elasticity has no units, as opposed to slope. Hence, it is irrelevant whether one uses versus, or liters versus pints (which is not the case for the slope). 53

8 6 Competitive equilibrium: Introduction Figure 6.7: Expenditure Perfectly elastic demand ɛ =, Elastic demand ɛ< 1, Unit elasticity demand ɛ = 1, Inelastic demand ɛ> 1, Perfectly inelastic ɛ =0. Elasticity can be defined for any behavioral function Tax incidence and elasticity How does it depend on price elasticity of demand/supply? (Read at home) Expenditures/Revenue and elasticity Total consumers expenditure (and firms revenue) is R = pq. If the price goes up, then there are two offsetting effects, p and q. Fact: if demand is inelastic ɛ> 1 then total R goes up (as price increases), otherwise it goes down. Graphically, R is the shaded rectangle on Figure