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Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Equilibrium, Welfare & Information

ECON 4240, Spring 2018 Piacquadio & Traeger

University of Oslo

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Content Part I: Christian Traeger

PART I: Equilibrium & Welfare

• 1. Partial Equilibrium

◮ Focus on one market ◮ E.g. how tax affects a market

• 2. General Equilibrium

◮ Feedback between different markets ◮ Welfare theorems on how the markets “perform”

• 3. Imperfect Competition

◮ How do firms really compete in many markets ◮ E.g. Bertrand/Cournot have very different implications

• 4. Externalities & Public Goods

◮ Market Failures & Policy fixes ◮ E.g. Pigovian Taxation, Voting

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Content Part II: Paolo Piacquadio

PART II: Welfare & Information

• 1. Introduction to asymmetric information

◮ a simple approach ◮ the contract theoretic approach

• 2. Adverse Selection

◮ example 1: the market for lemons (Akerlof, 1970) ◮ example 2: life insurance (health conditions)

• 3. Moral Hazard

◮ example 1: a university hiring a researcher ◮ example 2: life insurance (health behavior)

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Organizational Items

Lecture Schedule: online here General: Thursdays 10:15-12:00 in Auditorium 5 Exceptions: Monday 14:15-16:00 in Auditorium 1

• n Feb 5, March 19, Apr 9 [maybe also moving March 8]

Seminar Instructor: Vegard Wiborg Seminar Timing: 2 options, Wednesday or Thursday, schedule Term Paper 1st attempt: out: March 15 in: March 19 Term Paper 2nd attempt: out: April 3 in: April 6 Exam: May 11 at 9:00 AM (3 hours) in Sal 4D Silurveien 2 Traeger’s office hours (room 1111): Thursdays 1-2pm (1st half of lecture) or by appointment Prerequisite: Econ 3200/4200 and 3120/4120 (Math 2) Disclaimer: check online for updates

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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The Partial Equilibrium Competitive Model

Lecture 1, ECON 4240 Spring 2018 Snyder et al. (2015) chapter 11

University of Oslo

18.01.2018

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Outline

Focus:

◮ Determine the market price of one good,

taking price of other goods as given

◮ What’s the use of such a model?

◮ To study the effect of taxes and price regulations ◮ To study the effect of changes in income levels

• n market prices and quantity of goods sold

◮ To think about how the gains from trade are divided between

sellers and buyers (guide redistribution policy?)

◮ To have a benchmark for later studying potential welfare losses

from the lack of competition (oligopolies)

◮ ... and much more...

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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The Market Demand Curve I

◮ ECON 4200 (see Part 2 of Snyder et al. (2015)):

Let there be two goods available (good x and good y). The individual demand function for good x xi(px,py,Ii) characterizes the quantity demanded of good x by consumer i as a function of market prices px,py and consumer i’s monetary income Ii

◮ If there are n consumers:

market demand for x: X =

n

∑

i=1

xi(px,py,Ii)

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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The Market Demand Curve II

◮ Note:

• 1. We allow different consumers to have different preferences

(how would you write market demand if consumers had same preferences?)

• 2. We allow consumers to have different incomes

(how would you write market demand if individuals had same income?)

• 3. We do not allow the prices faced by different consumers to

differ

As a result of 1 and 2: this partial equilibrium model can analyze how distribution of income among consumers affects demand

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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The Market Demand Curve III

◮ Market demand X is a function of 2 prices and n incomes.

It is common to graph the relation between X and px, for given values of py and I1,..,In

◮ Changes in px: moving along the curve

• changes in quantity demanded

◮ Changes in py or some/all Ii: shifting the curve

• changes in demand

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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The Market Demand Curve IV

From now on let’s denote

◮ demand for good x by QD ◮ price of good x by P, price of other good(s) by P′ (possibly

vector) QD(P,P′,I) where I is the aggregate income of all consumers. (Income distribution matters, so implicit assumptions taken) Alternative partial equilibrium model 1:

◮ Focus on a single good’s response to another good’s price. ◮ Then we can graph x over P′.

Alternative partial equilibrium model 2:

◮ Focus on a single good’s response to aggregate income. ◮ Then we can graph x over I.

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Market Demand and Elasticities

◮ Demand is QD(P,P′,I) with

◮ P price of demanded good, ◮ P′ price of other good ◮ I aggregate income

We introduce three convenient elasticities characterizing demand:

◮ Price elasticity of market demand: eQ,P = ∂QD(P,P′,I) ∂P P QD ◮ Cross-price elasticity of market demand: eQ,P′ = ∂QD(P,P′,I) ∂P′ P′ QD ◮ Income elasticity of market demand: eQ,I = ∂QD(P,P′,I) ∂I I QD

What are the effects of these elasticities on the shape of the demand curve in the standard Q-P space?

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Supply: The Timing of Supply Response

We analyze market equilibria at 3 different time horizons. The time horizon determines the supply response to changing demand conditions:

◮ Very short run: Quantity supplied is fixed ◮ Short run: Number of firms in the industry is fixed,

but the quantity supplied by each firm, and hence the overall quantity supplied, can vary

◮ Long run: Firms can enter or exit the market

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Pricing in the Very Short Run

Very short run markets:

◮ Supply is a vertical line ◮ In this case the only role of price is to ration demand ◮ not very common. Examples:

◮ perishable goods ◮ tickets for a concert/game ◮ carbondioxide permits in the EUETS

◮ often auctions are used in such settings

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Competitive Markets

For now we deal with competitive markets

Definition 1

A perfectly competitive market obeys the following assumptions

• 1. A large number of firms produces the same homogeneous

good,

• 2. Each firm attempts to maximize profits,
• 3. Each firm is a price-taker

(it assumes that own actions don’t affect market price)

• 4. Prices are assumed to be known to all market participants

(perfect information)

• 5. Transactions are costless
• 6. Analogous assumptions 1-3 for buyers

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Short Run Price Determination

Market supply curve: sum of n individual-firms supply curves: QS(P,v,w) =

n

∑

i=1

qi(P,v,w) v: price of capital; w: price of labor Short-run supply elasticity: eS,P = ∂QS(P,v,w)

∂P P QS

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Equilibrium Price Determination

Definition 2

An equilibrium price P∗ is a price at which quantity demanded is equal to quantity supplied. At such price, neither consumers nor suppliers have an incentive to alter their economic decisions. The equilibrium price solves: QD(P∗,P′,I) = QS(P∗,v,w) In the short run the price has two roles: 1) a way to ration demand 2) a signal to producers informing them of how much to produce The equilbrium price changes with the given parameters P′,I,v,w.

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Shifts in Demand and Supply Curves

Demand Curve can shift as a result of changes in:

◮ income, ◮ price of substitutes or complements, ◮ preferences

Supply Curve can shift as a result of changes in:

◮ input prices, ◮ number of producers, ◮ technologies

The effect of a shift in the demand or supply curve on P∗ depends

• n the shape of the two curves. (see blackboard)

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Mathematical Model of Market Equilibrium

◮ Demand: QD = D(P,α)

where α is a shift-parameter, e.g., income

◮ Supply: QS = S(P,β)

where β is a shift-parameter, e.g., price of labor

◮ Equilibrium: QD = QS.

We will analyze how empirical estimates of the elasticities of demand and supply can help predicting the equilibrium price response of a change in, e.g., income (α).

Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring 2018.

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Mathematical Model of Market Equilibrium

Effect of small change in α:

◮ dQD dα = dD(P,α) dα

= DP dP

dα +Dα, ◮ dQS dα = dS(P,β) dα

= SP dP

dα ◮ Equilibrium requires: dQD dα = dQS dα ◮ Hence: dP dα = Dα SP−DP ◮ SP > 0 > DP ⇒ SP −DP > 0 ⇒ sign of dP dα = sign of Dα ◮ We can express this remark in terms of elasticities:

eP,α ≡ dP dα α P = Dα SP −DP α P = Dα α

Q

SP P

Q −DP P Q

= eQ,α eS,P −eQ,P (following the book with “Q” for demand elasticity and “S” for supply)

◮ Look at equation (11.31) & Example 11.3