Market Demand Market Equilibrium

The Partial Equilibrium Competitive Model Lecture 1, ECON 4240 Spring 2017

summary of Snyder et al. (2015)

University of Oslo

17.01.2017

1/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Outline

Focus: Determination of market price of 1 good, while taking the price of all other goods as "given" (= not explained) Why we need this? To study the effect of taxes and price regulations To study the effect of changes in income levels or income distribution on market prices and quantity of goods sold To think about how the gains from trade are divided between sellers and buyers (maybe to use this information to guide policies aimed at redistributing wealth among citizens?) To have a benchmark for comparison to study potential welfare losses due to lack of competition (oligopolies)

2/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium The Market Demand Curve I

As discussed in ECON 4200 (and in Part 2 of Snyder et al. (2015)), when there are two goods available (good x and good y) the individual demand function for good x is summarized as:

quantity demanded of good x by consumer i: xi (px ,py ,Ii )

where px ,py are market prices, Ii is consumer i’s monetary income If there are n consumers:

n market demand for x: X = Σi=1xi (px ,py ,Ii )

3/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium The Market Demand Curve II

Note: 1 We allow different consumers to have different preferences (how would you write the market demand if consumers had all the same preferences?) 2 We allow consumers to have different incomes (how would you write the market demand if individuals had all the same income?) 3 We do not allow the prices faced by different consumers to differ As a result of 1 and 2: this model can be used to think about how the distribution of income among consumers affects demand

4/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium The Market Demand Curve III

Market demand X is a function of 2 prices and n incomes. It is common to show graphically the relation between X and px , for given values of py and I1,..,In

Changes in px : shifts along the demand curve - changes in quantity demanded

Changes in py or some/all Ii : shifts of the curve - changes in demand

5/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium The Market Demand Curve IV

Alternative partial equilibrium model: focus on one good with price P but consider the effects on the market for that good of changes in prices of other goods (prices of all these other goods measured in vector P0) Demand for good x denoted

0 QD (P,P ,I )

where I is the income of all consumers. 0 ∂QD (P,P ,I ) P Price elasticity of market demand: eQ,P = ∂P QD 0 0 ∂QD (P,P ,I ) P Cross-price elasticity of market demand: e 0 = 0 Q,P ∂P QD 0 ∂QD (P,P ,I ) I Income elasticity of market demand: eQ,I = ∂I QD What are the effects of these elasticities on the shape of the demand curve in

the standard Q-P space? 6/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Timing of Supply Response

We look at market equilibrium 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

7/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Pricing in the Very Short Run

Very short run markets: not very common. Examples: perishable goods - tickets for a concert/game (auctions have features in common with very short run markets) Supply is a vertical line In this case the only role of price is to ration demand

8/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Pricing in the Short Run

Short run: firms can change the quantity supplied, and (for durable goods), owners of used goods can sell them

Definition In a perfectly competitive market: 1 A large number of firms, producing the same homogeneous good, 2 Each firm attempts to maximize profits, 3 Each firm is a price-taker 4 Prices are assumed to be known to all market participants 5 Transactions are costless

9/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Short Run Price Determination

Market supply curve: sum of n individual-firms supply curves:

n QS (P,v,w) = Σi=1qi (P,v,w)

v: price of capital; w: price of labor

10/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Equilibrium Price Determination

Definition An equilibrium price P∗ is one 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:

∗ 0 ∗ 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

11/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium 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 on the shape of the two curves.

12/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Mathematical Model of Market Equilibrium

Demand: QD = D(P,α). α: parameter that shifts the demand curve.

Supply: QS = S(P,β).

Equilibrium: QD = QS . This model allows to understand how elasticities of demand and supply (which can be estimated empirically) can be used to estimate/predict the effect of a change of external factors on the equilibrium price

13/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Mathematical Model of Market Equilibrium

Effect of small change in α:

∂QD ∂D(P,α) ∂P dα = dα = DP dα + Dα , ∂QS ∂S(P,β) ∂P dα = ∂α = SP ∂α ∂QD ∂QS Equilibrium requires: ∂α = ∂α Hence: ∂P = Dα ∂α SP −DP ∂P SP > 0 > DP → SP − DP > 0 → sign of ∂α = sign of Dα We can express this remark in terms of elasticities:

α ∂P α D α Dα e e = = α = q = Q,α P,α P S − D P P P e − e ∂α P P SP q − DP q S,P D,P

Look at Example 11.3

14/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Long Run Analysis

Long run: Each firm has time to change its input mix optimally: for each firm short and long run supply curve can be different (see digression on next slide) Unless profits are 0, firms enter or exit the market. Profit=0 ↔ P = AC. As in the short run, P = MC from profit maximization Definition A perfectly competitive market is in long-run equilibrium if there are no incentives for profit-maximizing firms to enter or to leave the market. This will occur when (a) the number of firms is such that P = MC = AC and (b) each firm operates at the low point of its long-run average cost curve. (b) is a consequence of (a) and of the (implicit) assumption of increasing marginal costs. 15/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Digression: Short VS Long Run Cost Curves

In the short run SOME inputs are fixed (see ch 9, from page 270) In the long run all inputs are flexible Hence: In the short run the Rate of Technical Substitution does not have to be equal to the ratio of the input prices (Fig. 9.12) The long run total cost curve is the lower than any short run total cost curve (any= for any level of the fixed input) (fig 9.13)

16/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Long Run: Constant Cost

Entry or exit of firms affect the demand for inputs, and hence can affect their price.

Simplest case: constant prices of inputs (E.g. the industry is a small fraction of the total demand of inputs)

With constant input prices, the long-run supply curve is horizontal.

17/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Long Run: Constant Cost

To understand why the long-run supply curve is horizontal: let the demand increase, then: The short-run supply is an increasing curve, so the equilibrium price increases Firms earn a positive profit In the long run, new firms enter, causing an increase in supply and a reduction in price and profit- but - by assumption - no effect on input prices Entry continues as long as firms earn positive profits, that is, as long as the price is above the original one. Note: in the short-run the supply curve is determined by the short-run marginal cost curve. In the long run, it is the low point of the long-run average cost curve that determines the supply curve 18/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Long Run: Increasing Cost Curve

Very common case: entry of new firms drives up price of inputs, hence the long-run supply curve is upward sloping In this case, if the demand increases, then: As the short-run supply is increasing, the equilibrium price increases Firms earn a positive profit In the long run, new firms enter, causing an increase in supply and a reduction in price and profit, and an increase in input prices Entry continues as long as firms earn positive profits. The new long run equilibrium will have: (a) a higher price of the good, (b) more firms in the market and (c) a higher price of input (note (a) increases individual firms’ profits, while (c) decreases them, in the long run equilibrium (a) and (c) compensate each other) 19/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Classification of Long Run Supply Curves

To summarize, an industry supply curve exhibits one of three shapes. Constant costs: entry does not affect input costs; the long-run supply curve is horizontal at the long-run equilibrium price Increasing Costs: Entry increases input costs; the long run supply curve is positively sloped Decreasing Costs: Entry reduces input costs; the long run supply curve is negatively sloped Examples of decreasing costs: entry of new firms allows to reach a "critical size" of the industry sufficient to finance infrastructure that enhances productivity (either with money from the firms, or with public funding)

20/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Producer Surplus in the Long Run

In the short run, producer surplus represents the return to a firm’s owners in excess of what would be earned if the output were 0. Producer surplus = sum of short-run profits + short-run fixed-costs. In the long-run: fixed-costs=0, profits=0, firm owners are indifferent to be in an industry or doing other economic activities In the long-run , sellers of inputs are NOT indifferent to the level of production in an industry. With increasing long-run supply curve, the producer surplus does not go to firm owners: it goes to input sellers. Graphically, the producer surplus in the ling run can be found in the same way as the producer surplus in the short run 21/22 summary of Snyder et al. (2015) Partial Equilibrium Market Demand Market Equilibrium Limits of Partial Equilibrium Analysis

A partial equilibrium analysis misses some effects of changes in technologies/preferences, for example: If overall income or the distribution of income changes, then demand for substitutes and complements should change, and with it the price of substitutes/complements, which in turn affects the demand of the good considered If supply shifts because of a change in technology the demand for inputs should change, and with it the price of inputs, which in turn affect supply

22/22 summary of Snyder et al. (2015) Partial Equilibrium