Partial Equilibrium Competitive Model Lecture 1, ECON 4240 Spring 2017

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Partial Equilibrium Competitive Model Lecture 1, ECON 4240 Spring 2017 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;a). a: parameter that shifts the demand curve. Supply: QS = S(P;b). 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 a: ¶QD ¶D(P;a) ¶P da = da = DP da + Da , ¶QS ¶S(P;b) ¶P da = ¶a = SP ¶a ¶QD ¶QS Equilibrium requires: ¶a = ¶a Hence: ¶P = Da ¶a SP −DP ¶P SP > 0 > DP ! SP − DP > 0 ! sign of ¶a = sign of Da We can express this remark in terms of elasticities: a ¶P a D a Da e e = = a = q = Q;a P;a P S − D P P P e − e ¶a 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.
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