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Chapter 12 The Partial Equilibrium Competitive Model Nicholson and Snyder, Copyright ©2008 by Thomson South-Western. All rights reserved. Market Demand • Assume that there are only two goods (x and y) – An individual’s demand for x is Quantity of x demanded = x(px,py,I) – If we use i to reflect each individual in the market, then the market demand curve is n Market demand for X xi ( px , py , Ii ) i 1 Market Demand • To construct the market demand curve, pX is allowed to vary while py and the income of each individual are held constant • If each individual’s demand for x is downward sloping, the market demand curve will also be downward sloping Market Demand To derive the market demand curve, we sum the quantities demanded at every price px px Individual 1’s demand curve Individual 2’s demand curve px Market demand curve px* x1 x1* X x2 x x2* x X* x1* + x2* = X* x Shifts in the Market Demand Curve • The market demand summarizes the ceteris paribus relationship between X and px – changes in px result in movements along the curve (change in quantity demanded) – changes in other determinants of the demand for X cause the demand curve to shift to a new position (change in demand) Shifts in Market Demand • Suppose that individual 1’s demand for oranges is given by x1 = 10 – 2px + 0.1I1 + 0.5py and individual 2’s demand is x2 = 17 – px + 0.05I2 + 0.5py • The market demand curve is X = x1 + x2 = 27 – 3px + 0.1I1 + 0.05I2 + py Shifts in Market Demand • To graph the demand curve, we must assume values for py, I1, and I2 • If py = 4, I1 = 40, and I2 = 20, the market demand curve becomes X = 27 – 3px + 4 + 1 + 4 = 36 – 3px Shifts in Market Demand • If py rises to 6, the market demand curve shifts outward to X = 27 – 3px + 4 + 1 + 6 = 38 – 3px – note that X and Y are substitutes • If I1 fell to 30 while I2 rose to 30, the market demand would shift inward to X = 27 – 3px + 3 + 1.5 + 4 = 35.5 – 3px – note that X is a normal good for both buyers Generalizations • Suppose that there are n goods (xi, i = 1,n) with prices pi, i = 1,n. • Assume that there are m individuals in the economy • The j th’s demand for the i th good will depend on all prices and on Ij xij = xij(p1,…,pn, Ij) Generalizations • The market demand function for xi is the sum of each individual’s demand for that good m X i xij ( p1,..., pn , I j ) j 1 • The market demand function depends on the prices of all goods and the incomes and preferences of all buyers Elasticity of Market Demand • The price elasticity of market demand is measured by eQ,P QD (P, P ' , I ) P P QD • Market demand is characterized by whether demand is elastic (eQ,P < -1) or inelastic (0> eQ,P > -1) Elasticity of Market Demand • The cross-price elasticity of market demand is measured by eQ,P QD (P, P ' , I ) P ' P ' QD • The income elasticity of market demand is measured by eQ,I QD (P, P ' , I ) I I QD Timing of the Supply Response • In the analysis of competitive pricing, the time period under consideration is important – very short run • no supply response (quantity supplied is fixed) – short run • existing firms can alter their quantity supplied, but no new firms can enter the industry – long run • new firms may enter an industry Pricing in the Very Short Run • In the very short run (or the market period), there is no supply response to changing market conditions – price acts only as a device to ration demand • price will adjust to clear the market – the supply curve is a vertical line Pricing in the Very Short Run Price S When quantity is fixed in the very short run, price will rise from P1 to P2 when the demand rises from D to D’ P2 P1 D’ D Q* Quantity per period Short-Run Price Determination • The number of firms in an industry is fixed • These firms are able to adjust the quantity they are producing – they can do this by altering the levels of the variable inputs they employ Perfect Competition • A perfectly competitive industry is one that obeys the following assumptions: – there are a large number of firms, each producing the same homogeneous product – each firm attempts to maximize profits – each firm is a price taker • its actions have no effect on the market price – information is perfect – transactions are costless Short-Run Market Supply • The quantity of output supplied to the entire market in the short run is the sum of the quantities supplied by each firm – the amount supplied by each firm depends on price • The short-run market supply curve will be upward-sloping because each firm’s short-run supply curve has a positive slope Short-Run Market Supply Curve To derive the market supply curve, we sum the quantities supplied at every price P Firm A’s supply curve sA P P sB Firm B’s supply curve Market supply curve S P1 q1A quantity q1B quantity Q1 Quantity q1A + q1B = Q1 Short-Run Market Supply Function • The short-run market supply function shows total quantity supplied by each firm to a market n Qs (P,v ,w ) qi (P,v ,w ) i 1 • Firms are assumed to face the same market price and the same prices for inputs Short-Run Supply Elasticity • The short-run supply elasticity describes the responsiveness of quantity supplied to changes in market price eS,P % change in Q supplied QS P % change in P P QS • Because price and quantity supplied are positively related, eS,P > 0 A Short-Run Supply Function • Suppose that there are 100 identical firms each with the following short-run supply curve qi (P,v,w) = 10P/3 (i = 1,2,…,100) • This means that the market supply function is given by 100 100 10P 1000P Qs qi 3 i 1 i 1 3 A Short-Run Supply Function • In this case, computation of the elasticity of supply shows that it is unit elastic eS,P QS (P,v ,w ) P 1000 P 1 P QS 3 1000P / 3 Equilibrium Price Determination • An equilibrium price is one at which quantity demanded is equal to quantity supplied – neither suppliers nor demanders have an incentive to alter their economic decisions • An equilibrium price (P*) solves the equation: QD( P *,P ' , I ) QS( P *,v ,w ) Equilibrium Price Determination • The equilibrium price depends on many exogenous factors – changes in any of these factors will likely result in a new equilibrium price Equilibrium Price Determination The interaction between market demand and market supply determines the equilibrium price Price S P1 D Q1 Total output per period Market Reaction to a Shift in Demand If many buyers experience an increase in their demands, the market demand curve will shift to the right Price S P2 P1 D’ Equilibrium price and equilibrium quantity will both rise D Q1 Q2 Total output per period Market Reaction to a Shift in Demand If the market price rises, firms will increase their level of output Price SMC SAC This is the short-run supply response to an increase in market price P2 P1 q1 q2 Output per period Shifts in Supply and Demand Curves • Demand curves shift because – incomes change – prices of substitutes or complements change – preferences change • Supply curves shift because – input prices change – technology changes – number of producers change Shifts in Supply and Demand Curves • When either a supply curve or a demand curve shift, equilibrium price and quantity will change • The relative magnitudes of these changes depends on the shapes of the supply and demand curves Shifts in Supply Small increase in price, large drop in quantity Price Large increase in price, small drop in quantity Price S’ S’ S S P’ P P’ P D D Q’ Q Elastic Demand Q per period Q’ Q Inelastic Demand Q per period Shifts in Demand Small increase in price, large rise in quantity Large increase in price, small rise in quantity Price S Price S P’ P’ P P D’ D’ D Q Q’ Elastic Supply D Q per period Q Q’ Inelastic Supply Q per period Mathematical Model of Supply and Demand • Suppose that the demand function is represented by QD = D(P,) – is a parameter that shifts the demand curve • D/ = D can have any sign – D/P = DP < 0 Mathematical Model of Supply and Demand • The supply relationship can be shown as QS = S(P,) – is a parameter that shifts the supply curve • S/ = S can have any sign – S/P = SP > 0 • Equilibrium requires that QD = QS Mathematical Model of Supply and Demand • To analyze the comparative statics of this model, we need to use the total differentials of the supply and demand functions: dQD = DPdP + Dd dQS = SPdP + Sd • Maintenance of equilibrium requires that dQD = dQS Mathematical Model of Supply and Demand • Suppose that the demand parameter () changed while remains constant • The equilibrium condition requires that DPdP + Dd = SPdP D P SP DP • Because SP - DP > 0, P/ will have the same sign as D Mathematical Model of Supply and Demand • We can convert our analysis to elasticities eP , e P , D P P SP DP P eQ , D Q ( S P DP ) P Q eS ,P eQ ,P Equilibria with Constant Elasticity Functions • Suppose the demand for automobiles is given by QD( P , I ) 0.1P 1.2 3 I • The supply for automobiles is QS( P ,w ) 6,400Pw 0.5 Equilibria with Constant Elasticity Functions • If I = $20,000 and w = $25 11 QD( P , I ) ( 8 10 )P 1.2 QS( P ,w ) 1,280P • Equilibrium occurs where P* = 9,957 and Q* = 12,745,000 Equilibria with Constant Elasticity Functions • If I increases by 10 percent 12 QD( P , I ) ( 1.06 10 )P 1.2 QS( P ,w ) 1,280P • Equilibrium occurs where P* = 11,339 and Q* = 14,514,000 Equilibria with Constant Elasticity Functions • If instead w increases to $30 per hour 11 QD( P , I ) ( 8 10 )P 1.2 QS( P ,w ) 1,2168P • Equilibrium occurs where P* = 10,381 and Q* = 12,125,000 Long-Run Analysis • In the long run, a firm may adapt all of its inputs to fit market conditions – profit-maximization for a price-taking firm implies that price is equal to long-run MC • Firms can also enter and exit an industry – perfect competition assumes that there are no special costs of entering or exiting an industry Long-Run Analysis • New firms will be lured into any market where economic profits are greater than zero – the short-run industry supply curve will shift outward – market price and profits will fall – the process will continue until economic profits are zero Long-Run Analysis • Existing firms will leave any industry where economic profits are negative – the short-run industry supply curve will shift inward – market price will rise and losses will fall – the process will continue until economic profits are zero Long-Run Competitive Equilibrium • A perfectly competitive industry is in long-run equilibrium if there are no incentives for profit-maximizing firms to enter or to leave the industry – this will occur when the number of firms is such that P = MC = AC and each firm operates at minimum AC Long-Run Competitive Equilibrium • We will assume that all firms in an industry have identical cost curves – no firm controls any special resources or technology • The equilibrium long-run position requires that each firm earn zero economic profit Long-Run Equilibrium: Constant-Cost Case • Assume that the entry of new firms in an industry has no effect on the cost of inputs – no matter how many firms enter or leave an industry, a firm’s cost curves will remain unchanged • This is referred to as a constant-cost industry Long-Run Equilibrium: Constant-Cost Case This is a long-run equilibrium for this industry P = MC = AC Price SMC Price MC S AC P1 D q1 A Typical Firm Quantity per period Q1 Total Market Quantity per period Long-Run Equilibrium: Constant-Cost Case Suppose that market demand rises to D’ Price SMC Price MC Market price rises to P2 S AC P2 P1 D’ D q1 A Typical Firm Quantity per period Q1 Q2 Total Market Quantity per period Long-Run Equilibrium: Constant-Cost Case In the short run, each firm increases output to q2 Price SMC Price MC Economic profit > 0 S AC P2 P1 D’ D q1 q2 A Typical Firm Quantity per period Q1 Q2 Total Market Quantity per period Long-Run Equilibrium: Constant-Cost Case In the long run, new firms will enter the industry Economic profit will return to 0 Price SMC MC Price S S’ AC P1 D’ D q1 A Typical Firm Quantity per period Q1 Q3 Total Market Quantity per period Long-Run Equilibrium: Constant-Cost Case The long-run supply curve will be a horizontal line (infinitely elastic) at p1 Price SMC Price MC S S’ AC LS P1 D’ D q1 A Typical Firm Quantity per period Q1 Q3 Total Market Quantity per period Infinitely Elastic Long-Run Supply • Suppose that the total cost curve for a typical firm in the bicycle industry is C(q) = q3 – 20q2 + 100q + 8,000 • Demand for bicycles is given by QD = 2,500 – 3P Infinitely Elastic Long-Run Supply • To find long-run equilibrium, we must find the minimum point on the typical firm’s average cost curve – where AC = MC AC = q2 – 20q + 100 + 8,000/q MC = 3q2 – 40q + 100 – this occurs where q = 20 • If q = 20, AC = MC = $500 – this will be the long-run equilibrium price Shape of the Long-Run Supply Curve • The zero-profit condition is the factor that determines the shape of the long-run cost curve – if average costs are constant as firms enter, long-run supply will be horizontal – if average costs rise as firms enter, long-run supply will have an upward slope – if average costs fall as firms enter, long-run supply will be negatively sloped Long-Run Equilibrium: Increasing-Cost Industry • The entry of new firms may cause the average costs of all firms to rise – prices of scarce inputs may rise – new firms may impose “external” costs on existing firms – new firms may increase the demand for tax-financed services Long-Run Equilibrium: Increasing-Cost Industry Suppose that we are in long-run equilibrium in this industry Price SMC P = MC = AC MC Price S AC P1 D q1 A Typical Firm (before entry) Quantity per period Q1 Total Market Quantity per period Long-Run Equilibrium: Increasing-Cost Industry Suppose that market demand rises to D’ Market price rises to P2 and firms increase output to q2 Price SMC MC Price S AC P2 P1 D’ D q1 q2 Quantity A Typical Firm (before entry) per period Q1 Q2 Total Market Quantity per period Long-Run Equilibrium: Increasing-Cost Industry Positive profits attract new firms and supply shifts out Entry of firms causes costs for each firm to rise SMC’ Price MC’ Price S AC’ S’ P3 P1 D’ D q3 A Typical Firm (after entry) Quantity per period Q1 Q3 Total Market Quantity per period Long-Run Equilibrium: Increasing-Cost Industry The long-run supply curve will be upward-sloping SMC’ Price MC’ Price S AC’ S’ LS p3 p1 D’ D q3 Quantity A Typical Firm (after entry) per period Q1 Q3 Total Market Quantity per period Long-Run Equilibrium: Decreasing-Cost Industry • The entry of new firms may cause the average costs of all firms to fall – new firms may attract a larger pool of trained labor – entry of new firms may provide a “critical mass” of industrialization • permits the development of more efficient transportation and communications networks Long-Run Equilibrium: Decreasing-Cost Case Suppose that we are in long-run equilibrium in this industry Price SMC P = MC = AC Price MC S AC P1 D q1 Quantity A Typical Firm (before entry) per period Q1 Total Market Quantity per period Long-Run Equilibrium: Decreasing-Cost Industry Suppose that market demand rises to D’ Market price rises to P2 and firms increase output to q2 Price SMC MC Price S AC P2 P1 D q1 q2 Quantity A Typical Firm (before entry) per period Q1 Q2 Total Market D’ Quantity per period Long-Run Equilibrium: Decreasing-Cost Industry Positive profits attract new firms and supply shifts out Entry of firms causes costs for each firm to fall Price SMC’ Price MC’ S S’ AC’ P1 P3 D’ D q1 q3 A Typical Firm (before entry) Quantity per period Q1 Total Market Q3 Quantity per period Long-Run Equilibrium: Decreasing-Cost Industry The long-run industry supply curve will be downward-sloping Price Price SMC’ S MC’ S’ AC’ P1 P3 D q1 q3 Quantity A Typical Firm (before entry) per period Q1 Total Market D’ Q3 LS Quantity per period Classification of Long-Run Supply Curves • Constant Cost – entry does not affect input costs – the long-run supply curve is horizontal at the long-run equilibrium price • Increasing Cost – entry increases inputs costs – the long-run supply curve is positively sloped Classification of Long-Run Supply Curves • Decreasing Cost – entry reduces input costs – the long-run supply curve is negatively sloped Long-Run Elasticity of Supply • The long-run elasticity of supply (eLS,P) records the proportionate change in longrun industry output to a proportionate change in price eLS ,P % change in Q QLS P % change in P P QLS • eLS,P can be positive or negative – the sign depends on whether the industry exhibits increasing or decreasing costs Comparative Statics Analysis • Comparative statics analysis of long-run equilibria can be conducted using estimates of long-run elasticities of supply and demand • In the long run, the number of firms in the industry will vary from one long-run equilibrium to another Comparative Statics Analysis • Assume that we are examining a constant-cost industry • Suppose that the initial long-run equilibrium industry output is Q0 and the typical firm’s output is q* (where AC is minimized) • The equilibrium number of firms in the industry (n0) is Q0/q* Comparative Statics Analysis • A shift in demand that changes the equilibrium industry output to Q1 will change the equilibrium number of firms to n1 = Q1/q* • The change in the number of firms is Q1 Q0 n1 n0 q* – determined by demand shift and the optimal output level for the typical firm Comparative Statics Analysis • The effect of a change in input prices is more complicated – we need to know how much minimum average cost is affected – we need to know how an increase in longrun equilibrium price will affect quantity demanded Comparative Statics Analysis • The optimal level of output for each firm may also be affected • Therefore, the change in the number of firms becomes Q1 Q0 n1 n0 * * q1 q0 Rising Input Costs and Industry Structure • Suppose that the total cost curve for a typical firm in the bicycle industry is C(q) = q3 – 20q2 + 100q + 8,000 and then rises to C(q) = q3 – 20q2 + 100q + 11,616 • The optimal scale of each firm rises from 20 to 22 (where MC = AC) Rising Input Costs and Industry Structure • At q = 22, MC = AC = $672 so the longrun equilibrium price will be $672 • If demand can be represented by QD = 2,500 – 3P then QD = 484 • This means that the industry will have 22 firms (484 22) Producer Surplus in the Long Run • Short-run producer surplus represents the return to a firm’s owners in excess of what would be earned if output was zero – the sum of short-run profits and fixed costs Producer Surplus in the Long Run • In the long-run, all profits are zero and there are no fixed costs – owners are indifferent about whether they are in a particular market • they could earn identical returns on their investments elsewhere • Suppliers of inputs may not be indifferent about the level of production in an industry Producer Surplus in the Long Run • In the constant-cost case, input prices are assumed to be independent of the level of production – inputs can earn the same amount in alternative occupations • In the increasing-cost case, entry will bid up some input prices – suppliers of these inputs will be made better off Producer Surplus in the Long Run • Long-run producer surplus is the extra return that producers make by making transactions at the market price over and above what they would earn if nothing were produced – the area above the long-run supply curve and below the market price Ricardian Rent • Assume that there are many parcels of land on which a particular crop may be grown – the land ranges from very fertile land (low costs of production) to very poor, dry land (high costs of production) Ricardian Rent • At low prices only the best land is used • Higher prices lead to an increase in output through the use of higher-cost land – the long-run supply curve is upward-sloping because of the increased costs of using less fertile land Ricardian Rent The owners of low-cost firms will earn positive profits Price MC Price AC S P* D q* Low-Cost Firm Quantity per period Q* Total Market Quantity per period Ricardian Rent The owners of the marginal firm will earn zero profit Price Price MC AC S P* D q* Marginal Firm Quantity per period Q* Total Market Quantity per period Ricardian Rent • Firms with higher costs (than the marginal firm) will stay out of the market – would incur losses at a price of P* • Profits earned by intramarginal firms can persist in the long run – they reflect a return to a unique resource • The sum of these long-run profits constitutes long-run producer surplus Ricardian Rent Each point on the supply curve represents minimum average cost for some firm Price For each firm, P – AC represents profit per unit of output Total long-run profits can be computed by summing over all units of output S P* D Q* Total Market Quantity Ricardian Rent • The long-run profits for the low-cost firms may be reflected in the prices of the unique resources owned by those firms – the more fertile the land is, the higher its price • Thus, profits are said to be capitalized into inputs’ prices – reflect the present value of all future profits Ricardian Rent • It is the scarcity of low-cost inputs that creates the possibility of Ricardian rent • In industries with upward-sloping longrun supply curves, increases in output not only raise firms’ costs but also generate factor rents for inputs Economic Efficiency and Welfare Analysis • The area between the demand and the supply curve represents the sum of consumer and producer surplus – measures the total additional value obtained by market participants by being able to make market transactions • This area is maximized at the competitive market equilibrium Economic Efficiency and Welfare Analysis Price S Consumer surplus is the area above price and below demand P* Producer surplus is the area below price and above supply D Quantity per period Q* Economic Efficiency and Welfare Analysis Price S At output Q1, total surplus will be smaller At outputs between Q1 and Q*, demanders would value an additional unit more than it would cost suppliers to produce P* D Quantity per period Q1 Q* Economic Efficiency and Welfare Analysis • Mathematically, we wish to maximize consumer surplus + producer surplus = Q Q 0 0 [U (Q ) PQ] [PQ P (Q )dQ] U (Q ) P (Q )dQ • In long-run equilibria along the long-run supply curve, P(Q) = AC = MC Economic Efficiency and Welfare Analysis • Maximizing total surplus with respect to Q yields U’(Q) = P(Q) = AC = MC – maximization occurs where the marginal value of Q to the representative consumer is equal to market price • the market equilibrium Welfare Loss Computations • Use of consumer and producer surplus makes it possible to calculate welfare losses caused by restrictions on voluntary transactions – in the case of linear demand and supply curves, the calculation is simple because the areas of loss are often triangular Welfare Loss Computations • Suppose that the demand is given by QD = 10 - P and supply is given by QS = P - 2 • Market equilibrium occurs where P* = 6 and Q* = 4 Welfare Loss Computations • Restriction of output to Q0 = 3 would create a gap between what demanders are willing to pay (PD) and what suppliers require (PS) PD = 10 - 3 = 7 PS = 2 + 3 = 5 Welfare Loss Computations The welfare loss from restricting output to 3 is the area of a triangle Price S 7 The loss = (0.5)(2)(1) = 1 6 5 D 3 4 Quantity per period Welfare Loss Computations • The welfare loss will be shared by producers and consumers – it will depend on the price elasticity of demand and the price elasticity of supply to determine who bears the larger portion of the loss • the side of the market with the smallest price elasticity (in absolute value) Price Controls and Shortages • Sometimes governments may seek to control prices at below equilibrium levels – this will lead to a shortage • The changes in producer and consumer surplus from this policy show its impact on welfare Price Controls and Shortages Price Initially, the market is in long-run equilibrium at P1, Q1 SS LS P1 Demand increases to D’ D’ D Q1 Quantity per period Price Controls and Shortages Price SS In the short run, price rises to P2 P2 LS P3 Firms would begin to enter the industry P1 D’ The price would end up at P3 D Q1 Quantity per period Price Controls and Shortages Price Suppose that the government imposes a price ceiling at P1 SS LS P3 P1 D’ There will be a shortage equal to Q2 - Q1 D Q1 Q2 Quantity Price Controls and Shortages Price Some buyers will gain because they can purchase the good for a lower price SS LS P3 P1 D’ This gain in consumer surplus is the shaded rectangle D Q1 Q2 Quantity per period Price Controls and Shortages Price The gain to consumers is also a loss to producers who now receive a lower price SS LS P3 P1 D’ D Q1 Q2 The shaded rectangle therefore represents a pure transfer from producers to consumers No welfare loss there Quantity per period Price Controls and Shortages Price SS LS P3 P1 D’ This shaded triangle represents the value of additional consumer surplus that would have been attained without the price control D Q1 Q2 Quantity per period Price Controls and Shortages Price SS LS P3 P1 D’ This shaded triangle represents the value of additional producer surplus that would have been attained without the price control D Q1 Q2 Quantity Price Controls and Shortages Price SS LS P3 This shaded area represents the total value of mutually beneficial transactions that are prevented by the government P1 D’ D Q1 Q2 This is a measure of the pure welfare costs of this policy Quantity Disequilibrium Behavior • Assuming that observed market outcomes are generated by Q(P1) = min [QD(P1),QS(P1)], suppliers will be content with the outcome but demanders will not • This could lead to a black market Tax Incidence • To discuss the effects of a per-unit tax (t), we need to make a distinction between the price paid by buyers (PD) and the price received by sellers (PS) PD - PS = t • In terms of small price changes, we wish to examine dPD - dPS = dt Tax Incidence • Maintenance of equilibrium in the market requires dQD = dQS or DPdPD = SPdPS • Substituting, we get DPdPD = SPdPS = SP(dPD - dt) Tax Incidence • We can now solve for the effect of the tax on PD: eS dPD SP dt SP DP eS eD • Similarly, dPS DP eD dt SP DP eS eD Tax Incidence • Because eD 0 and eS 0, dPD /dt 0 and dPS /dt 0 • If demand is perfectly inelastic (eD = 0), the per-unit tax is completely paid by demanders • If demand is perfectly elastic (eD = ), the per-unit tax is completely paid by suppliers Tax Incidence • In general, the actor with the less elastic responses will experience most of the price change caused by the tax dPS / dt eD dPD / dt eS Tax Incidence Price S A per-unit tax creates a wedge between the price that buyers pay (PD) and the price that sellers receive (PS) PD P* t PS D Q** Q* Quantity per period Tax Incidence Price S Buyers incur a welfare loss equal to the shaded area PD P* But some of this loss goes to the government in the form of tax revenue PS D Q** Q* Quantity per period Tax Incidence Price S Sellers also incur a welfare loss equal to the shaded area PD But some of this loss goes to the government in the form of tax revenue P* PS D Q** Q* Quantity per period Tax Incidence Price S PD Therefore, this is the deadweight loss from the tax P* PS D Q** Q* Quantity per period Deadweight Loss and Elasticity • All nonlump-sum taxes involve deadweight losses – the size of the losses will depend on the elasticities of supply and demand • A linear approximation to the deadweight loss accompanying a small tax, dt, is given by DW = -0.5(dt)(dQ) Deadweight Loss and Elasticity • From the definition of elasticity, we know that dQ = eDdPD Q0/P0 • This implies that dQ = eD [eS /(eS - eD)] dt Q0/P0 • Substituting, we get 2 dt DW 0.5 [eD eS /( eS eD )]P0Q0 P0 Deadweight Loss and Elasticity • Deadweight losses are zero if either eD or eS are zero – the tax does not alter the quantity of the good that is traded • Deadweight losses are smaller in situations where eD or eS are small Transactions Costs • Transactions costs can also create a wedge between the price the buyer pays and the price the seller receives – real estate agent fees – broker fees for the sale of stocks • If the transactions costs are on a per-unit basis, these costs will be shared by the buyer and seller – depends on the specific elasticities involved Gains from International Trade Price S P* In the absence of international trade, the domestic equilibrium price would be P* and the domestic equilibrium quantity would be Q* D Q* Quantity per period Gains from International Trade Price S If the world price (PW) is less than the domestic price, the price will fall to PW Quantity demanded will rise to Q1 and quantity supplied will fall to Q2 P* PW D Q2 Q* Q1 imports Imports = Q1 - Q2 Quantity per period Gains from International Trade Price S Consumer surplus rises Producer surplus falls There is an unambiguous welfare gain P* PW D Q1 Q* Q2 Quantity per period Effects of a Tariff Price S Suppose that the government creates a tariff that raises the price to PR Quantity demanded falls to Q3 and quantity supplied rises to Q4 PR PW Imports are now Q3 - Q4 D Q2 Q4 Q3 Q1 imports Quantity per period Effects of a Tariff Price S Consumer surplus falls Producer surplus rises The government gets tariff revenue PR PW These two triangles represent deadweight loss D Q2 Q4 Q3 Q1 Quantity per period Quantitative Estimates of Deadweight Losses • Estimates of the sizes of the welfare loss triangle can be calculated • Because PR = (1+t)PW, the proportional change in quantity demanded is Q3 Q1 PR PW eD teD Q1 PW Quantitative Estimates of Deadweight Losses Price S The areas of these two triangles are DW1 0.5(PR PW )(Q1 Q3 ) DW1 0.5t 2eDPW Q1 PR PW DW2 0.5(PR PW )(Q4 Q2 ) D Q2 Q4 Q3 Q1 DW2 0.5t 2eS PW Q2 Quantity per period Other Trade Restrictions • A quota that limits imports to Q3 - Q4 would have effects that are similar to those for the tariff – same decline in consumer surplus – same increase in producer surplus • One big difference is that the quota does not give the government any tariff revenue – the deadweight loss will be larger Trade and Tariffs • If the market demand curve is QD = 200P-1.2 and the market supply curve is QS = 1.3P, the domestic long-run equilibrium will occur where P* = 9.87 and Q* = 12.8 Trade and Tariffs • If the world price was PW = 9, QD would be 14.3 and QS would be 11.7 – imports will be 2.6 • If the government placed a tariff of 0.5 on each unit sold, the world price will be PW = 9.5 – imports will fall to 1.0 Trade and Tariffs • The welfare effect of the tariff can be calculated DW1 = 0.5(0.5)(14.3 - 13.4) = 0.225 DW2 = 0.5(0.5)(12.4 - 11.7) = 0.175 • Thus, total deadweight loss from the tariff is 0.225 + 0.175 = 0.4 Important Points to Note: • Short-run equilibrium prices are determined by the intersection of what demanders are willing to pay (demand) and what firms are willing to produce (supply) – both demanders and suppliers act as price takers Important Points to Note: • In the long run, the number of firms may vary in response to profit opportunities – the assumption of free entry and exit implies that firms in a competitive industry will earn zero economic profits in the long run (P = AC) Important Points to Note: • The shape of the long-run supply curve depends on how entry affects input prices – in the constant-cost case, input prices do not change and the long-run supply curve is horizontal – if entry raises input costs, the long-run supply curve will have a positive slope Important Points to Note: • If shifts in long-run equilibrium affect input prices, the welfare of the suppliers of these inputs will be affected – such changes can be measured by changes in the value of long-run producer surplus Important Points to Note: • The concepts of consumer and producer surplus provide useful ways of measuring the welfare impact of economic changes – changes in consumer surplus represent changes in utility – changes in producer surplus represent changes in the monetary returns that inputs receive Important Points to Note: • The competitive model can be used to study the impact of various economic policies – it can be used to measure the transfers and welfare losses associated with price controls Important Points to Note: • The competitive model can also be applied to study taxation – the model illustrates tax incidence and the welfare losses associated with taxation – similar conclusions can be derived by using the competitive model to study transactions costs Important Points to Note: • A final, important application uses the competitive model to study international trading relationships – it can help us identify those who win and those who lose with the opening of trade – it can also be used to study the welfare implications of trade restrictions