Chapter Two Supply and Demand 2007 Pearson Addison-Wesley. All rights reserved.22 Supply and Demand In this chapter, we examine six main topics. Demand Supply Market Equilibrium Shocking the Equilibrium: Comparative Statics Elasticities Effects of Government Interventions: Effects of a Sales Tax When to use the supply-and-demand model 2007 Pearson Addison-Wesley. All rights reserved.23 Demand Potential consumers decide how much of a good or service to buy on the basis of its price and many other factors, including their own tastes, information, prices of other goods, incomes, and government actions. 2007 Pearson Addison-Wesley. All rights reserved.24 The Demand Curve Quantity demanded The amount of a good that consumers are willing to buy at a given price, holding constant the other factors that influence purchases Demand curve The quantity demanded at each possible price, holding constant the other factors that influence purchases 2007 Pearson Addison-Wesley. All rights reserved.25 Figure 2.1 A Demand Curve Demand curve for pork, D Q, Million kg of pork per year 2007 Pearson Addison-Wesley. All rights reserved.26 The Demand Curve One of the most important things to know about a graph of a demand curve is what is not shown. All relevant economic variables that are not explicitly shown on the demand curve graph tastes, information, prices of other goods (such as beef and chicken), income of consumers, and so on are hold constant. 2007 Pearson Addison-Wesley. All rights reserved.27 Effect of Prices on the Quantity Demanded Many economists claim that the most important empirical finding in economics is the Law of Demand: Consumers demand more of a good the lower its price, holding constant tastes, the prices of other goods, and other factors that influence the amount they consume. According to the Law of Demand, demand curves slope downward, as in Figure 2.1. 2007 Pearson Addison-Wesley. All rights reserved.28 Effect of Other Factors on Demand Economists use a simpler approach to show the effect on demand of a change in a factor that affects demand other than the price of the good. A change in any factor other than price of the good itself causes a shift of the demand curve rather than a movement along the demand curve. 2007 Pearson Addison-Wesley. All rights reserved.29 Figure 2.2 A Shift of A Demand Curve Effect of a 60 increase in the price of beef D 1 D Q, Million kg of pork per year 2007 Pearson Addison-Wesley. All rights reserved.210 The Demand Function In addition to drawing the demand curve, you can write it as a mathematical relationship called the demand function. The processed pork demand function is Q D (p, p b, p c, Y), (2.1) where Q is the quantity of pork demanded, p is the price of pork, p b is the price of beef, p c is the price of chicken, and Y is the income of consumers. 2007 Pearson Addison-Wesley. All rights reserved.211 Summing Demand Curves We can use the demand functions to determine the total demand of several consumers. Suppose that the demand function for Consumer 1 is Q 1 D 1 (p) and the demand function for Consumer 2 is Q 2 D 2 (p) At price p, Consumer 1 demand Q 1 units, Consumer 2 demands Q 2 units, and the total demand of both consumers is the sum of the quantities each demands separately: Q Q 1 Q 2 D 1 (p) D 2 (p) We can generalize this approach to look at the total demand for three or more consumers. 2007 Pearson Addison-Wesley. All rights reserved.212 Q s = 10 Q = 21.5 Q, Broadband access capacity in millions of Kbps Large firms demand Small firms demand Total demand Q l = Application: Aggregating the Demand for Broadband Service 2007 Pearson Addison-Wesley. All rights reserved.213 Supply Firms determine how much of a good to supply on the basis of the price of that good and other factors, including the costs of production and government rules and regulations. Usually, we expect firms to supply more at a higher price. 2007 Pearson Addison-Wesley. All rights reserved.214 The Supply Curve Quantity supplied The amount of a good that firms want to sell at a given price, holding constant other factors that influence firms supply decisions, such as costs and government actions Supply curve The quantity supplied at each possible price, holding constant the other factors that influence firms supply decisions 2007 Pearson Addison-Wesley. All rights reserved.215 Figure 2.3 A Supply Curve Supply curve, S Q, Million kg of pork per year 2007 Pearson Addison-Wesley. All rights reserved.216 Effect of Price on Supply The supply curve for pork is upward sloping. As the price of pork increases, firms supply more. An increase in the price of pork causes a movement along the supply curve, resulting in more pork being supplied. 2007 Pearson Addison-Wesley. All rights reserved.217 Effect of Other Variable on Supply A change in a variable other than the price of pork causes the entire supply curve to shift. It is important to distinguish between a movement along a supply curve and a shift of the supply curve. 2007 Pearson Addison-Wesley. All rights reserved.218 Figure 2.4 A Shift of a Supply Curve Effect of a 25 increase in the price of hogs S 1 S Q, Million kg of pork per year 2007 Pearson Addison-Wesley. All rights reserved.219 The Supply Function We can write the relationship between the quantity supplied and price and other factors as a mathematical relationship called the supply function. Written generally, the processed pork supply function is Q S (p, p h ) (2.5) where Q is the quantity of processed pork supplied, p is the price of processed pork, and p h is the price of a hog. 2007 Pearson Addison-Wesley. All rights reserved.220 Summing Supply Curves The total supply curve shows the total quantity produced by all suppliers at each possible price. For example, the total supply of rice in Japan is the sum of the domestic and foreign supply curves of rice. 2007 Pearson Addison-Wesley. All rights reserved.221 Figure 2.5 Total Supply: The Sum of Domestic and Foreign Supply Q d * S d S f (ban) Q f * Q = Q d * Q * = Q d * + Q f * Q d, Tons per year Q f Q (a) Japanese Domestic Supply(b) Foreign Supply(c) Total Supply p * p * p * S (ban) S (no ban) S f p p p 2007 Pearson Addison-Wesley. All rights reserved.222 Market Equilibrium When all traders are able to buy or sell as much as they want, we say that the market is in equilibrium: a situation in which no participant wants to change its behavior. A price at which consumers can buy as much as they want and sellers can sell as much as they want is called an equilibrium price. The quantity that is bought and sold at the equilibrium price is called equilibrium quantity. 2007 Pearson Addison-Wesley. All rights reserved.223 Figure 2.6 Market Equilibrium D S e Q, Million kg of pork per year Excess supply = 39 Excess demand = 39 2007 Pearson Addison-Wesley. All rights reserved.224 Using Math to Determine the Equilibrium We use the supply and demand functions to solve for the equilibrium price at which the quantity demanded equals supplied (the equilibrium quantity). The demand function shows the relationship between the quantity demanded, Q d, and the price: Q d 286 20p The supply function tells us the relationship between the quantity supplied, Qs, and the price: Q s 88 40p We want to find the p at which Q d Q s Q, the equilibrium quantity. 2007 Pearson Addison-Wesley. All rights reserved.225 Forces That Drive the Market to Equilibrium A market equilibrium occurs without any explicit coordination between consumers and firms. In a competitive market such as that for agricultural goods, millions of consumers and thousands of firms make their buying and selling decisions independently. Yet each firm can sell as much as it wants; each consumer can buy as much as he or she wants. It is as though an unseen market force, like an invisible hand, directs people to coordinate their activities to achieve a market equilibrium. 2007 Pearson Addison-Wesley. All rights reserved.226 Forces That Drive the Market to Equilibrium Excess demand The amount by which the quantity demanded exceeds the quantity supplied at a specified price Excess supply The amount by which the quantity supplied is greater than the quantity demanded at a specified price 2007 Pearson Addison-Wesley. All rights reserved.227 Forces That Drive the Market to Equilibrium At any price other than the equilibrium price, either consumers or suppliers are unable to trade as much as they want. These disappointed people act to change the price, driving the price to the equilibrium level. 2007 Pearson Addison-Wesley. All rights reserved.228 Shocking the Equilibrium: Comparative Statics The equilibrium changes only if a shock occurs that shifts the demand curve or the supply curve. These curves shift if one of the variables we were holding constant changes. 2007 Pearson Addison-Wesley. All rights reserved.229 Figure 2.7 Effects of a Shift of the Demand Curve D 1 D 2 S 1 S 2 S Q, Million kg of pork per year Excess demand = 12 Q, Million kg of pork per year e 2 e 1 e 1 e 2 D (a) Effect of a 60 Increase in the Price of Beef(b) Effect of a 25 Increase in the Price of Hogs Excess demand = 15 2007 Pearson Addison-Wesley. All rights reserved.230 How Shapes of Demand and Supply Curves Matter The shapes of the demand and supply curves determine by how much a shock affects the equilibrium price and quantity. A supply shock would have different effects if the demand curve had a different shape. 2007 Pearson Addison-Wesley. All rights reserved.231 Figure 2.8 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve (a)(b)(c) Q, Million kg of pork per year S 1 D 1 S 2 e 1 e Q, Million kg of pork per year S 1 S 2 D 2 e 1 e Q, Million kg of pork per year 3.30 S 1 S 2 D 3 e 1 e 2 2007 Pearson Addison-Wesley. All rights reserved.232 Price Elasticity of Demand Elasticity the percentage change in a variable in response to a given percentage change in another variable 2007 Pearson Addison-Wesley. All rights reserved.233 Price Elasticity of Demand The price elasticity of demand (or simply elasticity of demand) is the percentage change in the quantity demanded,, in response to a given percentage change in the price,, at a particular point on the demand curve. The price elasticity of demand (represented by , the Greek letter epsilon) is where the symbol (the Greek letter delta) indicates a change. 2007 Pearson Addison-Wesley. All rights reserved.234 Price Elasticity of Demand For a linear demand curve,, the elasticity of demand is 2007 Pearson Addison-Wesley. All rights reserved.235 Figure 2.9 Elasticity Along the Pork Demand Curve a /2 =143 a /5 = 57.2 D a = Q, Million kg of pork per year a / b = a /(2 b ) = 7.15 Elastic: >1 Perfectly inelastic Perfectly elastic 2007 Pearson Addison-Wesley. All rights reserved.236 Horizontal Demand Curve A small increase in price causes an infinite drop in quantity, so the demand curve is perfectly elastic. Vertical Demand Curve The elasticity of demand is zero. A demand curve is vertical for essential goodsgoods that people feel they must have and will pay anything to get. Elasticity along the Demand Curve 2007 Pearson Addison-Wesley. All rights reserved.237 Figure 2.10 Vertical and Horizontal Demand Curves (a) Perfectly Elastic Demand Q, Units per time period p * (b) Perfectly Inelastic Demand Q * Q, Units per time period 2007 Pearson Addison-Wesley. All rights reserved.238 Other Demand Elasticities Income elasticity of demand (or income elasticity) the percentage change in the quantity demanded in response to a given percentage change in income 2007 Pearson Addison-Wesley. All rights reserved.239 Other Demand Elasticities cross-price elasticity of demand the percentage change in the quantity demanded in response to a given percentage change in price of another good 2007 Pearson Addison-Wesley. All rights reserved.240 Elasticity of Supply price elasticity of supply (or elasticity of supply, ) the percentage change in the quantity supplied in response to a given percentage change in the price 2007 Pearson Addison-Wesley. All rights reserved.241 The elasticity of supply may vary along the supply curve. The elasticity of supply varies along most linear supply curve. Only constant elasticity of supply curves have the same elasticity at every point along the curve. Elasticity along the Supply Curve 2007 Pearson Addison-Wesley. All rights reserved.242 Elasticity along the Supply Curve Two extreme examples of both constant elasticity of supply curves and linear supply curves are the vertical and horizontal supply curves. Constant elasticity of supply curves are one of the form, where B is a constant and is the constant elasticity of supply at every point along the curve. 2007 Pearson Addison-Wesley. All rights reserved.243 Derivation of Constant Elasticity of Supply 2007 Pearson Addison-Wesley. All rights reserved.244 Long Run Versus Short Run The shapes of demand and supply curves depend on the relevant time period. Short-run elasticities may differ substantially from long-run elasticities. Demand elasticities over time Two factors that determine whether short- run demand elasticities are larger or smaller than long-run elasticities are ease of substitution and storage opportunities. 2007 Pearson Addison-Wesley. All rights reserved.245 Supply elasticities over time In the short run, how much a manufacturing firm can expand its output is limited by the fixed size of its manufacturing plant and the number of machines it has. In the long run, however, the firm can build another plant and buy or build more equipment. Long Run Versus Short Run 2007 Pearson Addison-Wesley. All rights reserved.246 Effects of Government Interventions A government can affect a market equilibrium in many ways. Sometimes government actions cause a shift in the supply curve, the demand curve, or both curves, which causes the equilibrium to change. Some government interventions, however, cause the quantity demanded to differ from the quantity supplied. 2007 Pearson Addison-Wesley. All rights reserved.247 Effects of a Sales Tax What effect does a sales tax have on equilibrium prices and quantity? Is it true, as many people claim, that taxes assessed on producers are passed along to consumers? That is, do consumers pay for the entire tax? Do the equilibrium price and quantity depend on whether the tax is assessed on consumers or on producers? 2007 Pearson Addison-Wesley. All rights reserved.248 Two Types of Sales Taxes The most common sales tax is called an ad valorem tax ( ) by economists and the sales tax by real people. For every dollar the consumers spends, the government keeps a fraction, , which is the ad valorem tax rate. The other type of sales tax is a specific or unit tax ( ), where a specified dollar amount, , is collected per unit of output. 2007 Pearson Addison-Wesley. All rights reserved.249 Figure 2.12 Effect of a $1.05 Specific Tax on the Pork Market Collected from Producers Q 2 = 206 Q 1 = T = $216.3 million Q, Million kg of pork per year 0 p 2 = 4.00 p 1 = 3.30 p 2 = 2.95 = $1.05 S 1 e 1 e 2 S 2 D 2007 Pearson Addison-Wesley. All rights reserved.250 Figure Effect of a $1.05 Specific Tax on Pork Collected from Consumers Q 2 = 206 Q 1 = T = $216.3 million Q, Million kg of pork per year0 p 2 = 4.00 p 1 = 3.30 p 2 = 2.95 = $1.05 Wedge, = $1.05 D 1 D 2 e 1 e 2 S 2007 Pearson Addison-Wesley. All rights reserved.251 How Specific Tax Effects Depend on Elasticities The effects of the tax on the equilibrium prices and quantity depend on the elasticities of supply and demand. In response to this change in the tax, the price consumers pay increases by where is the demand elasticity and is the supply elasticity at the equilibrium. How Specific Tax Effects Depend on Elasticities New equilibrium is determined by: D(p( )) = S(p( ) ) The effect of tax on price (dD/dp)(dp/d ) = (dS/dp)(d(p( )- )/d ) =(dS/dp)((dp/d )-1) dp/d = (dS/dp)/((dS/dp) (dD/dp)) = / ( ) 2007 Pearson Addison-Wesley. All rights reserved.252 2007 Pearson Addison-Wesley. All rights reserved.253 Tax Incidence of a Specific Tax The incidence of a tax on consumers is the share of the tax that falls on consumers. The incidence of the tax that falls on consumers is, the amount by which the price to consumers rises as a fraction of the amount the tax increases. 2007 Pearson Addison-Wesley. All rights reserved.254 The Same Equilibrium No Matter Who Is Taxed In the supply-and-demand model, the equilibrium and the incidence of the tax are the same regardless of whether the government collects the tax from consumers or producers. 2007 Pearson Addison-Wesley. All rights reserved.255 Figure 2.13 Comparison of an Ad Valorem and a Specific Tax on Pork Q 2 = 206 Q 1 = T = $216.3 million Q, Million kg of pork per year0 p 2 = 4.00 p 1 = 3.30 p 2 = 2.95 e 1 e 2 D a D s S D 2007 Pearson Addison-Wesley. All rights reserved.256 The Similar Effects of Ad Valorem Specific Taxes The specific tax shifts the pretax demand curve, D, down to D s, which is parallel to the original curve. The ad valorem tax shifts the demand curve to D a. The incidence of an ad valorem tax is generally shared between consumers and suppliers. Because the ad valorem tax of = 26.25% has exactly the same impact on the equilibrium pork price and raises the same amount of tax per unit as the $1.05 specific tax, the incidence is the same for both types of taxes. 2007 Pearson Addison-Wesley. All rights reserved.257 Policies That Cause Demand to Differ From Supply Some government policies do more than merely shift the supply or demand curve. For example, governments may control prices directly, a policy that leads to either excess supply or excess demand if the price the government sets differs from the equilibrium price. 2007 Pearson Addison-Wesley. All rights reserved.258 Price Ceilings Price ceilings have no effect if they are set above the equilibrium price that would be observed in the absence of the price controls. However, if the equilibrium price, p, would be above the price ceiling p, the price that is actually observed in the market is the price ceiling. As a result, an enforced price ceiling causes a shortage: a persistent excess demand. 2007 Pearson Addison-Wesley. All rights reserved.259 Figure 2.14 Price Ceiling on Gasoline Q s Q 2 Q 1 = Q d Price ceiling S 1 D S 2 Q, Gallons of gasoline per month Excess demand p 2 e 2 e 1 p 1 = p 2007 Pearson Addison-Wesley. All rights reserved.260 Price Floors Governments also commonly use price floors. One of the most important examples of a price floor is the minimum wage in labor markets. The minimum wage law forbids employers from paying less than the minimum wage, w. If the minimum wage bindsexceeds the equilibrium wage, w*the minimum wage creates unemployment, which is a persistent excess supply of labor. 2007 Pearson Addison-Wesley. All rights reserved.261 Figure 2.15 Minimum Wage L d L * L s Minimum wage, price floor S D L, Hours worked per year Unemployment e w * w 2007 Pearson Addison-Wesley. All rights reserved.262 Why Supply Need Not Equal Demand The price ceiling and price floor examples show that the quantity supplied does not necessarily equal the quantity demanded in a supply-and-demand model. Because we define the quantities supplied and demanded in terms of peoples wants and not actual quantities bought and sold, the statement that supply equals demand is a theory, not merely a definition. This theory says that the equilibrium price and quantity in a market are determined by the intersection of the supply curve and the demand curve if the government does not intervene. 2007 Pearson Addison-Wesley. All rights reserved.263 When to Use the Supply-and-Demand Model Supply-and-demand theory can help us to understand and predict real-word events in many markets. In this semester, we discuss competitive markets in which the supply-and- demand model is a powerful tool for predicting what will happen to market equilibrium if underlying conditions tastes, incomes, and prices of inputs change. 2007 Pearson Addison-Wesley. All rights reserved.264 When to Use the Supply-and-Demand Model This model is applicable in markets in which: Everyone is a price taker Firms sell identical products Everyone has full information about the price and quality of goods Costs of trading are low Markets with these properties are called perfectly competitive markets.