2. Supply and DemandSlide Number 2DemandDemandDemand Example: Canadian PorkExample: Canadian PorkSupplySupplyExample: Canadian PorkExample: Canadian PorkSlide Number 11Market EquilibriumMarket EquilibriumShocking the Equilibrium: Comparative StaticsComparative Statics with Discrete (large) ChangesComparative Statics with Discrete (large) ChangesComparative Statics with Small ChangesComparative Statics with Small ChangesElasticitiesElasticitiesExample: Elasticity of DemandSlide Number 22Slide Number 23Slide Number 24Slide Number 25Constant-Elasticity Demand CurvesElasticitiesConstant-Elasticity Supply CurvesSlide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Aggregation of Demand or Supply Curve2. Supply and Demand • Demand • Supply • Market Equilibrium • Shocking the Equilibrium: Comparative Statistics • Elasticities 1Example: The Price of Corn in the United States, 1900-1999 2Demand • The quantity of a good or service that consumers demand depends on price and other factors such as consumers’ incomes and the prices of related goods. • The demand function describes the mathematical relationship between quantity demanded (Qd), price (p) and other factors that influence purchases: • p = per unit price of the good or service • ps = per unit price of a substitute good • pc = per unit price of a complementary good • Y = consumers’ income 3Demand • We often work with a linear demand function. • Example: estimated demand function for pork in Canada. • Q = quantity of pork demanded (million kg per year) • p = price of pork (in Canadian dollars per kg) • pb = price of beef, a substitute good (in Canadian dollars per kg) • pc = price of chicken, another substitute (in Canadian dollars per kg) • Y = consumers’ income (in Canadian dollars per year) • Graphically, we can only depict the relationship between Q and p, so we hold the other factors constant. 4Demand Example: Canadian Pork Assumptions about pb, pc, and Y to simplify equation • pb = $4/kg • pc = $3.33/kg • Y = $12.5 thousand 5Example: Canadian Pork • Changing the own-price of pork simply moves us along an existing demand curve. • Changing one of the things held constant (e.g. pb, pc, and Y) shifts the entire demand curve. • pb rises to $4.60 /kg 6Supply • The quantity of a good or service that firms supply depends on price and other factors such as the cost of inputs that firms use to produce the good or service. • The supply function describes the mathematical relationship between quantity supplied (Qs), price (p) and other factors that influence the number of units offered for sale: • p = per unit price of the good or service • ph = per unit price of other production factors 7Supply • We often work with a linear supply function. • Example: estimated supply function for pork in Canada. • Q = quantity of pork supplied (million kg per year) • p = price of pork (in Canadian dollars per kg) • ph = price of hogs, an input (in Canadian dollars per kg) • Graphically, we can only depict the relationship between Q and p, so we hold the other factors constant. 8• Assumption above to simplify equation • ph = $1.50/kg 40=dpdQsslopedQdps==401Example: Canadian Pork 9Example: Canadian Pork • Changing the own-price of pork simply moves us along an existing supply curve. • Changing one of the things held constant (e.g. ph) shifts the entire supply curve. • ph to $1.75 /kg 10A market equilibrium is a pair of price and quantity (p*,Q*) such that at price p*, the quantities demanded and supplied are both Q* (market clears). • An equilibrium is a point of stability – a point at which the price will remain the same as long as exogenous conditions (e.g., rainfall, national income) remain unchanged. • Demand and supply curves intersect at equilibrium. Market Equilibrium 11Market Equilibrium • The interaction between consumers’ demand curve and firms’ supply curve determines the market price and quantity of a good or service that is bought and sold. • Mathematically, we find the price that equates the quantity demanded,Qd, and the quantity supplied,Qs: • Given and , find p such that Qd = Qs: p = $3.30 pQd20286−=pQs4088+=286 20 88 40pp−=+⇒12Market Equilibrium • Graphically, market equilibrium occurs where the demand and supply curves intersect. • At any other price, excess supply or excess demand results. • Natural market forces push toward equilibrium Q and p. 13Shocking the Equilibrium: Comparative Statics • Changes in a factor that affects demand, supply, or a new government policy alters the market price and quantity of a good or service. • Changes in demand and supply factors can be analyzed graphically and/or mathematically. • Graphical analysis should be familiar from your introductory microeconomics course. • Mathematical analysis simply utilizes demand and supply functions to solve for a new market equilibrium. • Changes in demand and supply factors can be large or small. • Small changes are analyzed with Calculus. 14Comparative Statics with Discrete (large) Changes • Graphically analyzing the effect of an increase in the price of hogs • When an input gets more expensive, producers supply less pork at every price. 15Comparative Statics with Discrete (large) Changes • Mathematically analyzing the effect of an increase in the price of hogs • If ph increases by $0.25, new ph = $1.75, then 178 40 60 73 40shQ pp p=+− =+55.3$407320286=+=−=pppQQsd( )21555.320286 =−=dQ( )21555.34073 =+=sQ16Comparative Statics with Small Changes • Demand is written as general functions of the price of the good, holding all else constant: • Supply is also a function of some exogenous (not in firms’ control) variable, a: • Because the intersection of demand and supply determines the price, p, we can write the price as an implicit function of the supply-shifter, a: • In equilibrium: ( )aapSQs),(=( ( ))DQ Dpa=17Comparative Statics with Small Changes • Given the equilibrium condition we differentiate with respect to using the chain rule to determine how equilibrium is affected by a small change in . • Rearranging: aa18Elasticities • The shape of demand and supply curves influence how much shifts in demand or supply affect market equilibrium. • Shape is best summarized by elasticity. 19Elasticities •