Chapter 2 Outline2.1Demand2.2Supply2.3Market Equilibrium2.4Shocking the Equilibrium: Comparative Statistics2.5Elasticities2.6Effects of a Sales Tax2.7Quantity Supplied Need Not Equal Quantity Demanded2.8When to Use the Supply-and-Demand Model

8 Main TopicsDemandThe quantity of a good or service that consumers demand depends on price and other factors (eg. income, prices of related goods)

SupplyThe quantity of a good or service that firms supply depends on price and other factors (eg. cost of inputs that firms use to produce the good or service)

8 Main TopicsMarket EquilibriumInteraction between consumers demand curve and firms supply curve determines the market price and quantity of a good or service that is bought/sold

Shocking the Equilibrium: Comparative StaticsChanges in a factor that affect demand (eg. a persons income), supply (eg. rise in the price of inputs), or a new government policy (eg. tax), alter the market price and quantity of a good

8 Main TopicsElasticitiesGiven estimates of summary statistics (elasticities), economists can forecast the effects of changes in taxes and other factors on market price and quantity

Effects of a Sales TaxHow a sales tax increase affects the equilibrium price and quantity of a good, and whether the tax falls more heavily on consumers or on suppliers, depend on the supply and demand curves

8 Main TopicsQuantity Supplied May Not Equal Quantity DemandedIf the government regulates the prices in a market, the quantity supplied might not equal the quantity demanded (eg. rent control, minimum wage)

When to Use the Supply-and-Demand ModelThe supply-and-demand model applies only to competitive markets (eg. sales of pens)

2.1 Demand

2.1 DemandWhat affects a persons demand for a good?PriceTastesInformation (or misinformation)Prices of other goodsSubstitutesComplementsIncomeGovernment rules/regulationsOther factors

2.1 Demand: Substitute GoodsIf goods A and B are substitutes, A can replace BAn increase (decrease) in the price of A leftward (rightward) movement along the demand curve of A demand curve for B to shift right (left). Positive cross elasticity of demandDemand increases (decreases) when price of other good is increased (decreased)Perfect substitutes are identical products

2.1 Demand: Substitute GoodsExamples:Margarine and butterTea and coffeeMilk and creamAT&T and VerizonAllstate and GeicoCar versus public transportationName brand versus store brand

2.1 Demand: Complement GoodsIf goods A and B are complements, They are demanded together.An increase (decrease) in the price of A leftward (rightward) movement along the demand curve of A the demand curve for B to shift left (right) Less (more) of each good will be demandedThey have a negative cross elasticity of demandDemand increases (decreases) when the price of another good is decreased (increased).Perfect complements good A must be consumed with good B

2.1 Demand: Complement GoodsExamples:

Hot dogs and bunsPeanut butter and jellyPrinters and ink cartridgesDVD players and DVDsLeft footed and right footed shoes

The Law of DemandConsumers demand more of a good the lower its price, holding constant tastes, prices of other goods, and other factors that might influence how much they consume

The derivative of the demand function is negative.Example: Qd = 40 2p; Qd = -2

Inverse DemandGiven Q = 30 10p, determine the inverse demand function.

Take the demand function and solve for price:

Inverse DemandGiven the following demand functions, find their corresponding inverse demand functions:Q = 4 3p

Q = 10 2p

Q = 80 20p

Movement along the curve vs. shifting a curveA change in the price of a good causes a movement along its demand (supply) curve.

A change in any other factor besides the price of the good causes a shift of the demand (supply) curve.

Shifting CurvesAn upward demand shift occurs when individuals are willing to purchase more output at each price level (downward demand shift is just the reverse)

An upward supply shift occurs when firms are willing to produce less output at each given price (downward supply shift is just the reverse)

Upward Demand ShiftA new study shows that salmon has a very high content of vitamin D and consumption of salmon is essential to physical well being.

Upward Supply ShiftA wildfire burns throughout the rice farms in India, which causes the world supply of rice to drop.

Examples:The demand curve for soda is given by QD = 6000 - 2y - 200p + 30pG, where QD is the quantity of soda demanded, y is the per capita income and pG is the price of Gatorade. An increase in per capita income will cause what effect in demand?

As the price of a good increases, the change in the quantity demanded can be shown byA) shifting the demand curve leftward.B) shifting the demand curve rightward.C) moving down along the same demand curve.D) moving up along the same demand curve.

Examples:An increase in the demand curve for orange juice would be illustrated as aA) leftward shift of the demand curve.B) rightward shift of the demand curve.C) movement up along the demand curve.D) movement down along the demand curve.

Examples:If the price of cars were to decrease substantially, the demand curve for gas would most likelyA) shift leftward.B) shift rightward.C) become flatter.D) become steeper.

If the price of cars were to decrease substantially, the demand curve for public transportation would most likelyA) shift leftward.B) shift rightward.C) remain unchanged.D) remain unchanged while quantity demanded would change.

2.1 DemandThe 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 serviceps = per unit price of a substitute goodpc = per unit price of a complementary goodY = consumers income

2.1 DemandWe often work with a linear demand function.Example: estimated demand function for pork in Canada.

Qd = 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 Qd and p, so we hold the other factors constant.

2.1 Demand Example: Canadian PorkAssumptions about pb, pc, and Y to simplify equationpb = $4/kgpc = $3.33/kgY = $12.5 thousand

2.1 Demand Example: Canadian PorkChanging the 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 to $4.60 /kg

2.1 Demand ExampleSuppose an individual inverse demand curve is given as p = 3 qi, where qi is the quantity demanded by individual i. There are 20 individual consumers with this identical, individual inverse demand curve. Solve for the market demand curve.

Solve for the individual, regular demand curve:

Multiply the individual demand curve by 20:

2.2 SupplyThe 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 serviceph = per unit price of other production factors

2.2 SupplyWe often work with a linear supply function.Example: estimated supply function for pork in Canada.

Qs = 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 Qs and p, so we hold the other factors constant.

Assumption about ph to simplify equationph = $1.50/kg

2.2 Supply Example: Canadian Pork

2.2 Supply Example: Canadian PorkChanging the 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

2.2 Supply ExampleSuppose the demand curve for a good shifts rightward, causing the equilibrium price to increase. This increase in the price of the good results inA) a rightward shift of the supply curve.B) an increase in quantity supplied.C) a leftward shift of the supply curve.D) a downward movement along the supply curve.

If the supply curve of a product changes so that sellers are now willing to sell two additional units at any given price, the supply curve willA) shift leftward by two units.B) shift rightward by two units.C) shift vertically up by two units.D) shift vertically down by two units.

2.2 Supply Example: QuotasThe U.S. government imposes a number of import quotas on dairy products, including Swiss cheese. The domestic supply of Swiss cheese is given by:QDom = 60p - 240The supply of Swiss cheese from foreign producers to the U.S. (mostly from Switzerland, of course), is given by:QFor = 100p - 400 In both equations above, Q is the quantity of cheese (100s of lbs/month), and p is the price per pound.

a. Using the equations above, derive the total supply of cheese equation to the U.S. in the absence of any quota.

b. Suppose that fears of neutral countries (like Switzerland) spark the U.S. to restrict imports of Swiss cheese to Q = 200. On a graph, draw (i) the domestic, (ii) foreign and (iii) total supply with the quota.

2.2 Supply Example: QuotasAnswer: a. Determine total supply by adding domestic and foreign supply (add quantities at any price):

b. To find the kink point, first find the price at which the quota restricts the foreign supply:

2.2 Supply Example: QuotasEquations:DomesticSolve for pForeign No quota: solve for pQuota: Q = _____Total No quota: solve for pQuota: Determine kink pointBefore kink: solve for pAfter kink: Add domestic supply + quota amount; solve for p

2.2 Supply Example: Quotas

2.3 Market EquilibriumThe 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

2.3 Market EquilibriumGraphically, 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.

2.3 Market Equilibrium Example:This figure shows a graph of the market for pizzas in a large town. At a price of $12, there will beAt a price of $6, there will beA) no pizzas supplied.B) equilibrium.C) excess supply.D) excess demand.

2.3 Market Equilibrium Example:The figure shows a graph of the market for pizzas in a large town. What are the equilibrium price and quantity?

At a price of $7, what is the amount of excess demand?A) 0; there is excess supply at $7.B) 20 unitsC) 30 unitsD) 10 units

2.3 Market Equilibrium ExampleGiven the following demand and supply functions, calculate the market equilibrium price and quantity: p = 20 - .1Qd p= 5 + .05Qs

2.4 Shocking the Equilibrium: Comparative StaticsA method used to analyze how variables controlled by consumers and firms (here: price/quantity) react to a change in exogenous variables (eg. Prices of substitutes, complements, income levels, prices of inputs)Changes in demand and supply factors can be analyzed graphically and/or mathematically.Graphical analysis should be familiar from intro micro Mathematical analysis uses the 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.

2.4 Shocking the Equilibrium: Comparative Statics with Discrete (large) ChangesGraphically analyzing the effect of an increase in the price of hogs

When an input gets more expensive, producers supply less pork at every price.

2.4 Shocking the Equilibrium: Comparative Statics with Discrete (large) ChangesMathematically analyzing the effect of an increase in the price of hogsIf ph increases by $0.25, new ph = $1.75 and

Why Shape of Demand Curve MattersThe shape of demand and supply curves influence how much shifts in demand or supply affect market equilibrium.In the images below, we see how a $0.25 increase in the price of hogs affects the equilibrium in each case.

2.4 Comparative Statics Example:This figure shows four different markets with changes in either the supply curve or the demand curve.

Which graph best illustrates the market for computers after technological advances in making computers occur?

Which graph best illustrates the market for computer accessories after technological advances in making computers occur?

Which graph best illustrates the market for typewriters after technological advances in making computers occur?

2.4 Comparative Statics Example:Suppose a market were currently at equilibrium. A rightward shift of the demand curve would causeA) an increase in price but a decrease in quantity.B) a decrease in price but an increase in quantity.C) an increase in both price and quantity.D) a decrease in both price and quantity.

Suppose a market were currently at equilibrium. A rightward shift of the supply curve would cause a(n)A) increase in price but a decrease in quantity.B) decrease in price but an increase in quantity.C) increase in both price and quantity.D) decrease in both price and quantity.

2.4 Comparative Statics Example:Suppose the demand for widgets is given by: Qd=100-5p+pc+2Y, where Y is average consumer income, p is the price of a widget, and pc is the price of a doodad. According to this equation, a doodad is a _____________ for a widget.

2.4 Comparative Statics: ExampleWhen two goods are substitutes, a shock that lowers the price of one good causes the price of the other good toA) remain unchanged.B) decrease.C) increase.D) change in an unpredictable manner.

A drought in the Midwest will raise the price of wheat because of aA) leftward shift in the supply curve.B) rightward shift in the supply curve.C) leftward shift in the demand curve.D) rightward shift in the demand curve.

2.4 Comparative Statics: ExampleIf chicken and turkey are substitutes, a decrease in the price of turkey would lead to aA) decrease in the demand curve for chicken.B) decrease in the quantity demanded of chicken.C) decrease in the price of chicken.D) All of the above.

The supply and demand for corn is given by QS=200+.6A+p and QD=800-2p, where p is the price of wheat and A is the amount of rainfall (inches per year). The effect of an incremental increase in rainfall on equilibrium will be a(n)Determine market equilibrium and solve for p:

2.4 Comparative Statics: ExampleIf the demand curve for a good is horizontal and the price is positive, then a leftward shift of the supply curve results in:

A vertical demand curve for a particular good implies that consumers areA) sensitive to changes in the price of that good.B) not sensitive to changes in the price of that good.C) irrational.D) not interested in that good.

2.4 Comparative Statics: ExampleThe supply and demand for wheat are given by QS = 20 + 100pQD = 4000 - 100p +10Ywhere Y is the average consumer income.Compute the partial derivative of quantity demand with respect to changes in average consumer income.

Find the equilibrium price & quantity as functions of the consumer income.

Compute the derivatives of the equilibrium price & quantity wrt income.

2.4 Comparative Statics ReviewDemand shifts left:Price of a substitute good dropsPrice of a complement good increasesIncome decreases

Demand shifts right:Price of a substitute good increasesPrice of a complement good dropsIncome increases

2.4 Comparative Statics ReviewSupply shifts left:Price of a factor of production rises. Price of alternative good rises (that can be supplied with same resources)

Supply shifts right:Price of a factor of production dropsImprovements in technology

2.5 ElasticitiesDefinition: The price elasticity of demand ( ) is the percentage change in quantity demanded brought about by a percent change in price:

2.5 ElasticitiesThe elasticity will be negative because the demand curve has a negative slope.

What does this value mean?

: perfectly inelastic demand : inelastic demand : unitary elastic demand : elastic demand : perfectly elastic demand

2.5 ElasticitiesElasticity indicates how responsive one variable is to a change in another variable.The price elasticity of demand measures how sensitive the quantity demanded of a good, Qd, is to changes in the price of that good, p.

If , then and elasticity can be evaluated at any point on the demand curve.

2.5 Example: Elasticity of DemandPrevious pork demand wasCalculating price elasticity of demand at equilibrium (p=$3.30 and Q=220):

Interpretation:Negative sign consistent with downward-sloping demandA 1% increase in the price of pork leads to a 0.3% decrease in quantity of pork demanded

2.5 Elasticity of DemandElasticity of demand varies along a linear demand curve

Can price elasticity be constant?Consider:

What is the price elasticity?

This is true in general for functions of this type.

Constant-Elasticity Demand Curves

2.5 ElasticitiesThere are other common elasticities that are used to gauge responsiveness.Income elasticity of demand (ratio of the percentage change of the quantity demanded and the percent change in income)

2.5 ElasticitiesCross-price elasticity of demand (ratio of the percentage change of the quantity demanded of one good with respect to the percent change in the price of another good)

Note: this number may be positive or negative

2.5 Complements and SubstitutesGood i is a substitute for good j if

Two goods are perfect substitutes if the consumer substitutes one good for another at a constant rate (linear indifference curve)Example: Coke and PepsiIf the price of Pepsi increases, people might be more inclined to buy Coke as a substitute

Good i is a complement of good j if

Two goods are perfect complements if they are consumed together in fixed portionsExample: hotdogs and bunsIf the price of hotdogs increases, people may be less inclined to buy buns.

Complements and SubstitutesGoods i and j are substitutes if both:

and

Goods i and j are complements if both:

and

Example: Given the demand curve for i and j as below, are the goods substitutes, complements, or neither?

2.5 ElasticitiesElasticity of supply (ratio of the percent change in quantity supplied and the percentage change in price)

Constant-Elasticity Supply Curves

2.5 Elasticities ExampleGiven Q = 120 2p, determine the value at which the demand is unitary elastic. At a price of $50, is the demand curve elastic or inelastic?

2.5 Elasticities: ExampleThis figure shows an inverse demand curve. If the market price is $10, what is the price elasticity of demand?A) -1/32B) -1C) -1/4D) -1/2The demand curve has unitary price elasticity when price equalsA) $1.B) $10.C) $15.D) $20.

2.5 Elasticities Example:If the price of cars increases by 15%, and the quantity demanded falls by 10%, what is the price elasticity of demand?

If a consumer increases a quantity consumed by 50% when her income rises by 25%, then her income elasticity of demand is:A) 8.0.B) 4.0.C) 2.0.D) .50.

2.5 Elasticities Example:If the supply curve for orange juice is estimated to be Q = 60 + 3p, thenA) supply is price elastic at all prices.B) supply is price inelastic at all prices.C) supply is elastic only at prices below 20.D) no general statements about price elasticity of supply can be made.

A given supply curve has a zero intercept. At the current equilibrium price the price elasticity of supply equalsA) 1.B) 0.C) 2.D) Not enough information.

2.5 Elasticities Example:The price elasticity of demand is estimated to be -1/5. A quantity of 50 is sold at a price of $2. Use this information to calculate a demand curve assuming it is linear.

2.6 Effects of a Sales TaxTwo types of sales taxes:Ad valorem tax is in percentage termsCalifornias state tax rate is 8.25%, so a $100 purchase generates $8.25 in tax revenueSpecific (or unit) tax is in dollar termsU.S. gasoline tax is $0.18 per gallonAd valorem taxes are much more common.

The effect of a sales tax on equilibrium price and quantity depends on elasticities of demand and supply.

2.6 Equilibrium Effects of a Sales TaxConsider the effect of a $1.05 per unit (specific) sales tax on the pork market that is collected from pork producers.

2.6 Comparative Statics with Small ChangesDemand and supply functions are 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:

2.6 Comparative Statics with Small ChangesGiven the equilibrium condition , we differentiate with respect to a using the chain rule to determine how equilibrium is affected by a small change in a:

Rearranging:

2.6 How Specific Tax Effects Depend on ElasticitiesIf a unit tax, , is collected from pork producers, the price received by pork producers is reduced by this amount and our equilibrium condition becomes:

Differentiating with respect to :

Rearranging indicates how the tax changes the price consumers pay:

2.6 Tax IncidenceThe equation can be expressed in terms of elasticities by multiplying through by p/Q:

2.6 Tax Incidence

Tax incidence on consumers, the amount by which the price to consumers rises as a fraction of the amount of the tax

Tax incidence on firms, the amount by which the price paid to firms rises, is 1 dp/d

ExampleIf a products demand curve is perfectly inelastic, and its supply curve is linear and upward sloping, what effect does a $1 specific tax collected from producers have on the products equilibrium price and quantity? What effect does the tax have on consumers? Why?

Solution1. Determine the equilibrium in the absence of a tax. 2. Show how the tax shifts the supply curve and determine the new equilibrium.3. Compare the before and after tax equilibria.4. Explain your solution.

Solution

2.6 Important Questions About Tax EffectsDoes it matter whether the tax is collected from producers or consumers?Tax incidence is not sensitive to who is actually taxed.A tax collected from producers shifts the supply curve back.A tax collected from consumers shifts the demand curve back.Under either scenario, a tax-sized wedge opens up between demand and supply and the incidence analysis is identical.

Does it matter whether the tax is a unit tax or an ad valorem tax?If the ad valorem tax rate is chosen to match the per unit tax divided by equilibrium price, the effects are the same.

2.6 Important Questions About Tax EffectsDoes it matter whether the tax is a unit tax or an ad valorem tax?

2.6 Effects of a Sales Tax Example:Suppose the supply curve and the demand curve both have unitary elasticity at all prices. The price increase to consumers resulting from a specific tax of $3 imposed on sellers will be

Consumers will always pay the entire amount of a specific tax whenever:

2.6 Effects of a Sales Tax Example:For a given positively sloped supply curve, the price increase to consumers resulting from a specific tax imposed on sellers will beA) greater the more price elastic demand is.B) greater the less price elastic demand is.C) equal to the entire tax when demand is perfectly elastic.D) equal to half of the tax whenever demand is unit elastic.

2.6 Effects of a Sales Tax Example:Suppose the demand curve for a good is downward sloping and the supply curve is upward sloping. At the market equilibrium, if demand is more elastic than supply in absolute value, a $1 specific tax willA) raise the price to consumers by 50 cents.B) raise the price to consumers by less than 50 cents.C) raise the price to consumers by more than 50 cents.D) raise the price to consumers by $1.

2.6 Effects of a Sales Tax Example:Suppose the market for grass seed can be expressed as:Demand: QD = 120 - 5pSupply: QS = 3pAt the market equilibrium, calculate the price elasticities of supply and demand. Use these numbers to predict the change in price resulting from a specific tax. If government imposes a $8 specific tax to be collected from sellers, what is the price consumers will pay? How much tax revenue is collected? What fraction is paid by sellers?

2.6 Effects of a Sales Tax Example:Answer: Market Equilibrium:

The change in price resulting from a specific tax =

Tax of $8

Thus, tax revenue =

2.7 Quantity Supplied Need Not Equal Quantity DemandedPrice determines whether Qs = QdA price ceiling legally limits the amount that can be charged for a product.Effective ceilings force the price below equilibrium price.

2.7 Quantity Supplied Need Not Equal Quantity DemandedPrice determines whether Qs = QdA price floor legally inflates the price of a product above some level.Effective floor forces the price above equilibrium price.

2.7 Quantity Supplied Need Not Equal Quantity Demanded Example:If a government-imposed price ceiling causes the observed price in a market to be below the equilibrium price,A) there will be excess demand.B) there will be excess supply.C) the curves will shift to make a new equilibrium at the regulated price.D) None of the above.

2.7 Quantity Supplied Need Not Equal Quantity Demanded Example:Suppose the market for corn can be expressed as follows:Supply: QS = -60 + 20pDemand: QD = 600 - 40pIf the government sets a maximum price of $10 per unit, what will be the quantity demanded and quantity supplied?

2.8 When to Use the Supply-and-Demand ModelThis model is appropriate in markets that are perfectly competitive:There are a large number of buyers and sellers.All firms produce identical products.All market participants have full information about prices and product characteristics.Transaction costs are negligible.Firms can easily enter and exit the market.

We will talk more about the perfectly competitive market in Chapter 8.