AAEC 3315 Agricultural Price Theory Chapter 3 Market Demand and Elasticity

Market Demand  To Gain an Understanding of: Derivation of Market Demand Demand Functions Own Price Elasticity of Demand Cross Price Elasticity of Demand Income Elasticity of Demand

Market Demand  Earlier, we derived the demand curve for an individual consumer that will maximize their utility based upon their preferences and budget constraint.  Remember that we derived an individual consumer’s demand curve from his/her Price Consumption curve (PCC).  The Demand Curve represents quantity demanded at various price levels. Q P Individual Demand Curve P1P1 P2P2 Q1Q1 Q2Q2

Market Demand Curve  D1 is the demand curve for consumer 1.  For every single consumer there will be a separate demand curve.  If we have two consumers in the market, then we will have two individual demand curves, D1 and D2. Q P P1P1 P2P2 Q1Q1 Q2Q2 D1 D2

Market Demand  Given the two demand curves D1 and D2 Note that at price=$2, Consumer 1 buys 10 units Consumer 2 buys 20 units Thus the market demand at P=$2 is 30 units At price=$1, Consumer 1 buys 22 units Consumer 2 buys 30 units. Thus the market demand is 52 units.  Thus, the aggregate or market demand is obtained by the horizontal summation of all individual consumer’s demand curves. Q P $2 $ D1 D Market Demand

 Market Demand - a schedule showing the amounts of a good consumers are willing and able to purchase in the market at different price levels during a specified period of time.  Change in its own price results in a movement along the demand curve. Q P P1P1 P2P2 Q1Q1 Q2Q2 Market Demand

Factors that Shift the Demand Curve  Population  Tastes  Income Normal good Inferior good  Price of Related Goods Substitutes - increase in the price of a substitute, the demand curve for the related good shifts outward (& vice versa) Complements - increase in the price of a complement, the demand curve for the related good shifts inward (& vice versa)  Expectations Expectations about future prices, product availability, and income can affect demand. Q P D D1D1 D2D2

Functional Relationship for Demand  Market Demand Function- Q d = f (P, T, I, R, N) Where, P = Own Price T = Tastes of consumers I = Consumer Income R = Price of related goods N = # of consumers in the market place  An example demand function for beer; Q b = 100 – 30 P b – 20 P c +.005I Where, Q b =Quantity demanded of beer in billion 6-packs P b =Price of beer per 6-pack P c =Price of a pack of chips I = Annual household income P Q P1P1 P2P2 Q1Q1 Q2Q2 Market Demand

Working with a Demand Function  Suppose the demand function for beer is given by: Q b = 100 – 30 P b – 20 P c +.005I, where, Q b = Quantity demanded of beer in billion 6-packs, P b = Price of beer per 6- pack, P c = Price of a pack of chips, and I = Annual household income.  If the price of a 6-pack of beer is $5, price of a bag of chips is $1, and the annual household income is $25,000 per year, what would be the total quantity of beer that will be sold per year? Q b = 100 – 30*(5) – 20*(1) +.005*(25000) Q b = 100 – 150 – Q b = 55 billion 6-packs.

Responsiveness of the Quantity Demanded to a Price Change  Earlier, we indicated that, ceteris paribus, the quantity of a product demanded will vary inversely to the price of that product. That is, the direction of change in quantity demanded following a price change is clear.  What is not known is the extent by which quantity demanded will respond to a price change. To measure the responsiveness of the quantity demanded to change in price, we use a measure called PRICE ELASTICITY OF DEMAND.

Own Price Elasticity of Demand (E D )  Own Price Elasticity of demand is defined as the percentage change in the quantity demanded relative to a percentage change in its own price.  Calculating Own Price Elasticity of Demand from a Demand Function: Using calculus:

Own Price Elasticity of Demand (E D ) Given a demand function: Q b = 100 – 30 P b – 20 P c +.005I, where, Q b = Quantity demanded of beer in billion 6-packs, P b = Price of beer per 6-pack ($5), P c = Price of a pack of chips ($1), and I = Annual household income ($25,000). Q b = 100 – 30*(5) – 20*(1) +.005*(25000) = 55 Taking partial derivative of the demand function with respect to price and substituting values for P and Q we get:

Using Own Elasticity of Demand  Elasticity is a pure ratio independent of units.  Since price and quantity demanded generally move in opposite direction, the sign of the elasticity coefficient is generally negative.  Interpretation: If E D = : A one percent increase in price results in a 2.72% decrease in quantity demanded

Classifications of Own-Price Elasticity of Demand  Classifications: Inelastic demand ( |E D | < 1 ): a change in price brings about a relatively smaller change in quantity demanded (ex. gasoline). Unitary elastic demand ( |E D | = 1 ): a change in price brings about an equivalent change in quantity demanded. Elastic demand ( |E D | > 1 ): a change in price brings about a relatively larger change in quantity demanded (ex. expensive wine).

Cross Price Elasticity of Demand  Shows the percentage change in the quantity demanded of good Y in response to a change in the price of good X.  Calculating Cross Price Elasticity of Demand from a Demand Function: Using calculus:

Cross Price Elasticity of Demand (E dyx ) Given a demand function: Q b = 100 – 30 P b – 20 P c +.005I, where, Q b = Quantity demanded of beer in billion 6-packs, P b = Price of beer per 6-pack ($5), P c = Price of a pack of chips ($1), and I = Annual household income ($25,000). Q b = 100 – 30*(5) – 20*(1) +.005*(25000) = 55 Taking partial derivative of the demand function for beer with respect to price of chips and substituting values for P c and Q we get:

Classification of Cross-price elasticity of Demand  Interpretation: If E dyx = : A one percent increase in price of chips results in a 0.36% decrease in quantity demanded of beer  Classification: If (E dyx > 0): implies that as the price of good X increases, the quantity demanded of Good Y also increases. Thus, Y and X are substitutes in consumption (ex. chicken and pork). (E dyx < 0): implies that as the price of good X increases, the quantity demanded of Good Y decreases. Thus Y & X are Complements in consumption (ex. bear and chips). (E dyx = 0): implies that the price of good X has no effect on quantity demanded of Good Y. Thus, Y & X are Independent in consumption (ex. bread and coke)

Income Elasticity of Demand (E I )  Shows the percentage change in the quantity demanded of good Y in response to a percentage change in Income.  Calculating Income Elasticity of Demand from a Demand Function: Using calculus:

Income Elasticity of Demand (E I ) Given a demand function: Q b = 100 – 30 P b – 20 P c +.005I, where, Q b = Quantity demanded of beer in billion 6-packs, P b = Price of beer per 6-pack ($5), P c = Price of a pack of chips ($1), and I = Annual household income ($25,000). Q b = 100 – 30*(5) – 20*(1) +.005*(25000) = 55 Taking partial derivative of the demand function with respect to income and substituting values for Q and I we get:

Income Elasticity of Demand (E I )  Interpretation: If E I = 2.27: A one percent increase income results in a 2.27% increase in quantity demanded of beer  Classification: If E I > 0, then the good is considered a normal good (ex. beef). If E I < 0, then the good is considered an inferior good (ex. roman noodles) High income elasticity of demand for luxury goods Low income elasticity of demand for necessary goods

Market Demand from the Seller’s Perspective  Consumer demand or consumer expenditure is the receipt or revenue for the seller.  So, let us look at demand from the other side of the market, i.e., the seller side of the market.  Total Revenue: From the market demand, we can easily determine the total revenue of the seller at each price by multiplying the price per unit by the quantity sold a that price TR = P. Q And let’s say TR = 20 Q – 0.5 Q 2

Market Demand from the Seller’s Perspective  Average Revenue: Average revenue is simply the total revenue divided by quantity. AR = P. Q / Q = P Or, forTR = 20 Q – 0.5 Q 2 AR = 20 – 0.5 Q  Marginal Revenue: Marginal revenue is the amount of change or addition to the total revenue attributed to the addition of 1 unit to sales. MR = ∂TR/∂Q Or, forTR = 20 Q – 0.5 Q 2 MR = 20 – 1Q

Market Demand from the Seller’s Perspective  Given that AR = 20 – 0.5 Q MR = 20 – 1Q  Note that both AR and MR have the same y-intercept.  Also note that the MR has a slope twice as that of the slope of the AR.  Graphically, this means that both the AR and MR curves have the same price-axis intercept and the MR curve is twice as steep as the AR or the demand curve. P Q AR or Market Demand MR

Relationships Among AR, MR, and TR  AR = Demand  MR curve is twice as steep as the AR Curve  MR is the slope of the TR Curve  As long as MR is + ve, TR is increasing with output  When MR = 0, TR is at its maximum  When MR is – ve, TR declines  When AR = 0, TR = 0 $/unit Q AR or Market Demand MR Q $ TR

Relationships Among Price, MR, and Elasticity of Demand Note that the price elasticity of demand is always negative; thus in using this relationship, the elasticity coefficient must always be entered as a negative number.

Relationships Among Price Elasticity of Demand, MR and TR Remember that :  When η is elastic MR is positive  When η is unitary MR = 0  When η is inelastic MR is negative Now Let us look at TR Q AR or Market Demand $/unit MR > 0 Elastic Inelastic Unitarily Elastic MR = 0 MR < 0 Q $ TR ηMRTR when P ElasticPositiveIncreasesDecreases UnitaryZeroConstant InelasticNegativeDecreasesIncreases