AAEC 3315 Agricultural Price Theory

1. AAEC 3315Agricultural Price Theory Chapter 3 Market Demand and Elasticity

2. 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

3. 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. P P1 P2 Individual Demand Curve Q1 Q2 Q

4. 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. P P1 P2 D2 D1 Q1 Q2 Q

5. 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. P Market Demand $2 $1 D2 D1 10 22 20 30 Q 52

6. 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. P P1 P2 Market Demand Q1 Q2 Q

7. 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. P D1 D D2 Q

8. P1 P2 Market Demand Q1 Q2 Q Functional Relationship for Demand • Market Demand Function- Qd = 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; Qb = 100 – 30 Pb – 20 Pc + .005I Where, Qb = Quantity demanded of beer in billion 6-packs Pb = Price of beer per 6-pack Pc = Price of a pack of chips I = Annual household income P

9. Working with a Demand Function • Suppose the demand function for beer is given by: Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity demanded of beer in billion 6-packs, Pb = Price of beer per 6-pack, Pc = 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? Qb = 100 – 30*(5) – 20*(1) + .005*(25000) Qb = 100 – 150 – 20 + 125 Qb = 55 billion 6-packs.

10. 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.

11. Own Price Elasticity of Demand (ED) • 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:

12. Own Price Elasticity of Demand (ED) • Given a demand function: Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity demanded of beer in billion 6-packs, Pb = Price of beer per 6-pack ($5), Pc = Price of a pack of chips ($1), and I = Annual household income ($25,000). • Qb = 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:

13. 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 ED = - 2.72: A one percent increase in price results in a 2.72% decrease in quantity demanded

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

15. 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:

16. Cross Price Elasticity of Demand (Edyx) • Given a demand function: Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity demanded of beer in billion 6-packs, Pb = Price of beer per 6-pack ($5), Pc = Price of a pack of chips ($1), and I = Annual household income ($25,000). • Qb = 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 Pc and Q we get:

17. Classification of Cross-price elasticity of Demand • Interpretation: • If Edyx = - 0.36: A one percent increase in price of chips results in a 0.36% decrease in quantity demanded of beer • Classification: • If (Edyx > 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). • (Edyx < 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). • (Edyx = 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)

18. Income Elasticity of Demand (EI) • 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:

19. Income Elasticity of Demand (EI) • Given a demand function: Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity demanded of beer in billion 6-packs, Pb = Price of beer per 6-pack ($5), Pc = Price of a pack of chips ($1), and I = Annual household income ($25,000). • Qb = 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:

20. Income Elasticity of Demand (EI) • Interpretation: • If EI = 2.27: A one percent increase income results in a 2.27% increase in quantity demanded of beer • Classification: • If EI > 0, then the good is considered a normal good (ex. beef). • If EI < 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

21. Market Demandfrom 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 Q2

22. Market Demandfrom the Seller’s Perspective • Average Revenue: Average revenue is simply the total revenue divided by quantity. • AR = P. Q / Q = P • Or, for TR = 20 Q – 0.5 Q2 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, for TR = 20 Q – 0.5 Q2 MR = 20 – 1Q

23. AR or Market Demand Q Market Demandfrom 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 MR

24. AR or Market Demand Q Q Relationships Among AR, MR, and TR $/unit • 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 MR $ TR

25. 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.

26. AR or Market Demand Q Q Relationships Among Price Elasticity of Demand, MR and TR $/unit 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 Elastic Unitarily Elastic Inelastic MR > 0 MR < 0 MR = 0 $ TR