1. Elasticity Demand curves can come in different shapes From very flat to very steep Very flat demand curve: a small change in price has a large effect on quantity demanded Very steep curve: even a large change in price does not affect quantity demanded too much Question: how sensitive is quantity demanded to price changes?

2. Elasticity We know that quantity demanded depends on many things So we can ask a more general question? How sensitive is demand to change in any of the relevant factors: -Own price -Income -Related prices -Etc.

3. Elasticities Consider the market demand for a commodity, q Let it depend on a factor y (which might be its own price, or the price of a related good, or income). Then the elasticity of demand for q with respect to y is defined as: the percentage change in q that results from a 1% change in y. It is the percentage change in q divided by the percentage change in y.

4. Since percentage changes are pure numbers, the elasticity measure will always be a unit-free pure number. Elasticity of q with respect to y  q  y = [ ----x100 ] divided by [ ----x100 ] q y  q y = ----x----  y q

5. Therefore elasticity of quantity demanded can be with respect to: - own price (price-elasticity of demand) - any other price (cross price- elasticity) - income (income elasticity) We will spend some time on the concept of the price-elasticity of demand

6. Price Elasticity of Demand For downward sloping curves, prices and quantities move in opposite directions, so that the elasticity value is negative. To avoid this problem, we consider the absolute value of the elasticity.  q p e = - ----x---- = - (p/q)x(  q/  p).  p q

7. Calculation of elasticity Situation 1 Situation 2 p 1 = Rs.10 p 2 = Rs.9.00 q 1 = 100 q 2 = 105 Consider finite changes in prices and quantity: e = - [  q/  p]x[p/q],  q = q 2 - q 1 = 5  p = p 2 - p 1 = -1

8. 1. Point-elasticity measures. e = - [  q/  p]x[p 1 /q 1 ] = -(-5)x(10/100) = 5/10 =.5 e = - [  q/  p]x[p 2 /q 2 ] = -(-5)x(9/105) = 9/21 = 3/7 =.42 “small changes” in price -> not much difference between these two. For larger changes, the differences become substantial.

9. Pop Quiz Price Quantity Demanded 60 22 80 20 100 18 120 16 Calculate the price elasticity of demand between p = 60 and p = 80.

10. Answer to quiz  q/  p = - 2/20 = - 1/10 e = - [  q/  p]x[p 1 /q 1 ] = -(-0.1)x(60/22) = 0.27 e = - [  q/  p]x[p 2 /q 2 ] = -(-0.1)x(80/20) = 0.4 The two figures are quite different.

11. 2. Arc-elasticity measure. To get rid of this ambiguity, take an average of the values:  q [(p 2 + p 1 )/2] e = - ---------------------------  p [(q 2 + q 1 )/2] = - [  q/  p][(p 2 + p 1 )/(q 2 + q 1 )] = 5(19/205) =.46.

12. Q P A B O C E D Consider the straight-line demand curve AB. What is e at the point C? Note: [  q/  p] = EB/CE, p = CE, q = OE

13. A Straight Line Demand Curve Then price-elasticity at a point C on the demand curve = (EB/CE)(CE/OE) = EB/OE = (BC/CA) (by property of similar triangles). At the mid-point of the demand curve, e = 1. All points above this have elasticity greater than 1. Demand at all points below the mid-point is inelastic.

14. If the percentage change in q > the percentage change in p, then e > 1, and we have elastic demand. If the percentage change in q = the percentage change in p, e = 1 and we say that demand is unit elastic. If the percentage change in q < the percentage change in p, so that e < 1, demand is said to be inelastic.

15. Three special cases If (inverse) demand curve is a horizontal straight line parallel to the quantity axis, then the price- elasticity measure goes to infinity. - demand is perfectly elastic. If the (inverse) demand curve is a vertical straight line, then e = 0 and demand is said to be perfectly inelastic. An example of a demand curve that is iso-elastic (has the same elasticity everywhere) is q = p -a.

16. Elasticities In general, the price elasticity of demand will be different at different points of the demand curve. There are three special cases where the price elasticity is the same at all points of the demand curve.

17. Perfectly Elastic Demand Curve Q P 0 DD

18. Perfectly Inelastic Demand Curve Q P 0 D D “Basic needs, minimum requirements, absolute necessities.”

20. Range of elasticities 0_______________1________________+∞ Perfectly Unit Perfectly Inelastic Elasticity Elastic Demand

21. Factors affecting price elasticity: 1. Availability of substitutes Larger the availability of close substitutes, the more elastic will demand be. 2. Time period: Product durability Durable goods tend to be more price-elastic in the short run: suppose price of TVs goes up by some amount (say 5%) purchase of TVs drops (say by 10%): e = 2 over time as TVs become old, people again buy TVs – in the longer run TV purchases go down by 8% (say) => e = 1.6

22. Factors affecting price elasticity: 3. Time period: Adjustment Larger the time period, the higher the elasticity of demand. Suppose petrol prices go up Short run demand falls somewhat because motorists drive less In the long run, people switch to smaller, more fuel-efficient cars – quantity demanded of petrol goes down by a larger amount

23. Some elasticity values Salt 0.1 Matches 0.1 Airline travel, short-run 0.1 Petrol, short-run 0.2 Tobacco products, short-run 0.45 Residential natural gas, long-run 0.5 Physician services 0.6 Movies 0.9 Housing, owner occupied, long-run 1.2 Restaurant meals 2.3 Airline travel, long-run 2.4

24. Relationship between elasticity and total revenue TR = pq dTR = d(pq) = pdq + qdp = qdp(1 – e) Consider what happens if price is lowered, so that dp < 0. dTR > 0 if 1 – e 1 dTR = 0 if 1 = e dTR < 0 if e < 1

25. Income-elasticity of Demand e m = (  q/  M)(M/q) In the case of a normal good, e m > 0, while for an inferior good, it is < 0. If 0 < e m < 1, then the good is called a necessity, otherwise it is a luxury.

26. Cross-price Elasticity of Demand The cross-price elasticity of the commodity x with respect to the price p of y is defined as e xy = (  x/  p)(p/x) If this is positive, x and y are said to be substitutes (Coke and Pepsi), while if this is negative, the commodities are said to be complements (tea and sugar).

27. Price Elasticity of Supply Suppose that q now refers to quantity supplied. The price elasticity of the supply of q with respect to the price p is defined as e s = (  q/  p)(p/q) Since supply curves are upward-sloping, this expression will be non-negative – no need to put a negative sign in front of the expression

28. Application - farming Suppose that university agronomists discover a new wheat hybrid that is more productive than existing varieties. What happens to wheat farmers? The discovery of the new wheat hybrid affects the supply curve – it shifts to the right. The demand curve remains the same

29. Application - farming Quantity of wheat Price of wheat D D S S’ S

30. Application - farming What happens to the total revenue received by the farmers? Q rises but P falls The demand for basic foodstuffs such as wheat is usually inelastic, for these items are relatively inexpensive and have few good substitutes Hence fall in P is substantial while rise in Q is small Revenue to all wheat farmers taken together falls

31. Application - farming If farmers are made worse off by the discovery of the new hybrid, why do they adopt it? Each farmer is a small part of the market For any price, it makes sense for each farmer to adopt the hybrid But when they all do it, the supply curve shifts and together, they are worse off

32. Application - farming Certain agricultural programs try to help farmers by inducing them not to plant crops on all their land The purpose is to reduce the supply of farm products and thereby raise prices With inelastic demand, farmers as a whole receive greater revenue No single farmer, by himself, would have found it profitable to leave some land fallow