Elasticity

1. Elasticity Chapter 9 – Mohr and Fourie

2. Today’s session • Point elasticity ….revisited… • Arc elasticity • Price elasticity of demand and total revenue • Five categories of price elasticity of demand

3. Calculating the price elasticity of demand • Price elasticity of demand (ep) = % change in quantity demanded of a product % change in the price of the product • ∆Q/Q x100 (can cancel out the 100s) ∆P/P x 100 = ∆Q/Q ∆P/P = ∆Q/ Q x P/∆P ep = ∆Q/∆P x P/Q (Derive this for yourself to check if you fully understand how we got to this final equation!)

4. Continued…Calculating the price elasticity of demand • The slope of the linear demand curve = ∆P/ ∆Q • So the one part of the equation is ∆Q/ ∆P which is the inverse of the slope of the linear demand curve. • Second part of the equation is P/Q which is the ratio of price to quantity at any point on the line (therefore the know as POINT ELASTICITY… ELASTICITY AT A POINT.

5. Continued…Calculating the price elasticity of demand • Since the ratio is different at any point on the demand curve, the price elasticity of demand will be different at any point on the curve, since the slope (orinverse of the slope) is constant.

6. Continued…Calculating the price elasticity of demand • The price elasticity of demand varies from infinity (∞) where the demand curve meets the price axis to zero (0) where the demand curve meets the quantity axis.

7. Continued…Calculating the price elasticity of demand • Calculating elasticity coefficient … ep = ∆Q/∆P x P/Q • ∆Q/∆P is fixed = 20/-10 = - 2 • At A, ep = ∆Q/∆P x P/Q = -2 x 10/0 (anything divided by 0 … infinity) = -2 x ∞= ∞

8. Continued…Calculating the price elasticity of demand • So as we move downward and to the right, the elasticity coefficient falls. • In the middle of the line, the elasticity coefficient = 1 (At C …2 x 5/10= 2 x ½ = 1) • To the left of this, the coefficient is greater than 1 and to the right the coefficient is less than 1. • At E… ep = -2x 0/20 (zero divided by anything is zero) = -2 x 0 = 0

9. Continued…Calculating the price elasticity of demand • Although this is technically correct, in practice only a part of the demand curves are encountered. • Example, it’s unlikely you’ll ever find the situation prices fall to zero or rises so high that quantity demanded is zero .

10. Continued…Calculating the price elasticity of demand • Example from Mohr and Fourie – page 177, using figure 9.2. • Section between 1. P1=10,Q1=17 and 2. P2=8,Q2=19. • Using our formula now, calculate. • ep = ∆Q/∆P x P/Q • ∆Q/∆P = -2/2 = 1 • P/Q = ?? Which point do we use? • 1. 1x10/17 = 10/17 • 2. 1 x 8/19 = 8/19 • Two different answers for the same question… to calculate elasticity of this section of the demand curve.

11. Continued…Calculating the price elasticity of demand • The answer depends on which point we use as a basis for calculation. • How can we ensure that the answer is independent of the starting point??

12. Continued…Calculating the price elasticity of demand • How do we ensure that the answer is independent of the starting point – use an average of the two points • The elasticity coefficient calculated by comparing two points on a demand curve is called ARC ELASTICITY

13. Continued…Calculating the price elasticity of demand • ep = ∆Q/∆P x P/Q is the point elasticity formula. • Instead of just using P and Q values, now use the average of the two P and Q value that is being looked at. • ep = ∆Q/∆P x AveP/AveQ

14. Continued…Calculating the price elasticity of demand 1. P1=10,Q1=17 and 2. P2=8,Q2=19 ep = (Q2-Q1)/(Q1+Q2)/2 (P2-P1)/(P1+P2)/2 = 2/(17+19)/2 -2/ (10+8)/2 = 2/(36/2) -2/(18/2) = 2/18 x -9/2 = -1/2

15. Price elasticity of demand and total revenue • Can determine by how much total expenditure by consumers on a product changes (as a result of the change in quantity demanded) when the price of the product changes. • Remember: total expenditure by consumers on a product =total revenue of firms for that product.

16. Continued…Price elasticity of demand and total revenue • Total revenue = price x quantity • E.g. 100 calculators sold at R80 each Total revenue = R80 x 100 = R8000. • Price and quantity move in opposite directions, e.g. if price increases, quantity decreases or if quantity increase, price decreases.

17. Continued…Price elasticity of demand and total revenue • If change in price leads to proportionally greater increase in quantity demanded (ep >1 (elastic) – top left of demand curve), total revenue will change in the opposite direction to price change… worthwhile for firm to decrease price!!! • If change in price leads to an equi-proportional change in the quantity demanded (ep =1, middle point of the demand curve), total revenue will remain unchanged… price change and quantity change offset each other… no difference in revenue to firm. • If change in price leads to a proportionally smaller change in quantity demanded (ep <1, inelastic, bottom right of demand curve), total revenue will change in the same direction as the price change… bad business to decrease price as will not make up revenue by selling more goods.

18. Continued…Price elasticity of demand and total revenue

19. Price elasticity of demand and total revenue • Consider what is happening to Total Revenue at every point on the demand curve.

21. Five categories of price elasticity of demand • Perfectly inelastic demand (ep = 0) • Perfectly elastic demand (ep = ∞) • Unit elastic demand (ep = 1) • Inelastic demand (ep lies between 0 and 1) • Elastic demand (ep lies between 1 and ∞)

22. 1. PERFECTLY INELASTIC DEMAND E: Where the demand curve cuts the x axis price elasticity of demand = 0 Perfectly Inelastic (Perfectly unresponsive)

23. 1. PERFECTLY INELASTIC DEMAND • Price has no effect Qd • Qd is independent from price • Consumers plan to purchase a fixed amount of the good irrespective of the price • ep = 0 • Vertical line parallel to the price axis Types of goods • Insulin, Very addictive substances

24. 2. PERFECTLY ELASTIC DEMAND A: Where the demand curve cuts the y axis price elasticity of demand = ∞ Perfectly Elastic (Perfectly responsive)

25. 2. PERFECTLY ELASTIC DEMAND • Perfectly responsive • Consumers are willing to purchase any quantity at a certain price, but if the price changes up only slightly the Qd is 0 • Elasticity coefficient: ∞ • Horizontal demand curve • E.g. 2 vending machines side by side. If the price of goods are the same, people buy from any. If the price of one machine’s goods is higher than the other, only buy from the cheaper one.

26. 3. UNITARY ELASTICITY (UNIT ELASTIC DEMAND) C: C = Midpoint of the demand curve Price elasticity of demand = 1 Unitary Elasticity

27. 3. UNITARY ELASTICITY (UNIT ELASTIC DEMAND) • % ∆ P = % ∆ Qd • Prices decreases by 10% then Qd increases by 10% • Elasticity coefficient: ep= 1

28. 4. INELASTIC DEMAND D: D = Between E and C on demand curve, price elasticity of demand is 0 <ep<1 Inelastic Demand

29. 4. INELASTIC DEMAND • Qd responds to price change but not greatly • % ∆ P > % ∆ Qd • 10% increase in P, 2% decrease in Qd • 10 % > 2% • Elasticity coefficient: 0 < eP < 1. Types of Goods: • E.g. Basic necessities: food, housing, electricity, health care, education, petrol

30. 5. ELASTIC DEMAND B: B = Between C and A on demand curve price elasticity of demand is 1< ep< ∞ Elastic Demand

31. 5. ELASTIC DEMAND • Elastic: Highly responsive • When price changes; Qd responds greater than the change in price • P increase by 10%, Qd decreases by 15% • 15 % > 10% • % ∆ Qd > % ∆ P • 1 < ep< ∞ Types of goods: • E.g. Luxury goods : Cars, CDs, magazines, fast foods

32. SUMMARY… complete table

33. Today’s session • Point elasticity ….revisited… • Arc elasticity • Price elasticity of demand and total revenue • Five categories of price elasticity of demand