- 1. Elasticity of Demand And Supply The focus of this lecture is the elasticity. Students will learn about the price elasticity of demand, price elasticity of supply, cross elasticity and income elasticity. OBJECTIVES 1. Understand the definition of elasticity. 2. Be able to compute the elasticity coefficients. 3. Analyze the elasticity characteristics. 4. Illustrate the determinants of the elasticity. 5. Explain the total revenue test and understand the relationship between total revenue and price elasticity of demand. TOPICS Please read all the following topics. PRICE ELASTICITY OF DEMAND DETERMINANTS OF Ed TOTAL REVENUE TEST PRICE ELASTICITY OF SUPPLY CROSS ELASTICITY OF DEMAND INCOME ELASTICITY OF DEMAND
- 2. Price Elasticity of Demand Definition: Law of demand tells us that consumers will respond to a price drop by buying more, but it does not tell us how much more. The degree of sensitivity of consumers to a change in price is measured by the concept of price elasticity of demand. Price elasticity formula: Ed = percentage change in Qd / percentage change in Price. If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qd = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd. Percentage change in P = (P2-P1) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price. Putting the two above equations together: Ed = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]} Because of the inverse relationship between Qd and Price, the Ed coefficient will always be a negative number. But, we focus on the magnitude of the change by neglecting the minus sign and use absolute value Examples: 1. If the price of Product A increased by 10%, the quantity demanded decreased by 20%. Then the coefficient for price elasticity of the demand of Product A is: Ed = percentage change in Qd / percentage change in Price = (20%) / (10%) = 2 2. If the quantity demanded of Product B has decreased from 1000 units to 900 units as price increased from $2 to $4 per unit, the coefficient for Ed is: Ed = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]} = {(900 - 1000) / 1/2(1000 + 900)} / {(4 - 2) / 1/2 (2+4)} = - 0.16 Take the absolute value of - 0.16, Ed = 0.16
- 3. Kinds Of Price Elasticity Of Demand 1) Perfectly elastic demand 2) Relatively elastic demand 3) Elasticity of demand equal to utility 4) Relatively inelastic demand 5) Perfectly inelastic demand
- 4. Cont. Ed approaches infinity, demand is perfectly elastic. Consumers are very sensitive to price change. Ed > 1, demand is elastic. Consumers are relatively responsive to price changes. Ed = 1, demand is unit elastic. Consumers’ response and price change are in same proportion. Ed < 1, demand is inelastic. Consumers are relatively unresponsive to price changes. Ed approaches 0, demand is perfectly inelastic. Consumers are very insensitive to price change. Ed is usually greater in the higher price range than in lower price range. Demand is more elastic in upper left portion of the demand curve than in the lower right portion of the curve. However, it is impossible to judge elasticity of a demand curve by its flatness or steepness. Along a linear demand curve, its elasticity changes. This relationship is demonstrated in the following example:
- 5. An Example DEMAND FUNCTION FOR PRODUCT X: P = 2.5-0.01Q P = PRICE; Q = QUANTITY, TR = TOTAL REVENUE Ed = PRICE ELASTICITY OF DEMAND A B C D E F G H I J Q: 0 50 100 150 200 250 300 350 400 450 P: 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 Ed: 17 5 2.6 1.57 1 0.64 0.38 0.2 0.06 ELASTICITY OF DEMAND; FROM A TO E Ed >1 FROM E TO F Ed =1 FROM F TO J Ed <1
- 6. Perfectly elastic demand P R I C E y 0 x Perfectly elastic demand curve D D When the demand for a product changes – increases or decreases even when there is no change in price, it is known as
- 7. Relatively elastic demand Relatively elastic demand curve P R I C E demand0 x y D D When the proportionate change in demand is more than the proportionate changes in price, it is known as relatively elastic demand.
- 8. Elasticity of demand equal to utility Elasticity of demand equal to utility curve y x0 demand P R I C E D D When the proportionate change in demand is equal to proportionate changes in price, it is known as unitary elastic demand
- 9. Relatively inelastic demand Relatively inelastic demand curve XO Y demand D D P R I C E When the proportionate change in demand is less than the proportionate changes in price, it is known as relatively inelastic demand
- 10. Perfectly inelastic demand demand D D Perfectly inelastic demand curve 0 Y X P R I C E When a change in price, howsover large, change no changes in quality demand, it is known as perfectly inelastic demand
- 11. ALL KINDS OF DEMAND CAN BE SHOWN IN ONE DIAGRAM AS FOLLOW D D1 D2 D3 D4 D5 Y X0 DEMAND P R I C E WHERE D1) Perfectly elastic demand D2)Relatively elastic demand D3)Elasticity of demand equal to utility D4)Relatively inelastic demand D5)Perfectly inelastic demand
- 12. Determinants of Price Elasticity of Demand Various factors influence the price elasticity of demand. Here are some of them: 1. Availability of Substitutes: If a product can be easily substituted, its demand is elastic, like Gap's jeans. If a product cannot be substituted easily, its demand is inelastic, like gasoline. 2. Luxury Vs Necessity: Necessity's demand is usually inelastic because there are usually very few substitutes for necessities. Luxury product, such as leisure sail boats, are not needed in a daily bases. There are usually many substitutes for these products. So their demand is more elastic. 3. Price/Income Ratio: The larger the percentage of income spent on a good, the more elastic is its demand. A change in these products' price will be highly noticeable as they affect consumers' budget with a bigger magnitude. Consumers will respond by cutting back more on these product when price increases. On the other hand, the smaller the percentage of income spent on a good, the less elastic is its demand. 4. Time lag: The longer the time after the price change, the more elastic will be the demand. It is because consumers are given more time to carry out their actions. A 1- day sale usually generate less sales change per day as a sale lasted for 2 weeks.
- 13. Total Revenue Test Total revenue (TR) is calculated by multiplying price (P) per unit and quantity (Q) of the good sold. TR = P x Q The total revenue test is a method of estimating the price elasticity of demand. As Ed will impact the total revenue, we can estimate the Ed by looking at the movement of the total revenue. Total Revenue Test Ed > 1, total revenue will decrease as price increases. P and TR moves in opposite directions. Producers can increase total revenue ( TR = Price x Quantity) by lowering the price. Therefore, most department stores will have sales to attract customers. Apparel's demand is elastic. Ed < 1, total revenue will increase as price increases. P and TR moves in the same direction. Producers can increase total revenue by raising the price. Inelastic demand for agricultural products helps to explain why bumper crops depress the prices and total revenues for farmers. You may look at the movement of TR in the example below. It demonstrated the relationship described above.
- 14. TR Test Example DEMAND FUNCTION FOR PRODUCT X: P = 2.5-0.01Q P = PRICE; Q = QUANTITY, TR = TOTAL REVENUE Ed = PRICE ELASTICITY OF DEMAND A B C D E F G H I J Q: 0 50 100 150 200 250 300 350 400 450 P: 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 TR: 0 200 350 450 500 500 450 350 200 0 Ed: 17 5 2.6 1.57 1 0.64 0.38 0.2 0.06 ELASTICITY OF DEMAND; FROM A TO E Ed >1 TR increases FROM E TO F Ed =1 TR remains same. FROM F TO J Ed <1 TR decreases.
- 15. Cross Elasticity of DemandDefinition: Cross elasticity (Exy) tells us the relationship between two products. it measures the sensitivity of quantity demand change of product X to a change in the price of product Y. Formula: Exy = percentage change in Quantity demanded of X / percentage change in Price of Y. If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qx = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qd of X, and Q2 = new Qd of X. Percentage change in Py = (P2-P1) / [1/2 (P1 + P2)] where P1 = initial Price of Y, and P2 = New Price of Y. Putting the two above equations together: Exy = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]} Characteristics: Exy > 0, Qd of X and Price of Y are directly related. X and Y are substitutes. Exy approaches 0, Qd of X stays the same as the Price of Y changes. X and Y are not related. Exy < 0, Qd of X and Price of Y are inversely related. X and Y are complements. Examples: 1. If the price of Product A increased by 10%, the quantity demanded of B increases by 15 %. Then the coefficient for the cross elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = (15%) / (10%) = 1.5 > 0, indicating A and B are substitutes. 2. If the price of Product A increased by 10%, the quantity demanded of B decreases by 15 %. Then the coefficient for the cross elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = (- 15%) / (10%) = - 1.5 < 0, indicating A and B are complements.
- 16. Income Elasticity of Demand Definition: Income elasticity of demand (Ey, here y stands for income) tells us the relationship a product's quantity demanded and income. It measures the sensitivity of quantity demand change of product X to a change in income. Price elasticity formula: Ey = percentage change in Quantity demanded / percentage change in Income If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qx = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd. Percentage change in Y = (Y2-Y1) / [1/2 (Y1 + Y2)] where Y1 = initial Income, and Y2 = New income. Putting the two above equations together: Ey = {(Q2-Q1) / [1/2 (Q1+Q2)] } / (Y2-Y1) / [1/2 (Y1 + Y2)] Characteristics: Ey > 1, Qd and income are directly related. This is a normal good and it is income elastic. 0< Ey<1, Qd and income are directly related. This is a normal good and it is income inelastic. Ey < 0, Qd and income are inversely related. This is an inferior good. Ey approaches 0, Qd stays the same as income changes, indicating a necessity. Example: If income increased by 10%, the quantity demanded of a product increases by 5 %. Then the coefficient for the income elasticity of demand for this product is:: Ey = percentage change in Qx / percentage change in Y = (5%) / (10%) = 0.5 > 0, indicating this is a normal good and it is income inelastic.
- 17. Price Elasticity of Supply Definition: Law of supply tells us that producers will respond to a price drop by producing less, but it does not tell us how much less. The degree of sensitivity of producers to a change in price is measured by the concept of price elasticity of supply. Price elasticity formula: Es = percentage change in Qs / percentage change in Price. If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qs = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qs, and Q2 = new Qs. Percentage change in P = (P2-P1) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price. Putting the two above equations together: Es = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]} Because of the direct relationship between Qs and Price, the Es coefficient will always be a positive number. Examples: 1. If the price of Product A increased by 10%, the quantity supplied increases by 5%. Then the coefficient for price elasticity of the supply of Product A is: Es = percentage change in Qs / percentage change in Price = (5%) / (10%) = 0.5 2. If the quantity supplied of Product B has decreased from 1000 units to 200 units as price decreases from $4 to $2 per unit, the coefficient for Es is: Es = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]} = {(200 - 1000) / 1/2(1000 + 200)} / {(2-4) / 1/2 (4+2)} = 2
- 18. Ranges of Elasticity © iTutor. 2000-2013. All Rights Reserved
- 19. A Variety of Supply Curves Perfectly Inelastic Supply - Elasticity equals 0 Inelastic Supply- Elasticity is less than 1 Price Quantity100 $10 $5 1. An increase in price... 2. ...leaves the quantity supplied unchanged. Price Quantity100 $5 $4 1. A 22 % increase in price... 2. ...leads to 10% increase in Quantity. 110 Supply Supply © iTutor. 2000-2013. All Rights Reserved
- 20. Unit Elastic Supply - Elasticity equals 1 Elastic Supply - - Elasticity is greater than 1 A Variety of Supply Curves Price Quantity $5 $4 1. A 25 % increase in price... 2. ...leads to a 25% increase in Quantity. 100 Price Quantity100 $5 $4 1. A 22 % increase in price... 2. …leads to a 67% increase in Quantity. 167 125 © iTutor. 2000-2013. All Rights Reserved
- 21. Quantity Price Supply$4 1. At any price above $4, quantity supplied is infinite. 2. At exactly $4, producers will supply any quantity. 3. At a price below $4, Quantity supplied is zero. Perfectly Elastic Supply - Elasticity equals infinity © iTutor. 2000-2013. All Rights Reserved
- 22. Determinants of supply elasticity The following list contains the main determinants of supply elasticity. 1. Product Type 2. Time 3. Production Capacity 4. Input substitution -- Flexibility and Mobility Product Type - The type of product impacts how quickly a producer is able to respond to a change in price. A manufacturing firm may be able to quickly adjust production levels with only minor adjustments in the equipment while other products such as apples require several years to establish a new orchard. Since child care services requires relatively few skills compared to the those of a physician, the supply elasticity of child care services is more elastic than that of physician services. Time - Time is a key determinant of supply. In the case of apples and some other agriculture products, the immediate elasticity of supply is very inelastic, i.e., there are only so many apples available for sale today. However, with time producers are able to respond to the increase in price, manufacturing firms can build new facilities, farmers can plant additional acres to the particular crop. Thus in time, the elasticity of supply becomes more elastic. © iTutor. 2000-2013. All Rights Reserved
- 23. Production Capacity - If a firm is already operating at full capacity, then to increase supply would require building additional facilities and purchasing new equipments. A firm that is operating at below full capacity, can respond to a price increase quicker than a firm that is already at full capacity. Input substitution -- Flexibility and Mobility Another determinant in the elasticity of supply is input substitution. As the price of a good increases, how easily can inputs that were used in the production of another good be switched over to producing the good with the higher price? P Q Short run Intermediate run Long run © iTutor. 2000-2013. All Rights Reserved
- 24. Oil and elasticity of supply World supply of oil following a large rise in world demand Variable amount of spare capacity among the major oil producers Can oil stocks be put onto the market to meet the rise in demand? Oil supply might be inelastic if current output is close to capacity © iTutor. 2000-2013. All Rights Reserved
- 25. Point elasticity of demand Meaning Point elasticity is the price elasticity of demand at a specific point on the demand curve instead of over a range of it. It uses the same formula as the general price elasticity of demand measure, but we can take information from the demand equation to solve for the “change in” values instead of actually calculating a change given two points.
- 26. Continue Here is the process to find the point elasticity of demand formula: • Point Price Elasticity of Demand = (% change in Quantity)/(% change in Price) • Point Price Elasticity of Demand = (∆Q/Q)/(∆P/P) • Point Price Elasticity of Demand = (P/Q) (∆Q/∆P)
- 27. Continue • Where (∆Q/∆P) is the derivative of the demand function with respect to P. • You don’t really need to take the derivative of the demand function, just find the coefficient (the number) next to Price (P) in the demand function and that will give you the value for ∆Q/∆P because it is showing you how much Q is going to change given a 1 unit change in P.
- 28. Example 1: • Demand curve: Q = 15,000 - 50P Given this demand curve we have to figure out what the point price elasticity of demand is at P = 100 and P = 10. • First we need to obtain the derivative of the demand function when it's expressed with Q as a function of P. Since quantity goes down by 50 each time price goes up by 1, This gives us (∆Q/∆P)= -50
- 29. Continue • Next we need to find the quantity demanded at each associated price and pair it together with the price: (100, 10,000), (10, 14,500) e = -50(100/10,000) = -.5 e = -50(10/14,500) = -.034 And these results make sense, first, because they are negative (downward sloping demand) and second, because the higher level results in a relatively more price elasticity of demand measure.
- 30. Example 2 • How to find the point price elasticity of demand with the following demand function: Q = 4,000 – 400P • We know that ∆Q/∆P in this problem is -400, and we need to find the point price elasticity of demand at a price of 10 and 8.
- 31. Continue • At a price of 10, we demand 0 of the good, so the measure is undefined. At a price of 8 demand will be 400 of the good, so the associated measure is: e = -400(8/400) = -8
- 32. Continue What about a demand function of: Q = 8,800 – 1,000P • find the associated measure at prices of 0, 2, 4, and 6. • e = -1,000(0/8,800) = 0 • e = -1,000(2/6,800) = -0.294 • e = -1,000(4/4,800) = -0.8333 • e = -1,000(6/2,800) = -2.14
- 33. Point elasticity of Supply Here is the process to find the point elasticity of supply formula: • Point Price Elasticity of Supply = (% change in Quantity)/(% change in Price) • Point Price Elasticity of Supply = (∆Q/Q)/(∆P/P) • Point Price Elasticity of Supply = (P/Q)(∆Q/∆P)
- 34. Example 1 Supply: Q = 2000 + 20P By using this supply function calculate price elasticity of supply at price 40,60 and 80? Es = Slope (P/Q) Es = 20 (40/2800) = 0.28 Es = 20 (60/3200) = 0.37 Es = 20 (80/3600) = 0.44
- 35. Question 1 Consider the ice cream market in Madison. In July, the ice cream market demand and supply curves are given by the following equations where Q is the quantity to ice cream units and P is the price in dollars per unit of ice cream: • Demand: Q = 14000 – 10P • Supply: Q = 2000 + 20P
- 36. a) Find the equilibrium price and quantity of ice cream in July. b) Calculate the price elasticity of demand and supply at the equilibrium price in July. Use the point elasticity formula to compute these two values of these elasticities. In October, ice cream demand in Madison decreases. So, the new demand curve is given by Demand: Q = 7000 – 30P Assume the supply curve doesn’t change.
- 37. c) Find the equilibrium price and equilibrium quantity in October, and calculate the price elasticity of demand and supply at this new equilibrium price. Use the point elasticity formula in calculating these values.