Elasticity PDF

ELASTICITY 3 CHAPTER Elasticity In chapters two, among other things, it has been shown that Generally, it has been shown that if the price of a commodity X increases, the quantity demanded of that particular commodity will fall, ceteris paribus. However, quite often we...

ELASTICITY 3 CHAPTER Elasticity In chapters two, among other things, it has been shown that Generally, it has been shown that if the price of a commodity X increases, the quantity demanded of that particular commodity will fall, ceteris paribus. However, quite often we are interested to know by how much the quantity supplied or demanded for a particular commodity will rise or fall following the changes in the price of the commodity. For example, how sensitive is the demand for sugar to its price? Suppose that the price of sugar is increased by 10 percent, by how much will quantity demanded change? What will be the impact of an increase in the price of sugar on the demand for Bread? Milk? Coffee? Similarly, we are interested to know by how much will demand for sugar change if consumer's income increases by 5 percent? The concept of elasticity is very useful in answering those questions. Price Elasticity of Demand In the Figure a change in supply brings a small increase in the quantity demanded and a large fall in price. Price Elasticity of Demand In this Figure, a change in supply brings a large increase in the quantity demanded and a small fall in price. Price Elasticity of Demand The price elasticity of demand is a units-free measure of the responsiveness of the quantity demanded of a good to a change in its price when all other influences on buyers’ plans remain the same. Price elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in price of the commodity. It is usually symbolized by the Greek letter,  called eta. percentage change in quantity demanded η= percentage change in price Algebraically, price elasticity of demand is written as follows ΔQ/Q ΔQ P η=− =− x ΔP/P ΔP Q Where; Q/Q represents the change in quantity demanded and P/P represents the change in price. P denotes initial price and Q denotes initial quantity Price Elasticity of Demand To calculate the price elasticity of demand: We express the change in price as a percentage of the average price—the average of the initial and new price, and we express the change in the quantity demanded as a percentage of the average quantity demanded—the average of the initial and new quantity. There are two ways of measuring the price elasticity of demand. If the changes in price are very small, we use point elasticity of demand as a measure of the responsiveness of demand. If, on the other hand, changes in price are not so small, we use arc elasticity of demand as the relevant measure. Let us explain these two elasticities. Point Elasticity of Demand The point elasticity of demand is defined as the proportionate change in the quantity demanded resulting from a very small proportionate change in price. The formula for price elasticity of demand given in equation 5.2 is also applicable for the point elasticity of demand. ΔQ/Q ΔQ P η=− =− x ΔP/P ΔP Q Arc Elasticity of Demand Arc elasticity is a measure of average elasticity. That is, the elasticity at the midpoint of the chord that connects the two points (A and B) on the demand curve defined by the initial and new price levels as. To calculate the arc elasticity, we use the following formula: ΔQ [P1 + P2]/2 ΔQ [P1 + P2] η= x = x ΔP [Q1 + Q2]/2 ΔP [Q1 + Q2] Interpretation of Price Elasticity of Demand As we have pointed out earlier, the coefficient of price elasticity of demand is a negative sign due to the inverse relationship between price and quantity demanded. In terms of interpretation, the negative sign is ignored and only absolute value is considered. In the following sub-section, we are going to provide an interpretation of: inelastic demand, elastic demand and unitary elasticity Inelastic Demand Inelastic demand occurs whenever the percentage change in quantity is less than the percentage change in price. In other words, demand is not very responsive to change in price. Under inelastic demand, the numeric value of the coefficient of price elasticity of demand is less than 1. In the extreme cases where the coefficient of price elasticity of demand is zero, demand is said to be perfectly inelastic. This is shown in figure 5.1. Under perfectly inelastic demand, a change in price has no whatsoever influence on quantity demanded. The demand curve for such a product is thus vertical Elastic Demand Elastic demand occurs whenever the percentage change in quantity demanded exceeds the percentage change in price. In other words, demand is more responsive to change in price. Under elastic demand, the numeric value of the coefficient of price elasticity is usually greater than 1 but less than infinity. In the extreme cases where the price elasticity of demand is infinitely large, demand is said to be perfectly elastic. The demand curve for such a product is thus horizontal. This is shown in figure 5.2. Unitary Elasticity The other peculiar case occurs when price elasticity of demand is equal to one. Under this particular case, the percentage change in price is exactly equal to the percentage change in quantity demanded. This case, which is called the unit elasticity, is the boundary between elastic and inelastic demand. A demand curve having unit elasticity over its whole range is shown in figure 5.3 Rectangular Hyperbola Demand Curve Determinants of Price Elasticity of Demand Our analysis of elasticity has concentrated solely on the measurement of elasticity of demand. But why do some goods display elastic demands while others seem quite unresponsive to price? The following are the factors, which influence the price elasticity of demand. (a) Number of closeness of substitute for the commodity. The more and better the available substitute for the commodity, the greater its price elasticity of demand is likely to be. Thus, when the price of tea rises, consumers readily switch to commodity substitute such as coffee and cocoa, so the coefficient of price elasticity of demand for tea is likely to be high. On the other hand, since there are no commodity substitutes for salt, its elasticity is likely to be very low. Expenditure on the commodity. The greater the percentage of income spent on a commodity the greater its elasticity is likely to be. Thus, the demand for car is likely to be much more price elastic. d) Adjustment time: The longer the allowed period of adjustment in the quantity of a commodity demanded, the more elastic its demand is likely to be. This is so because it takes time for consumer to learn new prices and products. In addition, even after a decision is made to switch to other products, some time may pass before the switch is actually made. In general, elasticity tend to be inelastic in the short run but elastic in the long run. Nature of the commodity: It is a common observation that different commodities depending on their nature tend to display different elasticities. For example, necessity commodities such as food tend to be inelastic while luxury commodities such as articles of ostentation tend to be more elastic. Habit: Some commodities such as tobacco and alcoholic drink are habit forming and demand will tend to be more inelastic over a fairly wide range of prices. In some countries the prices of tobacco and alcoholic drinks have been greatly increased by taxation, but demand has been relatively unaffected. Smoking and drinking seem to be acquired habits which consumers are reluctant to change. Hence demand tends to be inelastic The Income Elasticity of Demand The coefficient of income elasticity of demand (m) measures the percentage change in the amount of the commodity purchased per unit of time (Qx/ Qx) resulting from a given percentage change in consumer’s income (M/M). Thus, ΔQ/Q ΔQ M ηm = = x ΔM/M ΔM Q Normal goods have a positive income elasticity of demand. This implies that as income rises more is demanded at each price level. Necessities have an income elasticity of demand of between 0 and +1. Demand rises with income, but less than proportionately. Often this is because we have a limited need to consume additional quantities of necessary goods as our real income rise. Luxuries on the other hand are said to have an income elasticity of demand greater than 1. Demand rises more than proportionate to a change in income). Luxuries are items we can (and often do) manage to do without during periods of below average income and falling consumer confidence. Inferior goods have a negative income elasticity of demand. Demand falls as income rises. The Cross Elasticity of Demand The cross elasticity of demand is defined as the proportionate change in the quantity demanded of commodity X resulting from proportionate change in the price of commodity Y. The cross elasticity of demand is given by the following formula: ΔQx/Qx ΔQx Py ηxy = ΔPy/Py = ΔPy x Qx Cross elasticity can vary from minus infinity to plus infinity. Complementary goods have negative cross elasticities and substitute goods have positive cross elasticities Bread and butter for example, are complements: a fall in the price of the butter causes an increase in consumption of both products. Thus change in the price of butter and in the quantity of bread demanded will have opposite signs. In contrast, butter and margarine are substitutes: a fall in the price of butter increases the quantity of butter demanded but reduces the quantity of margarine demanded. Changes in the price of butter and in the quantity of margarine demanded will, therefore, have the same sign.  Relationship between Elasticity and Total Revenue The relationship between price elasticity of demand and total revenue is of particular importance to producers when setting the price of the commodity Producers are interested in the price elasticity of demand because they are interested in questions like: will an increase in price result in an increase in the total amount spent by the consumers on the product? Or will an increase in price result in a decrease in the total amount spent by consumers on the product? The answers to these questions depend on the price elasticity of demand. Suppose that the demand for the product is price elastic, i.e. the price elasticity of demand exceeds one. The total amount of money spent by consumers on the product equals the quantity demanded times price per unit. In this situation, if the price is reduced, the percentage increase in quantity demanded is greater than the percentage reduction in price. It then follows that a price reduction must lead to an increase in the total amount spent by the consumers on the commodity. If the demand is price elastic, a price increase leads to a reduction in the amount of money spent on the commodity. If the demand is price inelastic, a price decrease leads to a reduction in the total amount spent on the commodity, and a price increase leads to an increase in the amount spent on the commodity. If the demand is of unitary elasticity, an increase or a decrease in price has no effect on the amount spent on the commodity.  Table 5.2: Elasticity and Total Revenue Poin Px Quantit Total Elastic ts y ity (LE of X Expenditu ) re A 8 0 0 B 7 1,000 7,000 7 C 6 2,000 12,000 3 D 5 3,000 15,000 5/3 E 4 4,000 16,000 1 F 3 5,000 15,000 3/5 G 2 6,000 12,000 1/3 H 1 7,000 7,000 1/7 I 0 8,000 0 As we move down the demand curve from A to E, the elasticity of demand gets smaller, but always exceed one. Thus, the total amount spent on the good increases continually as we move from A to E. At point E, since there is unitary elasticity, there is no change in the total amount spent on the goods. Moving from E to I, the elasticity of demand is always less than one. Thus, the total amount spent on the goods decreases continually as we move from E to I. Elasticity of Supply Elasticity of supply is defined as the percentage change in quantity supplied divided by the percentage change in the price that brought it about. Letting the Greek letter epsilon,, stand for this measure, its formula is: percentagechange in quantity supplied ε= percentage change in price Determinant of Elasticity of Supply Time In the momentary period, supply is limited to the quantities already available in the market In the short run, supply can be increased by employing more variable factors of production In the long run, the quantities of all factors of production can be increased. Existing firms can be expanded, and new firms may enter the industry THE END  1) Demand determines price entirely when A) demand is downward sloping. B) demand is perfectly inelastic. C) supply is perfectly inelastic. D) supply is perfectly elastic. 1) When the price of radios decreases 5%, quantity demanded increases 5%. The price elasticity of demand for radios is and total revenue from radio sales will. A) elastic; decrease B) elastic; increase C) inelastic; decrease D) unit elastic; not change 1) When the price of fresh fish increases 10%, quantity demanded is unchanged. The price elasticity of demand for fresh fish is A) perfectly inelastic. B) elastic. C) inelastic. D) unitary elastic. 1) The ABC Computer Company wants to increase the quantity of computers it sells by 5%. If the price elasticity of demand is ‐2.5, the company must A) increase price by 2.0%. B) decrease price by 2.0%. C) increase price by 0.5%. D) decrease price by 0.5%. 1) A government wants to reduce electricity consumption by 10%. The price elasticity of demand for electricity is ‐5. The government must the price of electricity by. A) raise; 2.0% B) raise; 0.5% C) raise; 1.25% D) lower; 0.5%