Elasticity of Demand and Supply

Transcription

1 ECO101 PRINCIPLES OF MICROECONOMICS Notes Elasticity of Demand and Supply Overview In this chapter, we will examine the price elasticity of demand a crucial concept in economics as it has direct connection with business revenues (and to a lesser extent cross elasticity, income elasticity, and elasticity of supply), and illustrate how to use this concept to specific situations, such as the pricing of airline tickets for first class or economy, bad harvests (for instance coffee or orange frost) and its impact on prices, or the imposition of excise taxes on cigarettes or alcohol. We will also make the distinction between long-run and short-run price elasticity. Elasticity of Demand All sellers (small or large, educated or street-wise) know very well the law of demand that there is an inverse relationship between price and quantity demanded. They know that if they lower their prices ceteris paribus, or other things being the same most probably their sales will increase, and vice-versa. The critical question is: Is it enough for a businessperson to know simply in which direction quantity would change as a result of a change in price? The answer is that it is not enough! They also need to know by how much. They need to know, in other words, the responsiveness (or sensitivity) of sales (quantity demanded) to price changes. The reason is that for the businessperson, what is important is the impact of prices changes on total revenue. In order to measure this responsiveness of quantity to price changes and ultimately the impact on total revenue economists have devised the concept of elasticity. It is defined as: elasticity = (% change in quantity) / (% change in price) = % Q / % P (where stands for change in ) To find the percentage change in quantity (or price) we divide the change in quantity (or price) by the level of quantity (or price): i.e, Q / Q (for quantity) and P / P (for price). We can therefore rewrite the expression for price elasticity as: E P = ( Q / Q) ( P / P) or E P = ( Q / P) X (P / Q) Calculating Elasticity Looking at the graph below lets see how we calculate elasticity. Lets take for instance the case of moving from point A to point B. The percentage (or proportionate) change in quantity (from 2 unit to 4 units) is 100%. Thus the value of the numerator in the elasticity expression is 100. The percentage change in price (from 5 to 4) is -20%, thus the value of the denominator is 20. Therefore, the price elasticity is: 100 / -20 = -5 Note that since price and quantity move in opposite direction for the majority of goods (normal goods), the value of price elasticity of demand usually has a negative value since either the denominator or the numerator would have a negative value. A result of greater than 1 denotes a price elastic good and a result of less than 1 denotes a price inelastic good (disregarding the negative sign). 1

2 Calculating Elasticity Demand Schedule Point P Qd Ep A B C A B D E C 4 D 2 E Quantity 5 A very important point becomes evident from the graph above. Although we often talk of goods being price elastic or price inelastic, elasticity is different at each point on the demand curve. On a linear (straight-line) demand curve, elasticity is greater than one on the portion of the curve above its geometric mid-point, and less than one on the portion below the geometric midpoint. E lasticity for a Linear C urve The price elasticity varies along the length of a straight-line dem and curve. 10 Elasticity P o in t A Ep -5 8 B C D E 2 A Elastic B C D Unitary Elastic Inelastic E Q uantity 7 You also have to understand that elasticity is different as we either move up or down by the same quantity. i.e. the price elasticity when moving from 4 to 5 will be different than the elasticity when moving from 5 to 4. We calculated elasticity above when moving from 5 to 4 (point B) to be 5. When we now move in the opposite direction, that is, from 4 to 5, the value of elasticity is now 2. Do the calculations! To avoid this complication, we usually use the mid-point (average value) of quantity and price. In the example above, the value of price would be 4.5 (the average or mid-point of 5 and 4), and in the case of quantity it would be 3 units (the average of 2 units and 4 units). Elasticity and Total Revenue (or Consumers Expenditures) Let us introduce at this stage the concept of total revenue. Simply stated, total revenue is quantity sold times the average price of the units sold (TR = P x Q). Revenue is more important than price alone (or quantity alone). Leaving aside for now the question of how costs change with output (this will be covered later in the course), elasticity is the factor that will determine whether a price change brings in more revenue or less. This is why suppliers are very interested in it. 2

3 Would it be better for businesses (in terms of higher revenue) to sell goods at high prices? Or is it better to undercut the competition and sell at low prices? The first impulsive answer would perhaps be that high prices bring in more revenue (and inevitably more profits) for businesses. This would certainly be true if higher prices do not affect the quantity demanded! But as shown above in the table, if the increase in price brings a proportionately higher reduction in quantity, then the result would be an unwelcome drop in revenue. In some situations a price rise may cause a fall in TR, and in other cases a price rise may cause a rise in TR. We can identify the goods that behave in the former case as price elastic goods (in the specific price range being examined) and the latter as price inelastic goods. The relationship between price changes and total revenue under different elasticity conditions is shown below: Elasticity and Total Revenue Assume a price reduction (1) Elastic demand: Increase in revenue (due to more sales, Q) will exceed the fall in revenue (due to fall in P) total revenue will rise. (+)TR > (-)TR (+)TR < (-)TR (2) Inelastic demand: Increase in revenue (due to more sales, Q) will be less than the fall in revenue (due to fall in P) total revenue will fall. 9 The table below summarises the final impact on revenue from price increases or price declines under elastic, inelastic, and unitary elastic conditions. The direction of the arrow point to the direction of change of total revenue. Relationship Between Elasticity & Revenue Elastic Demand Unitary Elastic Demand Inelastic Demand Increase Decrease 8 What products would consumers still purchase despite a price rise? In general, these would include alcohol, cigarettes, gasoline and food (necessities). If suppliers know that consumers will continue to buy certain goods, what will be their attitude towards price? 3

4 Determinants of Elasticity Below we provide a summary of the various factors that determine the value of price elasticity: Demand for a commodity will be more elastic if: It has many close substitutes It is narrowly defined EXAMPLE: consumers can readily substitute one brand of detergent for another if the price rises,so we expect demand to be elastic. But if all detergent prices rise, the consumer cannot switch, So we expect demand to be inelastic More time is available to adjust to a price change. Demand thus tends to be more elastic in the long run, but relatively inelastic in the short run. is a big percent in the overall budget of consumer To verify that price elasticity is different in the short-run and in the long-run for the same goods, look at the table below which shows estimates for a number of product categories in the United States. Note that for some products, the difference is dramatic, whereas for some others there is no significant difference. SR & L R P rice E lasticities in U S Commodity Radio & TV Repair Motion Picture Tobacco Products E le ctricity (H o u se h o ld ) Bus Transport (local) Medical Insurance G a so lin e Stationery SR Elasticity LR Elasticity Cross- Elasticity Cross-price elasticity measures the responsiveness of quantity of one product to changes in the price of another related (substitute or complement) product. It is defined as the percentage change in quantity demanded of good A as a result of a percentage change in the price of good B. The expression for cross-price elasticity is: E AB = % Q A / % P B For instance, knowing the cross-price elasticity, we can determine by how much the demand for Big Mac is affected (% Q A ) when the price of Burger King s Whopper changes (% P B ). Note that a positive value for the cross-price elasticity would indicate that the two goods in question are substitutes, whereas a negative value would indicate that they are complements. Can you explain why? Income Elasticity Income elasticity measures the responsiveness of quantity to income changes and can be defined as the percentage change in quantity demanded as a result of a percentage change in income. It is expressed as: E Y = % Q / % Y (where Y denotes Income) Income elasticity is relevant to the concept of normal and inferior goods introduced in Chapter 3, as is the distinction between luxury goods and necessities. Normal goods have positive income elasticity, whereas 4

5 inferior goods have negative income elasticity. An income elasticity greater than one is indicative of a luxury good, whereas an income elasticity of between 0 and 1 is characteristic of necessities. & Incom e Elasticities for A irline Travel Type of Ticket Elasticity Incom e Elasticity First Class Regular Economy Excursion fare Elasticity of Supply Elasticity of supply--the percentage change in quantity supplied as a result of a percentage change in the price of the good. 18 E S = % Q S / % P (where Q S denotes quantity supplied) As in the case of demand, there may be two extreme cases: that of totally inelastic supply where a price change leads to no change in quantity (E S = 0), and the one of totally elastic supply where supply is totally elastic at one price (E S = ) where a slight reduction in price would bring quantity to zero. Of course, the normal situation would be the standard upward-sloping supply curve, where there is a positive relationship between quantity and price changes, and consequently elasticity of supply is some positive value (E S > 0). Elasticity of Supply P ε = 0 ε <1 ε >1 ε = infinity 45 0 Q 22 Elasticity of Supply is positively related to the time of adjustment. Thus, in the long-run supply elasticity is larger than in the short-run. ε LR > ε SR 1. New and more productive (efficient) processes are developed 2. More resources are attracted in the industry as Q increases (new firms, growth of existing ones 5

6 References for further reading: Bade, R. and Parkin, (2007). Foundations of Economics 3 rd edition (Pearson Education). Begg, D., Fischer, S. and Dornbusch, R. (2005). Economics 8 th edition (McGraw-Hill). Mankiew N. Gregory (2007). Principles of Economics 4 th edition (Thomson, South-Western). McConnel C. and S. Brue (2005). Economics 16 th edition (McGraw-Hill). Miller, R.L (2006). Economics Today 13 th edition (Pearson Addison Wesley). Sloman John (2006). Economics 6 th edition (Prentice Hall). 6