Introduction to Microeconomics. Elasticity

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1 Introduction to Microeconomics ity Introduction In economic analysis and various business models we are always concerned with the effect one variable has on another. Understanding the impact one variable has on another allows for a more optimal allocation of resources. The concept of elasticity is central to Neo-classical economic theory. In particular elasticity is used in consumption analysis and the permanent income hypothesis, marginality, distribution of wealth and understanding the firms theory of production and revenue (mark up rule). Another use for elasticity is the evaluation of market impacts on consumer and producer surplus. There are many types of elasticity such as price elasticity of demand and supply, income elasticity of demand, elasticity of factors of production, elasticity of intertemporal substitution, cross price elasticity of demand and elasticity of scales of production. Although previous economists had stumbled upon this concept it was formalised and developed by Alfred Marshall. In particular he defined the price elasticity of demand in his works rinciples of Economics (189) where he examined the responsiveness of goods and used differential calculus to calculate elasticities. In this document we focus our attention on the most useful applications of elasticity mentioned above. General efinition The method for calculating the elasticity is the same for all types. Basically we are always dividing percentage changes of two variables. In general terms the elasticity of y with respect to x is given by the following, E x,y = lny lnx = y x %Δy %Δx We sometimes say E x,y as the x elasticity of y. For example E p,q is the price elasticity of demand. The approximation becomes exact in the limit as the change become very small. o when the change is large the approximation is less accurate. In addition the elasticity can vary at different points along the curve because of it being a percentage and percentage changes are not symmetric. However we usually the approximation because it is simple to use and generally accurate for small changes. We cover oint elasticity and Arc elasticity in below under the section ity of emand. If the elasticity produces a result of one we say that the variable has a unit elasticity to changes in the other variable. This means that if x changes by a certain percentage, the y variable will change proportionately by the same percentage. If the elasticity is greater than one we say that y is elastic to a change in x and this means that a change in x will result in a greater change in y. Likewise for an elasticity of less than one we say that y is inelastic to changes in x. This means that y changes by less than the change in x. 1

2 E x,y = erfectly inelastic 1 > E x,y > Inelasitic E x,y = 1 > E x,y > 1 Elasitic E x,y = erfectly In econometric analysis where the functional form is logarithmic the coefficients are the elasticities. In other words if the dependent and explanatory variables are both natural logarithms then coefficient of x is the elasticity of y with respect to x (the x elasticity of y). It is important to understand that the sign of the quotient can be important for certain types of elasticity. Generally the lowest the elasticity can be is zero which is perfect inelasticity. When the maximum of one is reached there is perfect elasticity. In these cases we know the elasticity is always positive or negative and therefore just use the absolute value of the quotient for simplification (as shown in the general formula). For example the price elasticity of demand is almost always negative. In cases where the relationship between the two variables can change we do not use absolute values but instead use the signs. A good example of this is the cross price elasticity demand, the change in demand for one good from the change in price of another good. A positive sign would infer that the goods are substitutes because as the price for good x increases the demand for good y increases. Following this logic a complimentary good would have a negative sign. ity of emand Whenever one is dealing with demand curves it is always useful to understand and know how elastic demand is to changes in other variables. ity of demand refers to the level of sensitivity of demand for a good is to changes in another variable such as quality, income or price. If demand is highly elastic then it moves a lot, meanwhile if demand is not elastic, or inelastic then it is less flexible and does not move much. Two popular types of demand elasticity are price elasticity and income elasticity of demand. rice ity of emand Essentially the price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. That is, E % d % Almost all goods have a negative price elasticity of demand except the good which do not conform to the law of demand such as Veblen and Giffen goods which have a positive price elasticity of demand. These goods have a price elasticity of demand greater than zero. All normal goods will have a price elasticity of demand between minus one and zero. To avoid confusion we use the negative sign for price elasticity of demand to illustrate the inverse relationship between price and quantity demanded. This avoids confusion. 2

3 E x,y = erfectly inelastic emand 1 < E x,y < Inelasitic E x,y = 1 < E x,y < 1 Elasitic E x,y = erfectly erfectly erfectly 1 ity of demand means the percentage change in quantity demanded is less than the percentage change in the price. ity of demand implies that a percentage change in price results in a greater percentage change in quantity demanded. ity Along the Linear emand Curve < E < 1 E = 1 1 < E < As we move down the demand curve the elasticity becomes less elastic then inelastic. erfectly erfectly E = E = 3

4 Relatively Relatively When we use a linear demand curve the elasticity will change as we move down the curve. ifferent points along the curve have different elasticities because although the absolute rate at which quantity demanded and prices change is constant, the proportional change is not. For nonlinear curves the elasticity generally changes as we move along the curve. However there are exceptions where the elasticity does not change. We include nonlinear curves for completeness and toreinforce that fact that the same fundamentals generally apply to elasticity along nonlinear curves E = 1 Relatively Relatively 1 < E < < E < 1 Note that the perfectly inelastic and elastic will be linear so we do not repeat them. The price elasticity of demand: As briefly mentioned earlier the price elasticity of demand has two shortcomings. Firstly it is a percentage while the demand curve is based on units used for price and quantity. econdly, percentage changes are not symmetric because the percentage change depends on which value is chosen as the starting value. For instance the quantity demanded could increase from 2 to 3 units which is a 5% but if the quantity demand changes from 3 to 2 units this is a 33% decrease. The following two measures of price elasticity limit these problems. 4

5 E p,q q % d 1 q % = q p 1 p p oint rice ity of emand: This approach minimises the difference between the starting and ending prices and quantities. This approach uses calculus to calculated the elasticity for a infinitesimal change in the price and quantity at a given point on the demand curve. The second term is the derivative of quantity with respect to price and the first term is that points price divided by its quantity. Hence the term point price elasticity of demand. oint price elasticity assumes that the demand function is known so the derivative can be calculated. E p,q = q q p Arc ity of emand: Another solution to the problem of asymmetry in percentage changes is to use the arc elasticity. The arc elasticity computes the average of the two quantities. o it is the average elasticity for that section, the arc between two points. We call the formula a "midpoint formula" because we the average of the straight line connecting two points in an arc, which is the midpoint. It is important to remember because we are taking the midpoint of a straight line there is an assumption of linearity and as such this method becomes inaccurate if the demand curve has a high degree of curvature over that section. Example 1 rice ity of emand E p,q = p + p 1 % d q + q 1 % uppose that the price of bread is $4. but increases to $5.. This is an increase of 25%. This change in price causes demand to fall from 1 loafs a week to 9 loafs a week sold. This is a decrease of 1%. Therefore using the formula above we have; 9 1 % d E p,q = % = 1 = 1% % =.4 We omit the point price elasticity but this could be easily done by creating a simple demand function and taking the derivative. Arc elasticity would not be ideal here as the relationship is most likely nonlinear. The Effect of rice ity on Total Revenue The total revenue is simply the price multiplied by the number of items sold. From the graphs below we notice that as prices increase in the elastic range the revenue earned decreases because if the good is elastic then people will not consume the same quantity when the price increases. If prices decrease in the elastic range the total revenue increases. In the inelastic range the revenue falls when prices fall in the inelastic range of the demand curve. This is because although the price is low people do not purchase more of it, because the demand is inelastic so people will usually buy approximately the same amount as they 5

6 demand at other prices. If the price increases when the product is inelastic the total revenue increases because the you gain a higher price for each unit which is greater than the loss from selling less units because the price has increased. o as price decreases (increases) in the elastic (inelastic) range revenue increases. At unit elasticity revenue is maximized. ity and Total Revenue Revenue E In all these scenarios there is a price effect and a quantity effect. An increase in price will increase (decrease) revenue for an inelastic (elastic) good. If the price increases (decreases) there will be less (more) units demanded. The Income ity of emand The income elasticity is the responsiveness of demand for a good to a change in the income of those demanding it. As with the price elasticity of demand, the income elasticity of demand is also a quotient of percentage changes. In this case it is the percentage change in the quantity demanded divided by the percentage change in income. For most goods there is a positive relationship between income and demand. A positive income elasticity of demand is associated with normal goods where an increase income leads to an increase in demand for the good. If the income elasticity is greater than one it is highly elastic and is deemed a superior good or luxury good. An inferior good where an increase in income leads to fall in demand have an elasticity less than one. A zero income elasticity of demand (inelastic) means that an increase in income will have no impact on the demand for that good. These goods are called stick goods. IE i,q q % d 1 q % Inc = q i 1 i i 6

7 Example 2 In a hypothetical example a product, say LC Televisions has a set of potential customers. The consumers income rises from $5, to $55, due to a uniform wage rise. As a result they purchase LC sales increase from 5 to 6 units. This implies an income elasticity of demand for LC televisions of 2. IE i,q q % d 1 q % Inc = q i 1 i i = =.2.1 = 2 Example 3 uppose Michael purchases 1 oranges a week and earns $5 per week. Then Michael is made redundant and has to live off unemployment benefits of $2 a week. When he is unemployed he still purchases 1 orange per week. IE i,q q % d 1 q % Inc = q i 1 i i = =.6 = In this case income elasticity of demand is perfectly inelastic. The change in income has no effect on Michaels demand for oranges. Example 4 In China where incomes have grown significantly in the past decade the income elasticity of demand for rice could well have an elasticity less than one. This means as income increases the demand for the product decreases proportionately. In this sense it could be classed as an inferior good compared to say meat or wine which has a very high income elasticity of demand. 7

8 ity of upply The elasticity of supply is analogous the elasticity of demand explained previously. Like the elasticity of demand the elasticity of supply can be the responsiveness of supply to other goods, the price of other goods E x,y = erfectly inelastic 1 > E x,y > Inelasitic E x,y = 1 > E x,y > 1 Elasitic E x,y = erfectly The price elasticity of supply is used as a measure of the responsiveness of the quantity of a good supplied to a change in its price or cost. The price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price. That is, E p,q q % s 1 q % = q p 1 p p The price elasticity of supply can be classified in the following ways. E x,y = erfectly inelastic upply 1 > E x,y > Inelasitic E x,y = 1 > E x,y > 1 Elasitic E x,y = erfectly erfectly erfectly 1 Notice that the relationship is positive between supply and price. This is because the supply curve has a positive slope. 8

9 ity Along the Linear upply Curve 1 > E > E = 1 > E > 1 As we move up the supply curve the elasticity become lesss elastic then inelastic. E = 1 erfectly erfectly E = E = Relatively Relatively When we use a linear supply curve the elasticity will change as we move down the curve. ifferent points along the curve have different elasticities because although the absolute rate at which quantity supplied and prices change is constant, the proportional change is not. For nonlinear curves the elasticity generally changes as we move along the curve. o as you move 9

10 up the supply curve you go from relatively elastic to inelastic just like the linear supply curve. However there are exceptions where the elasticity does not change. We include nonlinear curves for completeness and to reinforce that fact that the same fundamentals generally apply to elasticity along nonlinear curves Nonlinear E = 1 Nonlinear Relatively Nonlinear Relatively < E < 1 > E > 1 Note that the perfectly inelastic and elastic will be linear so we do not repeat them. eterminants of the rice ity of upply There are many factors which determine the elasticity of supply. ome of them are listed below. There are many factors that could be discussed but we limit it to a few determinants. Level of excess capacity: If the producer is operating below maximum they have the ability to quickly increase supply. Therefore the quantity supplied is very responsive to a change in price. The access to raw materials: If a product or the raw materials used to produce a good are not readily available it is likely to make the price elasticity of demand less elastic. For example goods in rural and remote areas may be inelastic because the raw materials need to be sourced from elsewhere and may take some time to arrive. Availability of time to produce: If the producer has a longer period of time to which they can respond to the price change the elasticity of supply will be greater. Basically this premise means that supply is more elastic in the long run relative to the short run. Complexity and length of production: If the process to produce a good is relatively simple and uses unskilled labour and little capital is used the price elasticity of supply is elastic. For instance much of the textile manufacturing in south east Asia is highly elastic 1

11 because it is very simple to increase labour when prices rise. If the good is produced through a complex labour and capital mechanism that is highly specialized the elasticity of supply will probably be less elastic. pecialized goods such as components used by NAA in a rocket or capsule are going to very inelastic. o even if NAA and the European pace Agency are willing to pay a contractor a higher price, supply would remain fairly unresponsive. Ability to switch factors of production: If a producer can switch their productive process to goods which have a higher demand then price elasticity of supply is relatively elastic. However if the producer is highly specialized and can only produce one particular product or range then the price elasticity of supply for this good will be relatively inelastic. The Impact of ity of upply and emand on the Tax Incidence When demand is less elastic than supply the tax burden is placed more on the consumer than the producer. Tax Incidence and Relatively E rice with tax with tax without tax without tax C tax incidence tax incidence tax per unit q 1 q ty Tax Incidence and Relatively E rice with tax with tax without tax without tax C tax incidence tax incidence tax per unit q 1 q ty From the above diagrams it is easy to see that the elasticity of demand determines whether the tax burden falls on the producer or consumer. If the good is inelastic consumers can not reduce demand easily so the consumer bears the majority of the burden. When demand is elastic consumers are less willing to purchase the good once the tax is imposed. As such the 11

12 producer bears the majority of the burden. Also the difference in quantities demanded shows the difference the elasticity of demand can have on revenue. 12