Chapter 6  -  Extensions of Demand and Supply  Analysis - Elasticity

Introduction:

    This chapter is the natural follow-up to Chapter 3 and may well be the most important chapter we cover in the first half of the course.  The concept of "elasticity" will appear over and over again, so getting a good grasp in the beginning will make it a lot easier down the road.  Conversely, failure to master this idea here will surely haunt you down the road.

    Don't let the terminology confuse you.  "Elasticity" simply is a measure of  responsiveness or sensitivity of quantity demanded or quantity supplied to a change in one of the independent variables that affect quantity, primarily price.  The chapter will deal primarily with price elasticity of demand and supply, but also will expose us to both income elasticity of demand and cross elasticity of demand.

Price Elasticity of Demand:

    Chapter 3 introduced us to the Law of Demand which simply refers to the observed inverse relationship between the price of a good and the quantity demanded.  It tells the direction of the response to a change in price, but nothing about how much quantity demanded will change in response to a given change in price.  In other words, how sensitive or responsive is quantity demanded to a change in price.

    Of course, the most logical way to measure the relationship between these two variables would be to measure the slope of the demand schedule (curve). 

                                            change in quantity demanded (rise)

                     slope  =        ______________________

                                                      change in price (run)

 

The problem with this approach is that altering the units of measurement will change the slope of the demand schedule.  To overcome this problem, it is customary to use percentage rather than absolute changes.  So,  price elasticity of demand simply becomes the ratio of the percentage change in quantity to the percentage change in price, or:

                    

                    Ed  =   _____________________

                                            

 

 

 

 

 

Interpreting Ed:

Ed > 1   -  Demand is price elastic

Ed  < 1   -  Demand is price inelastic

Ed =  1  -  Demand is unit elastic

Ed =  0  -  Demand is perfectly inelastic

Ed = infinity  -  Demand is perfectly elastic

 

Midpoints formula:  Because we have chosen to use percentage changes, the same absolute change in price would be a different percentage price depending on whether price increased or decreased.  (If price increases from $4 to $5, it would be 25%.  but if price falls from $5 to $4, the percentage change would be 20%).  To overcome this nasty little problem, we calculate the absolute change in price as a percentage of the average of the old and new price. Likewise, we calculate the absolute change in quantity as a percentage of the old and new quantity.

 

    Ed  =   _____________________

 

An additional result of our use of percentages is that on any straight-line demand curve, there will be a segment or range of prices over which demand will be price elastic and a range over which demand will be price inelastic.  This is a function of the arithmetic properties of the price elasticity measure.  Specifically, in the upper left segment of any demand curve, the percentage change in quantity is large because the original quantity is small, and the percentage change in price is small because the original price is large.   Conversely, in the lower right segment, the percentage change in quantity is small because the original quantity is large, and the percentage change in price is large because the original price is small. See Figure 6.3

 

 

 

 

 

Total Revenue test for determining price elasticity/inelasticity of demand:

So, here's the rule!!  If total revenue changes in the opposite direction from price, demand is price elastic.  If total revenue changes in the same direction as price, demand is price inelastic.

Now, the rule is nice, but of little use if you don't understand why.  Read and understand the rationale on pages 108 - 110. 

    

 

Determinants of price elasticity:

Number of close substitutes:

 

Necessity or luxury:

 

Proportion of consumer's budget:

 

Time:

 

 

 

Price elasticity of supply:    We will not spend much time on supply, because everything we said about price elasticity of demand applies to supply, except determinants.  Price elasticity of supply is determined by the market period or time.  In some cases, sellers are able to respond very quickly to a change in price. But for some sellers, changing output takes time and in some cases, sellers are unable to change output (see text example of the tomato farmer).

 

 

 

 

 

 

Cross-elasticity of demand:  Measures the responsiveness of quantity demanded of one good to a change in the price of a related good (substitute or complement).

 

                    Exy  =    ________________________

 

 

The Rule:  If the coefficient is positive, the two goods are substitutes and the larger the positive coefficient the greater the substitutability.   If the coefficient is negative, the two goods are complements and the larger the negative coefficient, the stronger the complementarity.

 

 

Income elasticity of demand:  Measures the responsiveness of quantity demanded to a change in consumer incomes.

 

                    Ei   =    ____________________________ 

 

 

The Rule:    If the coefficient is positive, the good is a normal good.  If the coefficient is negative, the good is an inferior good.

 

 

 

 

 

 

 

Elasticity application exercises:

  1.                  If the price of peanuts falls from $3 to $2 per bushel and that, as a result the total revenue received by farmers changes from $16 to $14 billion, what assumption can we make about the price elasticity of demand over this range of prices?

  2.                  The Metropolitan Transit Authority recently announced a 50% increase in the fare price.  The administrators said they needed to increase revenue in order to cover rising costs.   Explain the rationale for this decision.                                                                                         

   3.                  A gasoline station near Williams-Brice Stadium parks cars on its lot to make money on  game days.  Last year, it charged $4.00 and parked an average of 1000 cars.  This year, it raised the price to $5.00 and parked only 850 cars.  Did the station owner make a good economic decision?  Explain.

4.                  The following data shows the relationship between price and quantity demanded at four different prices:

                        P = $11,                     Qd = 16

P = $9,                        Qd = 24

P = $7,                        Qd = 32

P = $5,                        Qd = 40

 

                   Using the midpoints formula, what is the price elasticity of demand between:

                    (a) $11 and $9; (b) $9 and $7; (c) $7 and $5.

 

5.                   Block’s Department Store sells 500 bottles of perfume at a price of $7.00.  An increase in shipping costs causes the price to increase to $9.00 and at that price, Block’s only manages to sell 460 bottles.  What is the price elasticity of demand over this price range?

 

6.        You are a consultant to the governor.  During his campaign, he promised to cut consumption of cigarettes by 20 percent.          He has decided that the only way to accomplish his goal is to raise the price of a pack of cigarettes by imposing a state excise tax.  You are tasked with recommending the amount of the tax.  If a pack currently sells for $2.50, and the coefficient of price elasticity of demand is .25, what will be the new price per pack after your tax? 

 

 

 

 

    7.    The price of widgets increases from $15 to $20.  During the same period, sales of widgets falls from 5000 to 2000.  Using the midpoints formula, calculate the coefficient of price elasticity of demand over this price range.

 

 

    

    8.    Sunrise Pet Store sells both dogs and cats.  In August, the average price of cats increased from $15 to $20.  During the same period the sale of dogs increased from 23 dogs to 35.  Are dogs and cats close substitutes among pet buyers?

 

 

 

    9.    The current price of yoyos is $1.20.  If  Ed  =  .30, how much will the price have to decrease in order to increase sales by 10%?

 

  10.    Assume that good X is classified as a luxury good. Raising the price would have what effect on revenues?

 

 

 

 

 

 

 

 

 

Application Questions:

 

Responses to the following are to be in essay form and printed (on a printer).  Include graphs if you feel it is necessary to make your response clear.  You are prospective business leaders and I expect your submission to be clear, concise and professional.  

 

I.     Federal and state governments often seek to raise tax revenue by levying excise taxes on specific products.  What economic factors should be considered in determining which products will raise the most revenue?  Be sure to provide examples.   

 

II.    Discuss the pros and cons of legalizing a drug such as cocaine or heroin from an economic perspective using the concepts of demand, supply and price elasticity.

 

III.    During the summer vacation season the demand for gasoline increases by ten percent.  In response, the price of a gallon of regular gas increases from $3.00 to $4.50.  Using the concepts of demand, supply and price elasticity, explain how this relatively small increase in demand could result in such a large increase in the short run price.