ECON1101: Week 5 Tutorial 4

7/30/2019 ECON1101: Week 5 Tutorial 4

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Chapter 4 Elasticity

Answers to review questions

1 Price changes affect quantity demanded for two reasons: they alter the attractiveness ofsubstitute goods and they alter the real value of consumers income, or their purchasing

power. These are called the substitution and the income effects of a price change. Thesecond effect grows larger as the share of consumers budgets spent on the good

increases. For example, a 10 per cent change in the price of salt, a good on which mostconsumers spend very little, will have a small effect on the purchasing power of aconsumers income. At the other extreme, a similar change in price for a good such as

housing, which comprises a large part of most peoples income, will have a large effect

on the purchasing powerof a consumers income. A consumer will find it worthwhileseeking ways of mitigating the effect of the increase in the price of housing, but notsalt.

2 Elasticity of demand at any point on the demand curve is the pricequantity ratio at thatpoint (P/Q) times the reciprocal of the slope of the demand curve (1/slope). The slope,and hence its reciprocal, is constant along a straight-line demand curve, but the pricequantity ratioand hence price elasticity of demand declines as we move down thecurve.

3 If the demand for a good is inelastic with respect to its price, an increase in price willlead to an increase in total expenditure. This is because a percentage change in price ofgiven magnitude results in a smaller percentage change in quantity. Consequently the

product of price and quantitythat is, total expenditureincreases.

4 Given the universality of the law of demand, the algebraic sign of the elasticity ofdemand for a good with respect to its own price is always negative. In this case,knowing that the sign is negative conveys no useful information. In contrast, theelasticity of demand for a good with respect to the price of another good can be either

positive or negative, so it is important to keep track of the sign. A positive sign tells usthat the two goods are substitutes; a negative sign that they are complements. Likewise,the sign of the income elasticity of demand tells us whether a good is normal (positivevalue) or inferior (negative value).

5 To increase the quantity of output supplied when price rises, firms need to increase theamount of inputs they buya time-consuming process for certain kinds of inputs. The

process can be speeded up, but only if the firm is willing to incur additional costs.

6 A price elasticity of demand of 0.5 means that a 1 per cent increase in the price ofbutter will lead to a 0.5 per cent fall in consumption. A 10 per cent reduction in butterconsumption would, therefore, require a 20 per cent increase in price. If, however, theelasticity of demand for butter were higher (for example, 2), butter consumption wouldfall by 10 per cent in response to a smaller 10 per cent increase in the price of butter.


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Answers to problems

1 For the demand curve shown, the slope is 1; therefore (1/slope) is also 1. The absolutevalue of the price elasticity of demand at any point on this demand curve is thus the

ratio (P/Q) at that point.

Point Elasticity

A Infinity

B 3

C 1

D 1/3

E 0

2 a

b Price elasticity of demand is calculated as (P/Q) (1/slope). When P = 3, Q = 9 and(1/slope) is 3. So elasticity = (3/9)3 = 1.

c If the price increases from $3.00 to $4.00, revenue will fall from $27 000 to $24000.

d Using the same formula as in part b, elasticity = (2/12)3 = 0.5.


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e If the price increases from $2.00 to $3.00, revenue will rise from $24 000 to $27000.


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3 To maximise revenue from the sale of tickets, price should be set at the midpoint of thedemand curve, P = $6/visit.

As shown in the graph below, demand is elastic above the midpoint of the demandcurve and is inelastic below the midpoint of the demand curve.

4 The price elasticity of a good generally increases with the number of substitutes it has.It is easier to substitute a Ford or Toyota for a Subaru than it is to substitute a bus ride,motorcycle or a skateboard for a car. Thus the market demand curve for cars is likely to

be less elastic with respect to price than the market demand curve for Subarus.

5 The more income a person has, the smaller a given expenditure will be as a proportion

of her overall budget, and hence the less likely she will be to respond dramatically to aprice change. Thus senior executives, the most highly paid of the three groups, shouldhave the least price-elastic demand curves for a professional membership. Students, theleast well paid, should have the most price-elastic demand curves.

6 The cross-price elasticity is calculated as the

(percentage change in Qsalsa/percentage change in Pcorn chips) =4/2 =2.

Since this cross elasticity is negative, the two goods are complements.

7 The expression for supply elasticity is (P/Q)(1/slope). Since the slope of this supply

curve over the price range $4 to $6 is P/Q = 2/3, the elasticity of supply at A is

(4/9)(3/2)=2/3. Using the same formula, the elasticity at B is (6/12)(3/2)=3/4.


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8 The inputs required to produce each sushi roll cost a total of $1.20, and this marginalcost is constant. The supply curve of sushi rolls is thus a horizontal line at P = $1.20.The price elasticity of a horizontal supply curve is infinity.

9 The absolute value of the slope of this demand curve is 1/3, so plugging in the P and Qvalues at point A into the elasticity formula, (P/Q)(1/slope), we have elasticity at A =(4/6)3 = 2. A 1 per cent price increase will thus translate into a 2 per cent decrease inthe quantity demanded. Total expenditure, which is (PQ), will thus now be(1.01P)(.98Q), which is approximately equal to .99Q. Therefore total expenditure willdecline by about 1 per cent.

10 What government officials failed to take into account was that people dont demand

electricity for its own sake, but rather as a means to accomplish other ends, such asproducing cooler air for their homes. By requiring people to buy air conditioners thatwere more efficient, the government effectively reduced the price of buying cooler air.If the demand for cool air is sufficiently elastic with respect to its price, people may buyso much more cool air that they end up using more electricity. This example highlightsthe fact that government policies may have unintended consequences and thateconomists must be skilled in recognising the way in which a knowledge of elasticitycan be used to predict the magnitude of the effect of changes in market conditions onmarket outcomes.


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ECON1101: Week 5 Tutorial 4