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Eon340 problems on Elasticities
1. The price elasticity of demand for chicken is estimated to be – 0.65. If the price of
chicken increased by 6 percent, what will be the expected percentage decrease in
the quantity of chicken sold?
2. The average price for personal computers has recently decreased from BD300 to
BD250. As a result, the quantity of personal computers bought has increased by 20
percent. What would be the price elasticity of demand for personal computers?
3. The demand for Penn's Oil motor oil can be characterized by the following point
elasticities: price elasticity = -2.5, cross-price elasticity with Value Lean motor oil = 1.5
and income elasticity = 0.75.
Indicate whether each of the following statements is true or false, and explain your
answer.
(a) A price increase for Penn's Oil will decrease both the number of units demanded
and the total revenue of sellers.
(b) The cross-price elasticity indicates that a 2% increase in the price of Value Lean
oil will cause a 3% increase in Penn's Oil demand.
(c) Demand for Penn's Oil is price inelastic and the motor oil is a superior good.
(d) Falling Value Lean prices will definitely increase revenues received by
manufacturers of both brands of oil.
(e) A 0.9% price reduction for Penn's Oil would be necessary to overcome the effects
of a 3% decline in income.
4. Given the demand for bicycles in Holland Q = 2000 + 15Y – 5.5P, where Y is income
in thousands of Guilders, Q is quantity demanded in units, and P is price (Guilders per
unit). When P is 150 Guilders and Y is 15,000 Guilders, determine the following:
(a) Price elasticity of demand. (b) income elasticity of demand
5. The manager of a supermarket accidentally miss-marked the price of 10-killo bag of
rice at BD4.38 instead of the regular price of BD5.18. At the end of a week, the store's
inventory of 200 bags of rice was completely sold out. The store normally sells an
average of 150 bags per week.
(a) What is the store's arc elasticity of demand for rice?
(b) Give an economic interpretation of the numerical value obtained in (a) above.
6. Hanna Corporation markets a compact microwave oven. This year they sold 23,000
units at $375 each. Per capita disposable income this year was $6,750. Hanna
economists have determined that the arc price elasticity for this microwave oven is 1.2.
(a) Next year Hanna is planning to lower the price of the microwave oven to $325.
Forecast sales volume for next year assuming that all other things remain equal.
(b) However, in checking with government economists, Hanna finds that per capita
disposable income is expected to rise to $7,000 next year. In the past the company
has observed an arc income elasticity of +2.5 for microwave ovens. Forecast next
year sales given that the price is reduced to $325 and that per capita disposable
income increases to $7,000. Assume that the price and income effects are
independent and additive.
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7. LG Corporation is considering lowering the price of its TV from $800 to $600. The LG
has estimated that the price elasticity of its TV to be -2 over this price range.
Presently the LG sells 1000 TV units per month.
(a) What will be the new quantity sold if the price is lowered to $600?
(b) What additional information does LG need to know before it can determine whether
or not a price decrease will increase the company's profit?
(c) Suppose that after LG lowers its price, its competitor, Sony, lowers price of its TV from
$900 to $800. The cross elasticity between the two firm's TVs is estimated to be +0.5.
What will be the effect of Sony's price decrease on the quantity sold by LG?
8. Kodak currently sells its camera at $90 and sells 200 cameras per month. A close
competitor, Olympic, has cut the price of a similar camera it makes from $100 to $80.
Suppose the cross elasticity of demand between the two cameras is 0.4.
(a) What impact, if any, will the action by Olympic have on total revenue generated by
Kodak, if Kodak leaves its current price unchanged? (Round your answer).
(b) Now suppose that Kodak decided to sell the same quantity as it used to sell at $90.
What would be the new price if price elasticity of demand between $90 and the new
price is -2? (Round your answer).
(c) Is the new price better for Kodak if its goal is to increase revenue? What if it wants to
increase profits?
9. A firm is selling a good with a marginal cost of BD70. Management think that demand
elasticity is -2.75. What price should the firm set in order to maximize profit?
10. Suppose that the price elasticity of demand for wheat is known to be -0.75. Will a good
wheat crop (which increases the supply of wheat) be likely to increase or decrease the
revenues of farmers? Carefully explain.
11. The income elasticity for most staple foods, such as wheat, is known to be between
zero and one.
(a) As incomes rise over time, what will happen to the demand for wheat?
(b) What will happen to the quantity of wheat purchased by consumers?
(c) What will happen to the percentage of their budgets that consumers spend on wheat?
(d) All other things equal, are farmers likely to be relatively better off or relatively worse
off in periods of rising incomes?
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Eon340 problems on Elasticities; Answers:
1. %Q = Ep (%P) = -0.65(0.06) = -3.9%.
2. %P = (250-300)/((250+300)/2) = -18.18
EP = %Q /%P = 20%/18.18% = -1.1.
3. (a) True. A price increase will always decrease units sold, given a downward sloping
demand curve. The negative sign on the price elasticity indicates that this is indeed the
case here. The fact that price elasticity equals -2.5 indicates that demand is elastic with
respect to price, and therefore that a price increase will also decrease total revenues.
(b) True. The positive cross-price elasticity indicates that a 2% increase in the price of
the substitute good Value Lean will have the effect of increasing Penn's Oil's demand
by 3%.
(c) False. Demand is price elastic (see part a). Because the income elasticity is positive,
Penn's Oil is a normal good. However, because the income elasticity is less than one,
Penn's Oil demand is not superior good.
(d) False. A positive cross-price elasticity indicates that the two motor oils are
substitutes. Therefore, falling Value Lean prices will decrease the demand for Penn's
Oil and resulting revenues for its manufacturers. However, we have no information
concerning the own price elasticity of demand for Value Lean, and therefore do not
know the effect of falling prices on its revenues.
(e) True. A 0.9% reduction in price will cause a 2.25% increase in the quantity of Penn's
Oil demanded. A 3% decline in income will cause a 2.25% fall in demand. These
changes will be mutually offsetting.
4.
(a) EP = (∂Q/∂P)(P/Q) = (-5.5)(150/1400) = -0.59
(b) EY = (∂Q/∂Y)(Y/Q) = (15)(15/1400) = 0.16
5. (a) EP = %Q
%P
Q1 = 150
ED 
= (Q2  Q1)/(Q2 + Q1)
(P2  P1)/(P2 + P1)
P1 = BD5.18
Q2 = 200
(200  150) /(200  150)
50 / 350

(4.38  5.18) /(4.38  5.18)  80 / 9.56
P2 = BD4.38
= 1.71
(b) A 1% increase in price will result in a 1.71% decrease in quantity demanded.
%Q
Q Q
P P
D , or E  2
1 2 1
6. (a) E D 
D
%P
P2  P1 Q 2  Q1
Q1 = 23,000
P1 = $375
P2 = $325
Q 2  23,000
325  375

or Q2 = 27,312.5 units
325  375
Q 2  23,000
P2  P1
325  375
(b) Price effect: %QD = ED%P  E D 
=
 1.2 
(P2  P1) / 2
(325  375) / 2
 1.2 
.1714 (=17.14%)
Income effect: %Q = EY%Y  E Y 
Y2 = 7,000
Y1 = 6,750
Y2  Y1
(Y2  Y1) / 2
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%Q  2.5 
7,000  6,750
= + .0909 (= 9.09%)
(7,000  6,750) / 2
Net effect = Price effect + Income effect = .1714 + .0909 = .2623 (=26.23%)
Using the initial quantity (Q1 = 23,000) as the base in computing the percentage change
yields:
Q2 = Q1 (1 + Net effect) = 23,000 (1 + .2623) = 29,033 units
Using the average quantity [(Q1 + Q2)/2] as the base in computing the percentage
change yields:
Q 2  Q1
(Q 2  Q1 ) / 2
Q 2  23,000
.262 
or
(Q 2  23,000) / 2
%Q 
Q2 = 29,934 units
7. (a) Q2 = 1800.
(b) Information on TC.
(c) Q2 = 1697.
8. (a) TR decreases by $15,300.
(b) $86
(c) Good, since TR increases by $7,300, but profit is indeterminate since TC is not
known.
9. The optimal price rule is: P = [EP/(1+ EP)]*MC. Therefore P = [-2.75/(1-2.75)]*70 =
BD110.
10. A good wheat crop that increases the supply of wheat will cause the equilibrium price
of wheat to decrease (and quantity to increase). Since demand is inelastic, total
revenues will fall, as the percentage change in quantity will be less than the
percentage change in price.
11. (a) Demand will increase, since wheat has a positive income elasticity.
(b) The quantity of wheat purchased will increase.
(c) The percentage of consumer budgets spent on wheat and other staple goods will
fall, since the percentage change in the demand for wheat will be less than the
percentage change in income.
(d) Farmers are likely to be relatively worse off, since the demand for what they are
selling will be rising less rapidly than the demand for other goods that they are
likely to purchase.