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Problem Set #4: Elasticity
Key Concepts
Elasticity of Demand = % change in Quantity Demanded
% change in Price
Income Elasticity of Demand = % change in Quantity Demanded
% change in Income
Cross Price Elasticity of Demand = % change in Quantity Demanded of X
% change in Price of Y
Price Elasticity of Supply = % change in Quantity Supplied
% change in Price
Formulas to calculate elasticity depending on information:
Elasticity of Demand = % Δ Qd
% ΔP
= (ΔQ)/Q
(ΔP)/P
= ΔQ * P
ΔP Q
= (1/slope)*P/Q
Arc Elasticity: Define P and Q in the usual formula as the average of the range
P = (P1+ P 2/2 and Q = (Q 1 Q )/2
Symbols: η = elasticity
ηd = elasticity of demand
ηy elasticity of income
ηxz = elasticity of X with respect to price of Z
ηs = elasticity of supply
Problems
1.a) What is the price elasticity of demand for peanuts if the quantity demanded of peanuts increases by
15% when the price of peanuts decreases by 10%?
b)What percentage change in price would cause a 12% decrease in quantity demanded given a price
elasticity of –0.75?
c) What is the point price elasticity of demand for refrigerators if a fallin price from $640 to $560
causes an increase in quantity demanded from 12,000 to 15,600 refrigerators?
2.a) Suppose that when the price of gasoline increases from $0.48 to $0.52 per litre, gasoline
consumption falls from 10.1 million litres per year to 9.9 million litres in a given town. Compute the
arc elasticity of demand for gasoline.
b) If the income elasticity of demand for a commodity is +0.5, is the commodity an inferior good?
Exactly what does an income elasticity of 0.5 mean?
3. The equations of the market demand and supply curves for potatoes are as follows:
P = 50 - 4.0 Q P = 25 + 1.0 Q (P is in cents/kilo and Q is in thousands of kilos)
(a) Graph the demand and supply curves and find the equilibriumprice and quantity. Note: Do not plot
the values but draw curves with appropriate intercepts and approximate slopes.
(b) Calculate the point elasticity of demand at: P = 40 cents ; P = 25 cents, P = 15 cents. As one moves
to lower prices, what happens to the "point elasticity of demand"? As one moves to lower prices,
what happens to the slope of the demand curve?
(c) Suppose that the government legislates a price floor of 32 cents per kilo as a farm support measure
and agrees to buy any surplus resulting from this program. Calculate the cost of this policy to the
government.
(d) Suppose a fungus destroys much of the potato crop and, as a result, the equilibrium price rises to
- 1 - Problem Set #4: Elasticity
40 cents per kilo. Calculate the "arc price elasticity" of demand between the original and the new
equilibrium prices. Willthe farm revenue rise or fallas a result of the crop failure?
4. You are an analyst employed by an automobile manufacturer that last year sold 50,000 compact
cars at $6,000 each. Your market research indicates that:
(i) price elasticity of demand for your cars is -3.0
(ii) income elasticity of demand for your cars is +0.7
(iii) cross price elasticity for your cars with respect to the price of a comparable car
made by a competitor is +1.2
a) Suppose that you expect a ceteris paribus decrease in average incomes of 5% this year compared to
last year. How many cars willyour company willsell this year?
b) Assume now that you do not think incomes willchange, but that you expect your competitor will
decrease price by 5%. Assuming that your company does not change the price of its cars, how
many cars would expect your company willsell this year?
c) Now estimate sales this year if the only change you expect is an increase in the price of your car to
$6,600.
5. The short-run market demand and supply curves for good X are as follows:
P = 100 - 2.0 Q P = 40 + 3.0 Q (P is in $ per unit)
(NB: Graphs are not necessary to answer the questions in this problem and are much less efficient
than algebra. A graph, though, may clarifyyour understanding)
a) Find the equilibrium price and quantity.
b) What is the equilibrium price and quantity due to a tax of $5 per unit on producers?
c) What is the arc elasticity of demand between the initial and after tax equilibria?
Is total revenue at the after tax equilibrium higher or lower than at the before tax equilibrium? Try
to answer the question before your calculate total revenue.
d) How much of the tax do consumers pay? How much of the tax do producers pay?
e) How would your answers to (c) change if the demand curve was vertical? horizontal?
How would your answers to (c) change if the supply curve was vertical? horizontal?
Given these results, what general conclusion can one make relating the relative elasticities of the
demand and supply curves to the fraction of the tax paid by consumers in the short run?
6. Suppose that the demand curve for carrots ( $/ton) is linear and has a slope of -0.2.
a) What is the elasticity of demand at equilibrium if supply intersects demand at P = $1,500 and Q =
5,000 tons?
b) Suppose that a carrot disease causes a shift in supply that results in a new equilibriumat P = $2,000
and Q = 2,500 tons. What is the arc elasticity of demand between the pre-disease equilibrium (part
a) and this new equilibrium?
c) i) If commodity Z has an income elasticity of -2.5, what type of good is good Z?
ii/ What is the percentage change in quantity demanded of good Z when income
increases by 10%?
iii)If commodity Z also has a price elasticity of Demand of +0.4, what type of good is Z?
d) The cross price elasticity of demand for good A given a change in price of good B is +0.25.
i/ What is A's relationship to B?
ii/ What is the percentage change in the quantity demanded of good A if the price of
good B falls $1 from $10 to $9?
e) What is the price elasticity of demand at the point where marginal revenue is zero?
What is the price elasticity of demand at the point where total revenue is at a maximum?
7. Look back at the milk diagram given in Question #1 of Problem Set #3.
- 2 - Problem Set #4: Elasticity
Suppose that the government abandons the price floor in favour of a subsidyto each farmer of
$0.40 per unit of milk produced.
a) Draw the impact of this program in the Demand/Supplydiagram.
b) What is the new equilibriumPrice and Quantity? Whyis Price not $0.40 below the original
equilibrium price?
c) How much does this program cost the government?
8. A student claims that a firm's total revenue always increases when there is an supply induced
increase in the price of its product. Brieflyexplain the truth or falsity of this statement.
9. A politician argues that the benefit of a per unit subsidy willaccrue entirely to producers if the
demand for a commodity is perfectly elastic and the supply curve is upward sloping.
Prove the truth or falsity of this statement by drawing a diagram incorporating this information. Be
sure to indicate the original equilibriumprice (Po), the equilibriumprice with the subsidy(Ps), and
the net price for the producers after the subsidy(Ps+s). Explain your answer briefly.
Multiple Choice
1. If a 10% increase in price results in a a 5% reduction in quantity demanded, the price elasticity of
demand (ignoring the minus sign) is
a) 5 b) 2 c) 1 d) 0.5 e) 0.2
2. The price elasticity of demand for Product W is calculated at 3 (technically, -3) for a small range on
the downward sloping demand curve. Within this range, if the price were to increase by 10%, then
the quantity demanded for Product W would:
a) rise by 10% b) fallby 10% c) rise by 30% d) fallby 30% e) none of these
3. If the price elasticity of demand for tape decks is -0.5, then a 20% increase in price will
a/ reduce quantity demanded by 40% b/ reduce quantity demanded by 5%
c/ increase total expenditure d/ reduce total expenditure
e/ none of the above
4. If the price for Good B were to decrease from $10 to $8 and as a result the quantity demanded
were to increase from 10 million units to 12 million units, then the demand curve, in the range
analyzed, using a formula for arc elasticity would be:
a) elastic b) unitary elastic c) inelastic d) perfectly elastic
5. Suppose that the quantity demanded of good X decreases by 2% when income increases by 5%.
The income elasticity of good X is
a/ +10% b/ -.1 c/ +.1 d/ -.4
6. If two goods are complements in consumption, their cross price elasticity of demand is
a/ zero b/ negative c/ positive
d/ either positive or negative depending on whether the goods are normal or inferior
e) inelastic
7. If the demand for a good is elastic, then
a/ as price rises, total revenue of producers falls
b/ as price falls, total revenue of producers falls
c/ as price rises, total revenue of producers rises
d/ as price rises, total revenue of producers is constant
e) as price rises, total expenditure of consumers rises
- 3 - Problem Set #4: Elasticity
8. If the cross elasticity of demand for a good X relative to good Y is -0.5 and the price of good Y
falls by 10%, the change in the quantity demanded of good X is:
a/ +5% b/ -5%c/ -0.5% d/ +0.5 e/ none of the above
9. If the price elasticity of demand for opera was inelastic

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