MSCI 3400 Lecture Notes - Ceteris Paribus, Demand Curve, Economic Equilibrium

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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 = % Qd
% P
= (Q)/Q
(P)/P
= Q * P
P Q
= (1/slope)*P/Q
Arc Elasticity: Define P and Q in the usual formula as the average of the range
P = (P1 + P2)/2 and Q = (Q1 + Q2)/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 fall in 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 equilibrium price 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
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Problem Set #4: Elasticity
40 cents per kilo. Calculate the "arc price elasticity" of demand between the original and the new
equilibrium prices. Will the farm revenue rise or fall as 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 will your company will sell this year?
b) Assume now that you do not think incomes will change, 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 will sell 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 clarify your 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 equilibrium at 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.
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