Transcript ECON 100 Tutorial: Week 2

ECON 100 Tutorial: Week 3
www.lancaster.ac.uk/postgrad/murphys4/
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office: LUMS C85
outline
Q1 – 5 min.
Q2 – 10 min.
Q3 – 5 min
Q4 – 5 min. (skip a &b)
Q5 – 10 min.
Q6 – 10 min.
Practice exam ?’s – 5 min.
Question 1
Outline three determinants of the price
elasticity of demand for a product and comment
on the importance of these in determining the
degree of elasticity.
Question 1: Price Elasticity of Demand
Less Elastic
• Few Close
Substitutes
• Necessities
• Broadly defined
Markets
• Lower Proportion of
Income devoted to
product
• Short Time Horizon
More Elastic
• Many Close
Substitutes
• Luxuries
• Narrowly-defined
markets
• Higher Proportion of
Income devoted to
Product
• Longer Time Horizon
Question 2(a)
Suppose The Times estimates that if it raises the
subscription price of its online newspaper from
£1.00 to £1.50 then the number of subscribers
will fall from 50,000 to 40,000.
a. What is the price elasticity of demand for the
Daily News when elasticity is calculated using
the midpoint method?
Question 2(a): Price Elasticity of
Demand
(𝑄2 − 𝑄1 )
(𝑄2 + 𝑄1 ) 2
(𝑃2 − 𝑃1 )
(𝑃2 + 𝑃1 ) 2
=
=
(−10,000)
45,000
0.5
1.25
(40,000 − 50,000)
(40,000 + 50,000) 2
(1.5 − 1)
(1.5 + 1) 2
= 0.56
Price Elasticity of Demand (midpoint method):
% Change in Quantity Demanded
% Change in Price
=
(Q2-Q1)/[(Q2+Q1)/2]
(P2-P1)/[(P2+P1)/2]
Income Elasticity of Demand:
% Change in Quantity Demanded
% Change in Income
Cross-Price Elasticity of Demand:
% Change in Quantity Demanded of Good 1
% Change in Price of Good 2
Price Elasticity of Supply:
% Change in Quantity Supplied
% Change in Price
Question 2(b) & (c)
(b)What is the advantage of using the midpoint
method?
With the midpoint method, the value of the
elasticity is the same whether you begin at a price
of £1.00 and raise it to £1.50 or begin at a price of
£1.50 and reduce it to £1.00.
(c) If The Times' only concern is to maximise total
revenue, should it raise the price of a newspaper
from £1.00 to £1.50? Why or why not?
Yes. In this price range, the price elasticity of
demand is less than one (inelastic), so an increase in
price will increase total revenue.
Question 3
The table below provides the demand schedule
for motel rooms at Small Town Motel. Use the
information provided to complete the table.
Answer the following questions based on your
responses in the table. Use the midpoint
method to calculate the percentage changes
used to generate the elasticities.
Price (£)
20
40
60
80
100
120
Quantity
Demanded
24
20
16
12
8
4
Total
Revenue
% Change % Change in Elasticity
in Price
Quantity
Question 3
Price (£)
20
40
60
80
100
120
Quantity
Demanded
24
20
16
12
8
4
Total
Revenue
480
800
960
960
800
480
% Change
in Price
0.67
0.40
0.29
0.22
0.18
% Change in Elasticity
Quantity
0.18
0.27
0.22
0.55
0.29
1.00
0.40
1.82
0.67
3.72
Question 3(a) & (b)
Price (£)
20
40
60
80
100
120
Quantity
Demanded
24
20
16
12
8
4
Total
Revenue
480
800
960
960
800
480
% Change
in Price
0.67
0.40
0.29
0.22
0.18
% Change in Elasticity
Quantity
0.18
0.27
0.22
0.55
0.29
1.00
0.40
1.82
0.67
3.72
a. Over what range of prices is the demand for motel
rooms elastic? To maximise total revenue, should Small
Town Motel raise or lower the price within this range?
Answer: £80 to £120; lower its prices
b. Over what range of prices is the demand for motel
rooms inelastic? To maximise total revenue, should Small
Town Motel raise or lower the price within this range?
Answer: £20 to £60; raise its prices
Question 3(c)
Price (£)
20
40
60
80
100
120
Quantity
Demanded
24
20
16
12
8
4
Total
Revenue
480
800
960
960
800
480
% Change
in Price
0.67
0.40
0.29
0.22
0.18
% Change in Elasticity
Quantity
0.18
0.27
0.22
0.55
0.29
1.00
0.40
1.82
0.67
3.72
c. Over what range of prices is the demand for motel
rooms unit elastic? To maximise total revenue,
should Small Town Motel raise or lower the price
within this range?
Answer: £60 to £80; it doesn’t matter. For
prices in this range, a change in price proportionately
changes the quantity demanded so total revenue is
unchanged.
Question 4
The demand schedule from Question 3 above is
reproduced below along with another demand
schedule when consumer incomes have risen to
£60,000 from £50,000. Use this information to answer
the following questions. Use the midpoint method to
calculate the percentage changes used to generate the
income elasticities.
a. What is the income elasticity
Price Quantity
Quantity
Demanded Demanded
(£)
of demand when motel rooms
Income = Income =
£50,000
£60,000
rent for £40?
20
24
34
40
20
30
Answer:
60
16
26
(10/25)/(£10,000/£55,000) = 2.2
80
12
22
100
120
8
4
18
14
Question 4
b. What is the income elasticity of demand when
motel rooms rent for £100?
Answer: (10/13)/(£10,000/£55,000) =4.2
c. Are motel rooms normal or inferior goods? Why?
Answer: Normal goods, because the income
elasticity of demand is positive.
d. Are motel rooms likely to be necessities or
luxuries? Why?
Answer: Luxuries, because the income elasticity of
demand is large (greater than 1). In each case, an
18 percent increase in income caused a much larger
increase in quantity demanded.
Income Elasticity of Demand
A few things we know:
+ Normal good
- Inferior good
>1 Luxury
<1 Necessity
Question 5
Use Excel and the following supply and demand
schedules for bicycles to answer the questions
below. Price
Quantity
Quantity
300
400
500
600
700
800
Demanded
60
55
50
45
40
35
Supplied
30
40
50
60
70
80
Question 5(a)
a. Plot the supply and demand curves for
bicycles. On the graph, impose a tax of £300 per
bicycle to be collected from the sellers. After the
tax, what has happened to the price paid by the
buyers, the price received by the sellers, and the
quantity sold when compared to the free market
equilibrium?
Answer: The price buyers pay rises to £700, the
price sellers receive falls to £400, and the
quantity sold falls to 40 units.
Question 5(b)
b. Again, plot the supply and demand curves for bicycles. On the
graph, impose a tax of £300 per bicycle to be collected from the
buyers. After the tax, what has happened to the price paid by the
buyers, the price received by the sellers, and the quantity sold when
compared to the free market equilibrium?
Question 5(b)
b. Again, plot the supply and demand curves for
bicycles. On the graph, impose a tax of £300 per
bicycle to be collected from the buyers. After
the tax, what has happened to the price paid by
the buyers, the price received by the sellers, and
the quantity sold when compared to the free
market equilibrium?
Answer: The price buyers pay rises to £700, the
price sellers receive falls to £400, and the
quantity sold falls to 40 units.
Question 5(c)
c. Compare your answers to questions (a) and
(b) above. What conclusion do you draw from
this comparison?
Answer: The impact of a tax collected from
sellers is equivalent to the impact of a tax
collected from buyers.
Question 5(d)
d. Who bears the greater burden of this tax, the
buyers or the sellers? Why?
Answer: The greater burden of the tax has fallen
on the buyers. The free market equilibrium price
was £500. After the tax, the price the buyers pay
has risen £200 while the price the sellers receive
has fallen £100. This is because demand is less
price elastic than supply at this price.
Question 6(a)
Suppose the government introduces a tax, t, on some good that is
priced at p. In the after tax equilibrium, D(p) = S(p-t). Note that p is a
function of t, i.e. p(t) . So, in equilibrium, D(p(t))=S(p(t)-t). Some (fairly)
simple geometry can be used to show that the incidence of a (small)
change in t, call this dt where d means “small change in”, on p depends
on the relative slopes of D and S. In particular, one can show that
𝑑𝑝
𝑑𝑆 𝑑𝑝
=
𝑑𝑡 𝑑𝑆 − 𝑑𝐷
𝑑𝑝 𝑑𝑝
We know that dD/dp<0 (D slopes downwards) and dS/dp>0 (S slopes
upwards) so the denominator is ambiguous – it could be positive or
negative depending on whether D or S is steeper. Show that this
implies that
𝑑𝑝
= 𝜀 𝑆 /(𝜀 𝑆 − 𝜀 𝐷 )
𝑑𝑡
where ε is the price elasticity and D and S refer to D and S curves.
HINT: multiply numerator and denominator by p/Q where Q is the
quantity demanded and supplied.
Question 6(a)
Write
𝑑𝑝
𝑑𝑡
in terms of 𝜀 𝑆 and 𝜀 𝐷 .
Question 6(b)
For many years the US government has subsidised
corn which is used in ethanol which is a petrol
substitute – supposedly to reduce US dependence
on imported oil. It also provided a direct subsidy.
The idea was to get consumers to shift away from
regular petrol. In 2010 the government spent $4b
on these two subsidies that amounted to about
$2.60 a gallon.
Just as a tax shifts the S curve up, a subsidy shifts it
down. The price elasticity of D is estimated to be
2.9 and the elasticity of S is estimated to be 0.25.
Using the above equation calculate the incidence of
this tax.
Question 6(b)
𝑑𝑝
= 𝜀 𝑆 /(𝜖 𝑆 − 𝜀 𝐷 )
𝑑𝑡
𝑑𝑝
.25
=
= 0.08
𝑑𝑡 .25 − −2.9
𝑑𝑝
= 0.08
2.6
𝑑𝑝 = 0.08 ∗ 2.6 = .24
Answer: About 0.24. In other words the $2.60
subsidy only reduced price by 24c – the producer
and corn growers pocketed almost all of the subsidy.
And the policy had little effect on oil use.
Question 6(c)
Do you think the subsidy is a good idea?
http://www.economist.com/node/18867278
Practice Multiple Choice Questions
An Inferior Good:
a)
b)
c)
d)
Is a Giffen good
Has a positive income elasticity of demand
Has a negative income elasticity of demand
Has an upward sloping demand function
Suppose a demand curve is written
D=60-3P. Find the intercept and slope
of the corresponding inverse demand
curve.
a)
b)
c)
d)
Slope of -20, intercept of 3
Slope of -1/3, intercept of 20
Slope of -3, intercept of 20
Slope of 1/3, intercept of 60
Suppose D=120-4P. Find the price
elasticity at a price of 10 and at a price
of 20. Use the standard mathematical
method, not the midpoint method.
a)
b)
c)
d)
-0.2, -2, respectively
-0.5, -2, respectively
-0.5, -4, respectively
Not possible to say without knowing what
the corresponding level of demand is.
Suppose D=200-2P and S=20+4P.
What is the equilibrium price and
quantity?
a)
b)
c)
d)
P*=20, Q*=100
P*=30, Q*=140
P*=50, Q*=220
P*=40, Q*=180