1. office hours: 3:45PM to 4:45PM tuesday LUMS C85
ECON 100 Tutorial: Week 2
office hours: 3:45PM to 4:45PM tuesday LUMS C85

2. outline
Q1 – 5 min. Q2 – 10 min. Q3 – skip Q4 – 5 min. (skip a &b) Q5 – 10 min. Q6 – 10 min. Practice exam ?’s – 10 min.

3. 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.

4. Question 1: Price Elasticity of Demand
Less Elastic More Elastic
Few Close Substitutes
Necessities
Broadly defined Markets
Lower Proportion of Income devoted to product
Short Time Horizon
Many Close Substitutes
Luxuries
Narrowly-defined markets
Higher Proportion of Income devoted to Product
Longer Time Horizon
Mankiw Page 95, Caroline Lecture 4 & 5

5. 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?

6. Question 2(a): Price Elasticity of Demand
( 𝑄 2 − 𝑄 1 ) ( 𝑄 2 + 𝑄 1 ) 2 ( 𝑃 2 − 𝑃 1 ) ( 𝑃 2 + 𝑃 1 ) 2 = (40,000−50,000) (40,000+50,000) 2 (1.5−1) (1.5+1) 2 = (−10,000) 45, = 0.56
Slides from 2012/13

7. % Change in Quantity Demanded = (Q2-Q1)/[(Q2+Q1)/2]
General Equations for different types of Elasticity: Price Elasticity of Demand (midpoint method): 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
% Change in Quantity Demanded = (Q2-Q1)/[(Q2+Q1)/2]
% Change in Price (P2-P1)/[(P2+P1)/2]
Slides from 2012/13

8. 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.

9. 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 (£)
Quantity Demanded
Total Revenue
% Change in Price
% Change in Quantity
Elasticity 20 24 40 60 16 80 12
100 8
120 4

10. Question 3 Price (£) Quantity Demanded Total Revenue % Change in Price
% Change in Quantity
Elasticity 20 24 40 60 16 80 12
100 8
120 4

11. Question 3(a) & (b)
Price (£)
Quantity Demanded
Total Revenue
% Change in Price
% Change in Quantity
Elasticity 20 24
480
0.67
0.18
0.27 40
800
0.40
0.22
0.55 60 16
960
0.29
1.00 80 12
1.82
100 8
3.72
120 4
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

12. Question 3(c)
Price (£)
Quantity Demanded
Total Revenue
% Change in Price
% Change in Quantity
Elasticity 20 24
480
0.67
0.18
0.27 40
800
0.40
0.22
0.55 60 16
960
0.29
1.00 80 12
1.82
100 8
3.72
120 4
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.

13. 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 of demand when motel rooms rent for £40?
Answer: (10/25)/(£10,000/£55,000) = 2.2
Price
(£)
Quantity Demanded
Income = £50,000
Income = £60,000 20 24 34 40 30 60 16 26 80 12 22
100 8 18
120 4 14

14. Question 4(a): Income Elasticity of Demand
( 𝑄 2 − 𝑄 1 ) ( 𝑄 2 + 𝑄 1 ) 2 ( 𝐼𝑛𝑐𝑜𝑚𝑒 2 − 𝐼𝑛𝑐𝑜𝑚𝑒 1 ) ( 𝐼𝑛𝑐𝑜𝑚𝑒 2 + 𝐼𝑛𝑐𝑜𝑚𝑒 1 ) 2 = (30−20) (30+20) 2 (60,000−50,000) (60,000+50,000) 2
= ,000 55,000 =2.2
Slides from 2012/13

15. Question 4(b): Income Elasticity of Demand
( 𝑄 2 − 𝑄 1 ) ( 𝑄 2 + 𝑄 1 ) 2 ( 𝐼𝑛𝑐𝑜𝑚𝑒 2 − 𝐼𝑛𝑐𝑜𝑚𝑒 1 ) ( 𝐼𝑛𝑐𝑜𝑚𝑒 2 + 𝐼𝑛𝑐𝑜𝑚𝑒 1 ) 2 = (18−8) (18+8) 2 (60,000−50,000) (60,000+50,000) 2
= ,000 55,000 =4.2
Slides from 2012/13

16. 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.

17. Income Elasticity of Demand
A few things we know: + Normal good - Inferior good >1 Luxury <1 Necessity

18. Question 5
Use Excel and the following supply and demand schedules for bicycles to answer the questions below.
Price
Quantity Demanded
Quantity Supplied
300 60 30
400 55 40
500 50
600 45
700 70
800 35 80

19. 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.

20. From Mankiw & Taylor. In the second edition, this is Figure 6.7.

21. 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?

22. 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.

23. 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.

24. 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.

25. 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 𝑑𝑡 = 𝑑𝑆 𝑑𝑝 𝑑𝑆 𝑑𝑝 − 𝑑𝐷 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 𝑑𝑡 = 𝜀 𝑆 /( 𝜀 𝑆 − 𝜀 𝐷 ) 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.
Note: there was a typo in the original worksheet question. The equation 𝑑𝑝 𝑑𝑡 = 𝜀 𝑆 /( 𝜀 𝑆 − 𝜀 𝐷 ), the S and D had been switched around, reading 𝑑𝑝 𝑑𝑡 = 𝜀 𝐷 /( 𝜀 𝐷 − 𝜀 𝑆 ). The corrected version should read: 𝑑𝑝 𝑑𝑡 = 𝜀 𝑆 𝜀 𝑆 − 𝜀 𝐷 .

26. Question 6(a)
we can re-phrase question 6(a): Write 𝑑𝑝 𝑑𝑡 in terms of 𝜀 𝑆 and 𝜀 𝐷 , where 𝑑𝑝 𝑑𝑡 = 𝑑𝑆 𝑑𝑝 𝑑𝑆 𝑑𝑝 − 𝑑𝐷 𝑑𝑝 . 𝑑𝑝 𝑑𝑡 is the change in price with respect to a tax; this is the tax incidence. From Caroline’s lecture slides, we learned: 𝜀 𝑆 = 𝑃 𝑄 ∗(𝑑𝑆 𝑑𝑝 ) 𝜀 𝐷 = 𝑃 𝑄 ∗(𝑑𝐷 𝑑𝑝 ) We are also given a hint in 6(a): multiply numerator and denominator by p/Q where Q is the quantity demanded and supplied.
Work out in class.

27. 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 Using the above equation calculate the incidence of this tax.

28. Question 6(b)
𝑑𝑝 𝑑𝑡 = 𝜀 𝑆 /( 𝜖 𝑆 − 𝜀 𝐷 ) 𝑑𝑝 𝑑𝑡 = −2.9 =0.09 Answer: About In other words the $2.60 subsidy only reduced price by $0.09 – the producer and corn growers pocketed almost all of the subsidy. And the policy had little effect on oil use.
If you used the equation with the typo, 𝑑𝑝 𝑑𝑡 = 𝜀 𝐷 /( 𝜖 𝐷 − 𝜀 𝑆 ) then you might have the following answer:
𝑑𝑝 𝑑𝑡 = 𝜀 𝐷 /( 𝜖 𝐷 − 𝜀 𝑆 )
𝑑𝑝 𝑑𝑡 = −.25 =1.05

29. Question 6(c)
Do you think the subsidy is a good idea?

30. Practice Multiple Choice Questions

31. An Inferior Good: Is a Giffen good
Has a positive income elasticity of demand
Has a negative income elasticity of demand
Has an upward sloping demand function

32. Suppose a demand curve is written D=60-3P
Suppose a demand curve is written D=60-3P. Find the intercept and slope of the corresponding inverse demand curve.
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

33. 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.
-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.
p/q * dq/dp = 10/80 * -4 = -1/2 and 20/40 * -4 = -2

34. Suppose D=200-2P and S=20+4P. What is the equilibrium price and quantity?
P*=20, Q*=100
P*=30, Q*=140
P*=50, Q*=220
P*=40, Q*=180