Download Solutions 8 - Emilio Cuilty

ECON 101– Discussion Section Week 8, Oct 24th – Fall 2014
Solutions
Problem 1 (Basics of Elasticity)
(a)

Regular percentage change in price = ($6 – $8)/$8 = - $2/$8 = - 25%
Regular percentage change in quantity demanded = (15 cups – 10 cups)/10 cups =
5/10 = 50%
% Change in Quantity
50%
regular price elasticity of demand = |
|=|
|=2
% Change in Price
− 25%
 Arc percentage change in price = ($6 – $8)/ [($6 + $8)/2] = - $2/$7 = - 2/7
= - 28.57% (Keep the fraction! It’s easier to work with.)
Arc percentage change in quantity = (15 cups – 10 cups)/ [(15 cups + 10 cups)/2]
= 5 cups/12.5 cups = 2/5 = 40%
Q 2 − Q1
2/5
Q + Q2
arc price elasticity of demand = | 1
|=|
| = 7/5 = 1.4
P2 − P1
− 2/7
P1 + P2
(b)

Regular percentage change in price = ($8 – $6)/$6 = $2/$6 = 1/3 = 33.33%
Regular percentage change in quantity demanded = (10 cups – 15 cups)/15 cups =
5/15 = - 1/3 = - 33.33%
% Change in Quantity
− 1/3
regular price elasticity of demand = |
|=|
|=1
% Change in Price
1/3

Arc percentage change in price = = ($8 – $6)/[($8 + $6)/2] = $2/$7 = 2/7 =
28.57%
Arc percentage change in quantity = (10 cups – 15 cups)/ [(10 cups + 15 cups)/2]
= - 5 cups/12.5 cups = - 2/5 = - 40%
Q 2 − Q1
− 2/5
Q + Q2
arc price elasticity of demand = | 1
|=|
| = 7/5 = 1.4
P2 − P1
2/7
P1 + P2
1
ECON 101– Discussion Section Week 8, Oct 24th – Fall 2014
We can observe that the arc price elasticity of demand will give the same result
regardless of the direction. This is not the case with the price elasticity of demand
calculated using standard percentage change formulas.
(c) Because cross price elasticity is positive (+2), brownies and chocolate chip cookies
are substitutes. Interpretation: suppose price of brownies increase 10%, Gabo’s quantity
demanded for chocolate chip cookies increases by 2*10% = 20%. If cross price elasticity
is zero, they are neither complements nor substitutable goods.
(d) Negative income elasticity implies that product is an inferior good to consumers.
Interpretation, if income increases by 15%, Dean’s quantity demanded for coke zero
drops by 15*(-1.5%) = -22.5%.
Problem 2 (Elasticity and Total Revenue)
a) The number of tickets sold is positively related with budget on ad-campaign since the
coefficient before A is positive.
b) Substituting given values of A and P into equation (P = 9 and A = 2), we then get Q =
8 + 4*Y. Income = $1000 implies Y1 = 1 and Income = $2500 implies Y2 = 2.5. Then Q
changes from Q1 = 8 + 4*1 = 12 to Q2 =8 + 4*2.5= 18.
point income elasticity of demand at initial income =
1
Y1
1
1
1
×
= ×
=
slope Q1 1 12 3
4
Q 2 − Q1
18 − 12
7
Q1 + Q 2
arc income elasticity of demand =
= 18 + 12 =
Y2 − 𝑌1
2.5 − 1
15
Y1 + Y2
2.5 + 1
c) Income = $250 implies Y = 0.25 and budget on ad-campaign = $1 million implies A =
1. Substituting them into demand equation gives Q = 24 – 2P. Ticket price drops from P1
= $9 to P2 = $8. Then Q changes from Q1 = 24 - 2*9 = 6 to Q2 = 24 - 2*8 = 8.
point price elasticity of demand at initial price = [−
2
1
P1
1 9
]×
= × =3
slope
Q1 1 6
2
ECON 101– Discussion Section Week 8, Oct 24th – Fall 2014
Q 2 − Q1
8−6
7
Q1 + Q 2
arc price elasticity of demand = |
| = |8 + 6| =
P2 − P1
8−9
17
P1 + P2
8+9
d) Maximize revenue when price elasticity is 1 (unit elasticity). For linear demand
equation, it is just the mid-point of the demand line. So demand has unit elastic at (P, Q)
= (6, 12). Maximize revenue is then $72 million.
Problem 3 (CPI and Inflation)
(a) From the table, calculate CPI using 1910 as base year. So CPI1910 = 100 and
CPI2010 =
400
50
× 100 = 800
$4
i) Real price of gas in 2010 = 800 × 100 = $0.5 (in 1910 dollars). TRUE
ii) Real price of gas in 1910 =
$0.25
100
× 100 = $0.25 (in 1910 dollars) and from i)
we know real price of gas in 2010 = $0.5 (in 1910 dollars). So percentage change of price
=
0.5−0.25
0.25
× 100% = 100%. TRUE
$20
iii) Real price of haircuts in 2010 = 800 × 100 = $2.5 in 1910 dollars and real
$2.5
price of haircuts in 1910 = 100 × 100 = $2.5 in 1910 dollars TRUE
iv) From iii), the real price of haircuts remain the same. FALSE
50
(b) Let 2010 be the base year, CPI2010 = 100 and CPI1910 = 400 × 100 = 12.5. The real
wage of 1910 in 2010 dollars is
$0.5
12.5
× 100 = $4 (in 2010 dollars). The increase in real
wage from 1910 to 2010 is $4 (in 2010 dollars) and percentage change is 100%.
(c) Percentage change in nominal price of gas =
4−0.25
Percentage change in nominal price of haircuts =
3
0.25
× 100% = 1500%.
20−2.5
2.5
× 100% = 700%.
ECON 101– Discussion Section Week 8, Oct 24th – Fall 2014
Percentage change in nominal price of hourly wage =
Percentage change in real price of gas =
0.5−0.25
0.25
Percentage change in real price of haircuts =
8−0.5
0.5
× 100% = 1500%.
× 100% = 100%.
2.5−2.25
2.25
Percentage change in real price of hourly wage =
× 100% = 0%.
8−4
4
× 100% = 100%.
From what we have calculated so far, the nominal prices of gas and labor increase the
most, by 1500%. Also the real prices of gas and labor increase the most, by 100%.
Problem 4 (Backtrack CPI and Inflation)
Since the nominal price and the real price in 2012 was $720 and $800 (in 2014 dollars)
$720
respectively, with the base year being 2014, it must be CPI2014 = 100 and CPI
2012
× 100 =
$800 (in 2014 dollars) which gives you CPI2012 = 90. Hence, the inflation from 2012 to
2014 is
100−90
90
× 100% = 11.11%.
4