Econ 200, Spring 2012
Suggested Answers to Exercise Set 4
1.
P
Q
6
0
4
10
Price is measured in US dollars.
P
4
2
Q
10
20
P
2
0
Q
20
30
We first calculate the percentage change in quantity and percentage change in price.
Calculations are done under the assumption that the price has increased. That is, the
initial price is given in the second rows of all tables.
Case I
Case II
Case III
(a) % P
2 4 6 = 40%
2 4 2 = 66.67%
2 0 2 = 200%
2
2
% Q
10 0
10
2
= 200%
10 10
20
2
2
= 66.67%
10 30
20
= 40%
2
Elasticities. We first compute elasticities at the lower price:
CASE 1. Slope of demand = P/ Q = 2/10 = 1/5. EP at P = 4 is (1/slope)(P/Q) =
5(4/10) = 2.
CASE 2. Slope of demand = P/ Q = 2/10 = 1/5. EP at P = 2 is (1/slope)(P/Q) =
5(2/20) = 1/2.
CASE 3. Slope of demand = P/ Q = 2/10 = 1/5. EP at P = 0 is (1/slope)(P/Q) =
5(0/30) = 0.
Now we compute elasticities at the higher price:
CASE 1. Slope of demand = P/ Q = 2/10 = 1/5. EP at P = 6 is (1/slope)(P/Q) = 5(6/0)
= ∞.
CASE 2. Slope of demand = P/ Q = 2/10 = 1/5. EP at P = 4 is (1/slope)(P/Q) =
5(4/10) = 2.
CASE 3. Slope of demand = P/ Q = 2/10 = 1/5. EP at P = 0 is (1/slope)(P/Q) =
5(2/20) = 1/2.
Now, we see how total revenue changes with changes in P. This time we think that price
has increased: in case I from 4 to 6, in case II from 2 to 4 etc. Remember: TR = P Q.
Price increase in
Price increase in
Price increase in
CASE I
CASE II
CASE III
0
40 $
TR
40 $
In case I no matter at which price we compute elasticity we have elastic demand so it is
not surprising that TR declines by $40 when P increases.
In case III no matter at which price we compute elasticity we have inelastic demand so it
is not surprising either that TR goes up by $40 when P increases.
It is bad news that we have inelastic demand at the lower price and elastic demand at the
higher price furthermore TR doesn’t change when P is increase from 2 to 4. You can
solve this riddle by the following reasoning: Compute EP at the mid point price between
2 and 4 and at the midpoint quantity between 10 and 20. Convince yourself that if
demand is linear, in Case II the quantity demanded at P = 3 must be 15 units.
(d) When demand is elastic, P and TR move in opposite directions. That means: if P
increases, TR decreases, if P decreases, TR increases.
When demand is inelastic, P and TR move in the same direction. That means: if P
increases, TR increases too, if P decreases, TR decreases too.
When demand is unit elastic, TR is unchanged when P changes.
2.
In equilibrium, quantity supplied equals quantity demanded. At P = $100, Qs = Qd = 18
mill. Therefore equilibrium price is $100 and equilibrium quantity 18 millions.
a) ed = (∆Qd/Qd)/(∆P/P)
for P = 100, ed = {(18–16)/18}/{(100–120)/100} = –5/9
b) es = (∆Qs/Qs)/(∆P/P)
for P = 100, ed = {(18–20)/18}/{(100–120)/100} = 5/9
3. P
6
EP = (∆Qd/Qd)/(∆P/P)=
=(∆Qd/∆P)( Qd/P)=-(1/2) ( Qd/P)
Elastic range
Point of unit elasticity
3
Inelastic range
0
1.5
3
Q
4. Using the expression for income elasticity of demand, Q/Q = EI ( I/I).
With 2.5 ≤ EI ≤ 3.9, and I/I = 0.05:
We have (2.5)(0.05) ≤ Q/Q ≤ (3.9)(0.05), so that 12.5% ≤ %( Q/Q) ≤ 19.5%.
5. (a) The demand for meat is more inelastic than the demand for lamb chops because
meat is a broad commodity category that includes lamb chops. Lamb chops have good
substitutes: all other red meat. The substitutes for red meat (fish, chicken) are not as
close substitutes.
(b) The demand for Insulin is more inelastic than the demand for Aspirin because
Insulin is a vital commodity for its consumers and has no substitutes. This is not the case
for Aspirin.
6. Substitute goods have positive cross-price elasticity of demand. Therefore, (b) wood
and metal window frames and (d) MBA degrees from Harvard and Stanford are likely to
have positive cross-price elasticity. Complements have negative cross-price elasticity of
demand. Therefore, (a) automobiles and gasoline, and (c) gin and tonic are likely to have
negative cross-price elasticity.
7. Inferior goods have negative income elasticities. Lentils and bread are likely to have
either positive but very small or negative income elasticity numbers. In contrast,
restaurant meals and lamb chops are normal (perhaps even luxury) goods and have
positive income elasticity numbers.