ECOS2001 Intermediate Microeconomics
Tutorial 3 – Answer key
Chapter 6: Demand
Chapter 8: Slutsky Equation
Chapter 10: Intertemporal Choice
Question 1
Mary’s utility function is ( ) 2U b,c =b+100c-c , where b is the number of silver bells in
her garden and c is the number of cockle shells. She has 500 square feet in her garden
to allocate between silver bells and cockle shells. Silver bells each take up 1 square
foot and cockle shells each take up 4 square feet. She gets both kinds of seeds for
free.
(1) To maximize her utility, given the size of her garden, how many silver bells should
she plant? How many cockle shells should she plant?
Utility Function: ( ) 2U b,c =b+100c-c
Budget Line: 1*b+4*c=500
Marginal Utility of a Silver Bell: SBMU 1=
Marginal Utility of a Cockle Shell: CSMU =100-2c
SB
CS
MU 1
MRS= - =-
MU 100-2c
1
slope=-
4
1 1
- =-
100-2c 4
 c*=48
Substitute c*=48 into the budget line and then solve for b; b*=308
( ) ( )b*,c* = 308,48
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(2) If she suddenly acquires an extra 100 squares feet for her garden, how much
should she increase her planting of silver bells? How much should she increase her
planting of cockle shells?
Utility Function: ( ) 2U b,c =b+100c-c
Budget Line: 1*b+4*c=600
SB
CS
MU 1
MRS= - =-
MU 100-2c
1
slope=-
4
1 1
- =-
100-2c 4
 c*=48
Substitute c*=48 into the budget line and then solve for b; b*=408
( ) ( )b*,c* = 408,48
(3) If she had only 144 square in her garden, how many cockle shells would she grow?
SB
CS
MU 1
MRS= - =-
MU 100-2c
1
slope=-
4
1 1
- =-
100-2c 4
 c*=48
Can she grow c*=48 ? No because 48*4 192 144=  . She can grow at most 36. This
is an example of “Corner Solution.”
( ) ( )b*,c* = 0,36
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Note: At this point, the MRS is not equal to the slope of the budget line.
(4) If Mary grows both silver bells and cockle shells, the number of square feet in her
garden must be greater than ?
192
Question 2
Assume that a consumer’s preferences are well behaved, and that there are two
goods (good 1 and 2). Holding price 2 and income constant, derive the demand curve
for good 1.
See lecture notes.
Question 3
Suppose we live in a world where there are just two goods to consume.
Can both of the goods be:
a. Normal?
Yes.
b. Income inferior?
No. If income increases, at least the consumption of a good should increase.
Def: A good for which quantity demanded falls as income increases is called inferior.
c. Ordinary?
Yes.
Def: A good is called ordinary if the quantity demanded of it always increases as its
own price decreases.
d. Giffen?
No. A higher budget level is required if both prices increase, and vice versa.
Def: if for some values of its own price, the quantity demanded of a good rises as its
own-price increases then the good is called Giffen.
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Question 4
Nancy spends all her income on good 1 and good 2. As p1 increases while p2 remains
fixed, Nancy’s price-offer path is horizontal.
a. How does Nancy’s expenditure on good 1 respond to changes in p1?
Nancy’s price-offer path is horizontal. It implies that given p2, x2 would not change if
only p1 changes.
Nancy’s expenditure on good 2 is fixed, as the price of good 2 does not change:
2 2 2m p x=
Her budget constraint is given as:
1 1 2 2m p x p x= +
As she allocates a fixed portion of expenditure on good 2, hence, change in p1 will not
alter Nancy’s expenditure on good for any given budget.
b. Is good 2 a complement or a substitute for good 1?
They can be neither substitutes nor complements.
Question 5
A perfect “Tequila Sunrise” requires 100 grams of tequila per 2 parts of orange juice
(fresh squeezed). pt is the price of 100 grams of tequila and po is the price of an
orange. Ingrid’s budget for drinks is $100 (she wants to spend the entire $100).
How many Tequila Sunrises will Ingrid consume? (Illustrate your answer with
a graph.)
Tequila and orange juice are perfect complements.
Ingrid’s budget constraint is given as:
100t t o op x p x+ = .
For convenience, his utility function can be written as:
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 ( , ) min 2 ,t o t oU x x x x=
Treat the amount of tequila as unknown, for him to be rational he will consume 2xt
amount of juice. That is:
2 100t t o tp x p x+ =
100
2
t
t o
x
p p
=
+
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Additional Questions
(These questions will not be discussed during the tutorial).
Question 1
Define the Slutsky substitution effect and income effect. Using well behaved (convex
and monotonically increasing) preferences show each effect on a diagram for a: (i)
price fall; and (ii) a price rise. Provide intuition for your diagram
See pp 137-141 in the text and the lecture notes
Question 2
Define the price-offer curve and, using a diagram, derive both a downward sloping
demand curve and a demand curve for a Giffen good.
See pp 104-107 in the text and the lecture notes.