Principles of Microeconomics (ECNC2101)
Higher Institute of Commerce and Management (HICM)
Semester: First Semester
Level: 200
Year: 2013
THE UNIVERSITY OF BAMENDA
HICM (Level 1)
Academic Year 2012/2013
Principles of Microeconomics
Problem Set One
Examiner: Prof. TAFAH EDOKAT / NDAMSA Dickson
Exercise 1
Given the following demand and supply schedules for toy watches per week in the “Bambui market”:
a)
Derive the demand and supply functions for toy watches.
b)
Determine the equilibrium price and quantity for toy watches in the “Bambui market”.
c)
What are the economic implications in the market for toy watches at “Bambui” if the price increases above
the equilibrium price and if it decreases below the equilibrium price? Use graphs to support your answer.
d) Define and calculate the price elasticity of demand for toy watches. Interpret your result
Exercise 2
The government can sometimes control prices of goods and services and such price controls are usually below or
above the market price. Explain with the aid of graphs the following intervention policies:
-Maximum price policy
- Minimum price policy
Exercise 3
In a given market there are only three consumers with respective demands for a commodity X. Due to some lack
of consistency in investigations, we only have information on the demand functions of the first two
consumers:
q1 = 10 - 2P
q2 = 7-P
1) What is effective demand
2) What do you understand by market demand for a commodity
3) Suppose the market demand function is Q
d
= 42 - 7P, derive the demand function of the third consumer.
4) Suppose commodity X has the following prices (0; 2; 4; 5). Determine the individual and aggregate demand
schedules.
Exercise 4
Suppose in the “food market” we have the following market demand and supply curve for a commodity: Q
d
= 1000
- 10P and Q
s
= -50 + 25P
a) Determine the equilibrium price and quantity
b) Determine the inverse form of the demand curve
c) Calculate the price elasticity of demand at the market equilibrium
d) Suppose the price in the market is 25 FCFA. What is the amount of excess demand?
Price Quantity Demanded Quantity Supplied
500 3000 6000
600 2000 8000
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Exercise 5
In a given market, the demand for commodity X is given by Q
x
d
= 500 — 10P
x
+ 2P
Y
+ 0.70I where P
x
is the price
of good X, P
Y
is the price of some other good Y, and / is consumer income. Assume that P
x
is currently 10 Fcfa, P
Y
is
currently 5 Fcfa, and I is currently 100 Fcfa.
a) What is the elasticity of demand for good X with respect to the price of good X at the current situation?
b) What is the cross-price elasticity of the demand for good X with respect to the price of good T at the current
situation? Use your result to determine the nature of the two goods.
c) What is the income elasticity of demand for good X at the current situation? What type of good is good X?
Exercise 6
Suppose in a market we have two goods, X and Y. For each of the following scenarios, develop the utility function
U(X,Y) that matches the given information.
a) The consumer believes that good X and Y are perfect substitutes with one unit of X equivalent to four units of Y.
b) The consumer believes that good X and Y are perfect compliments and always uses three unites of Y for every
unit of X.
Exercise 7
Consider the utility function U(x, y) = 3x
2
+ 5y with MUx = 6x and MUy = 5.
a) Is the assumption that “more is better” satisfied for both goods?
b) What is the MRSx.y for this utility function?
c) Is the MRSx.y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference
curve?
d) Will the indifference curves corresponding to this utility function be convex to the origin (bowed toward the
origin), concave to the origin (bowed away), or straight lines? Explain.
Exercise 8
A consumer named ‘Poli’ likes to eat both apples and bananas. At the grocery store, each apple costs $0.20 and each
banana cost $0.25. Poli’s utility function for apples (A) and bananas (B) is given by
U(A, B) = 6
√
where MU
A
= 3
/ and MU
B
= 3
/. Suppose ‘Poli’ has $4 to spend on apples and
bananas, how many of each should he buy to maximize his satisfaction?
Exercise 9
A consumer has income of 180 francs per week and buys two goods, x and y . Initially, the prices are (P
X1
, P
y1
)
=(15,10), and the consumer chooses basket 1 containing (x1 , y1 ) = (10,3) . Later, the prices change to (P
X2
, Py
2
)
=(12,12). At these prices the consumer chooses basket 2 containing (
x2
,
y2
) = (5,10) . The income is still 180 francs
per week. Do the consumer’s choices in these two situations maximize utility?
Exercise 10
A consumer buys two goods, food (F) and clothing (C). Her utility function is given by U(F,C) = FC + F. The
marginal utilities are MU
F
= C +1 and MU
C
= F. The price of food is PF, the price of clothing is PC, and the
consumer’s income is I.
a)
What is the equation for the demand curve for clothing?
b)
Is clothing an inferior good?
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Exercise 11
Consider a consumer who purchases two goods, x and y . The consumer’s utility function is U(x, y)=xy with MU
X
=y
and MU
y
= x . In addition, the demand curve for y is given by y =
1
2
. Assume initially that the consumer’s
income is 160 francs, the price of x is 8 francs, and the price of y is 1 franc.
a)
Hinging on the given information, determine (1) the utility maximizing amount of x , (2) the utility
maximizing amount of y , and (3) the total utility at the utility maximizing bundle.
b)
Now assume the price of y increases to 2 francs. Recalculate the values from part a) at the new price.
Exercise 12
Peter purchases two goods, food F and clothing C, with the utility function U = FC +F. His marginal utility of food
is MUF = C + 1 and his marginal utility of clothing is MUC = F. He
has an income of 20 francs. The price of clothing is 4.
a)
Derive the equation representing Peter’s demand for food, and draw this demand curve for prices of food
ranging between 1 and 6.
b) Calculate the income and substitution effect on Peter’s consumption of food when the price of food rises from
1 to 4, and draw a graph illustrating these effects
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