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Microeconomic Theory 3 Question Paper

Microeconomic Theory 3

Course: Bachelor Of Arts In Economics

Institution: Kenyatta University question papers

Exam Year:2011

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KENYATTA UNIVERSITY
UNIVERSITY EXAMINATION 2011/20112
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR
OF ECONOMICS, BACHELOR OF ECONOMICS AND FINANCE,
BACHELOR OF ECONOMICS AND STATISTICS, BACHELOR OF ARTS
AND BACHELOR OF COMMERCE.
EET 300: MICROECONOMICS THEORY III
DATE: Thursday 1st December, 2011 TIME: 4.30 p.m. – 6.30 p.m.
INSTRUCTIONS
Answer question one (compulsory) and any other two questions.
Question One
Write brief notes on each of the following concepts. Be as precise as you can. (5 Marks each)
a) Optimization and equilibrium
b) Net put vector
c) Shepherd’s Lemma
d) Marginal rate of Technical Substitution
e) Stackelberg equilibrium
Question Two
a) Given the following production function 2 / 5 Y ? X . Obtain the corresponding profit
function assuming that w is the price of input x and P is the price of output. (10 Marks)
b) A profit function is said to be convex and positively linearly homogeneous in all prices.
From the profit function in (a) above, test for these two properties. (5 Marks)
c) Differentiate between Hicks and Slutsky’s compensation (5 Marks)
Question Three
a) “The cost function is a sufficient statistic for the technology since all the economically
relevant information about the technology can be obtained from the cost function”.
Using a cobb-douglas cost function C w w Q w w Q ? ?? ? 1
1 2 1 2 ( , , ) , where 1 w and 2 w are
prices of two inputs 1 X and 2 X respectively , and Q is the output, demonstrate this
statement. (12 Marks)
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b) Consider the following CES production function:
? ? ? ? ?
?
? ?
? ? ? Q ? A L ? (1? )K , where Q is output and L and K are inputs labour and
capital, respectively.
i) Interpret the parameters A ,? ,? and ? . (3 Marks)
ii) Show that if ? =0, the two input Labour and capital are imperfect substitutes in
production (5 Marks)
Question Four
“The minimum expenditure necessary for a consumer to reach the maximum utility
V( p,M) is the level of incomeM ”. Given the maximum
utilityV p M ?p p ? 2M
1
2
2
2
1 ( , )
?
? ? , where 1 P and 2 P are the prices of two goods 1 X and
2 X respectively, and M is the consumer’s income:
a) Find the consumer’s expenditure function (5 Marks)
b) Find the compensated and the uncompensated demand functions for good 1 X .
(5 Marks)
c) Using the information in (b) above, state and demonstrate the Slutsky’s equation.
(15 Marks)
Question Five
a) A long run average cost function for each firm in a competitive industry is given as:
2 13
3
( )
2
? ? q ?
q
c q , where q represents output. The market demand for the
product is given as q ?1250 ?50p, where p is the unit price of output in shillings.
i) Determine the equilibrium output for each firm in the industry (2 Marks)
ii) What is the optimal number of firms in this industry? (2 Marks)
iii) Suppose a quantity tax of K.sh6 is imposed in the market, what will be the optimal
number of firms in the industry? (2 Marks)
b) A duopoly industry faces a linear inverse demand function given by P ?100 ?Y ,
where 1 2 Y ? Y ?Y , and 1 Y and 2 Y are the outputs by firms 1 and 2 respectively. The cost
functions for the two firms are 1 1 C ?10Y and
2
2
2
2
Y
C ? .
i) Suppose firm 1 is a quantity leader, find the equilibrium price and quantities in
the industry. (4 Marks)
ii) Suppose firm 1 is a price leader, how would the answers in (i) above change?
(4 Marks)
iii) Suppose the two firms colluded to maximize their joint profits, how much would
each produce, and at what price would profits be maximized? (6 Marks)

Microeconomic Theory 3 Question Paper

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