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Advanced Microeconomic Theory Question Paper
Advanced Microeconomic Theory
Course:Advanced Microeconomic Theory
Institution: Kenyatta University question papers
Exam Year:2011
INSTRUCTIONS:
Answer question ONE and any other TWO questions.
Question One
Clearly differentiate the following economic terms using the appropriate economic
methodologies where applicable as clearly as possible.
i)
Marginal rate of technical substitution and elasticity of substitution
ii)
Hicksian and marshalling demand functions
iii)
Indirect utility function and the expenditure function
iv)
Conditional input demand functions and factor input demand curves
v)
Hotellings lemma and shepherd lemma
vi)
Roy’s identity and duality concept
(30 marks)
Question Two
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.” Given the following cost function, verify this statement as
thoroughly as you can.
1
2
C ?w ,w , y ? w w y
1
2
? 10 3 3 ,
1
2
Where both Ws are the unit prices of two inputs respectively, and Y is output.
(10 marks)
b)
A maize farmer produces using two inputs labour, (L), and fertilizer, (K), the
farmers total cost function is given by
TC ?? 5
.
0 r ? rw ? 5
.
0
?w ,q
Page 1 of 2
Where q is output of maize in bags and ? and w are the unit prices of fertilizer
and labour respectively. Fertilizer is measured in bags. If the farmer’s objective
is to produce 10,000 bags of maize, and fertilizer will the farmer require to
minimize cost?
(10 marks)
Question Three
Consider the following indirect utility function:
V ? ,
p M ?
?a
?1
?
a
MP P
, where M is the level of income, and P
1
2
1 and P2 are prices of two
goods X1 and X2, respectively. Derive the following
i)
Marshallian demand functions for X1 and X2,
(8 marks)
ii)
The expenditure function,
(6 marks)
iii)
Hicksian demand functions for X1 and X2.
(8 marks)
Question Four
A monopolist’s demand function is given as Q = 2000 – 10P, where Q the quantity is
produced and sold and P is the price per unit in K.sh. If the firm’s marginal cost is K.sh
100:
i)
Calculate the monopolist’s equilibrium quantity, profits and price (6 marks)
ii)
Suppose the monopolist behaves competitively, how would the answers in (i)
above change?
(6 marks)
iii)
Find the value of the deadweight loss due to the monopoly.
(8 marks)
Question Five
A firm production function is given as Y ? La where 0? a a ? 1 where Y is output and L
is labour. Let P be the output price and W be the price of labour.
Required
a)
Derive the profit function for the firm
(10 marks)
b)
A legitimate profit function is said to be positively linearly homogeneous; and
convex in both output and input prices. Is the function in (a) above legitimate?
Show your working.
(5 marks)
c)
Suppose the output price and the price of labour are Ksh.1000 and Ksh.100
respectively, compute the profit maximizing levels of output and input.
(5 marks)
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