Advanced Microeconomics Question Paper
Advanced Microeconomics
Course:Bachelor Of Science (Economics)
Institution: Kabarak University question papers
Exam Year:2012
KABARAK
UNIVERSITY
UNIVERSITY EXAMINATIONS
2011/2012 ACADEMIC YEAR
FOR THE DEGREE OF BACHELOR OF SCIENCE IN
ECONOMICS AND MATHEMATICS
ECON 310 – ADVANCED MICROECONOMICS
DAY: MONDAY
DATE: 30/07/2012
TIME: 9.00 – 11.00 A.M.
STREAM: Y3S1
INSTRUCTIONS:
? Answer Question ONE and ANY other TWO questions
1. (a) Suppose the utility function of peter is given by
Price of
commodity is
per unit and price of commodity is
per unit. How
many units of the two commodities, will peter buy given that his income
is
equal to
(7 mks)
(b) Three oligopolists operate in a market with inverse demand given by
Where
. Each firm has a constant marginal cost of production c and
no fixed cost. The firms choose their quantities as follows. First firms
simultaneously choose
and respectively. Then firm observes
and chooses
and chooses . Find the subgame perfect Nash equillibria of
this game. (10 mks)
(c) Capital labour ratio has been increasing in the Kenyan manufacturing industry over
time. What possible explanations can you offer for this increase in capital intensity?
(7 mks)
(d) The technology of a firm can be represented by the following function:
Required
(i)
Derive the firm’s conditional input demand function. (2 mks)
(ii)
Derive the firm’s cost function. (2 mks)
(iii)
Derive the firm’s profit function. (2 mks)
2. (a) Given a production function
+
, a>0
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Required:
(i)
Calculate the conditional input demand functions. (5 mks)
(ii)
Derive the cost function. (5 mks)
(b) Using the convexity property of the profit function with respect to output price (p)
demonstrate how the output supply function can be derived from the profit function
using the hotelings lemma. (10 mks)
3. (a) Suppose the cost function of a firm is given by.
What is the firm’s production function? (6 mks)
(b) Using the concavity property of the cost function with respect to input prices,
demonstrate how the conditional input demand function can be derived from the cost
function using the shepherd lemma. (8 mks)
(c) A frim has two plants with cost function
.
Required:
What is the firm’s cost function? (6 mks)
4. Given a utility function:
(i)
Calculate the Marshallian demands for this consumer. (5 mks)
(ii)
Derive the indirect utility function for this consumer. (5 mks)
(iii)
Calculate the expenditure function for this consumer. (5 mks)
(iv)
Calculate the Hicksian demands for this consumer. (5 mks)
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