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Econ 310: Advanced Microeconomics Question Paper
Econ 310: Advanced Microeconomics
Course:Bachelor Of Economics And Mathematics
Institution: Kabarak University question papers
Exam Year:2008
2008/2009 ACADEMIC YEAR
FOR THE DEGREE OF BACHELOR OF ECONOMICS AND
MATHEMATICS
COURSE CODE: ECON 310
COURSE TITLE: ADVANCED MICROECONOMICS
STREAM: Y3S1
DAY: TUESDAY
TIME: 2.00-4.00 P.M.
DATE: 9/12/2008
INSTRUCTIONS:
1. Answer Question ONE and any other TWO questions
2. Apart from question ONE; all other questions carry equal marks. Marks for
subdivisions are shown in brackets.
3. Calculators are allowed in the examination room provided they are not
programmable and can store or recall information.
4. Marks will be awarded to candidates who demonstrate clarity and accuracy of
presentation.
5. Diagrams should be used where helpful.
QUESTION ONE
a) i. What do you understand by consumer preferences? (2mks)
ii. Distinguish between strict and week preference relation. (3mks)
iii. Explain the properties of preference relation. (3mks)
b) Define and derive Marginal Rate of Commodity Substitution (MRCS) of say
commodity X for commodity Y. (5mks)
c) What does a consumer’s utility function look like if two commodities say X and Y
are perfect substitutes? Show that the MRCS for perfect substitute commodities
are equal. (4mks)
d. Given the utility function and budget constraint of the form:
M P X PY
U X Y XY
1 2
( , )
= +
=
i. Determine the Utility maximizing quantities of X and Y in terms of income (M) and
prices (P1 and P2). (6mks)
ii. Show that by consuming the Utility maximizing quantities the consumer exhausts
his budget. (3mks)
QUESTION TWO
a) Distinguish between Direct and Indirect Utility functions. (4mks)
b) Suppose a rational consumer seeks to maximize,
1 1 2 2
1 2 1 2
.
( )
S t P X P X
Max U X X X X
+
=
i. Derive the Ordinary demand curve and the indirect utility function. (8mks)
ii. Verify Roy’s Identity. (4mks)
iii. Explain the properties of indirect Utility function. (6mks)
QUESTION THREE
a) What is a production function? (2mks)
b) Distinguish between marginal rate of technical substitution and elasticity of
substitution. Show that marginal rate of technical substitution diminishes as you
move along an isoquant. (6mks)
c) Define and explain the various types of technological progress. (6mks)
d) Suppose initially a firm’s production function took the form:
Q=500(L+3K)
However, as a result of a manufacturing innovation, its production function is now,
Q=1000(0.5L+10K)
i. Show that the innovation has resulted in technological progress. (4mks)
ii. What is the nature of technological progress in (i) above? (4mks)
QUESTION FOUR
a) Define costs. (2mks)
b) What is an inferior input? Graphically derive an expansion path assuming one
factor input is an inferior input. (6mks)
c) What is an input requirement/demand function? Given the production function of
the form,
2
1
2
1
Q = 50K L , determine the labor requirement function in the short run. (7mks)
d) Show graphically that input demand is a function of output and input price.
(7mks)
QUESTION FIVE
a) The market consists of 300 identical firms and the market demand curve is given
by,
D(p)=60-P
Each firm has a short run total cost curve given by,
STC=0.1+150Q2
Assuming that the entire firm’s fixed costs are sunk costs,
i) Show that minimum level of AVC is zero. (3mks)
ii) Determine the short run market equilibrium price and quantity. (7mks)
iii) Determine the firm’s economic profit at the market equilibrium. (3mks)
b) Consider monopolist that faces demand function given by,
TC cQ
P a bQ
=
= -
Show that the monopolist profit maximizing price is midpoint/halfway the price
intercept and marginal cost. (6mks)
c) State and explain the three degrees of price discrimination. (3mks)
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