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SCHOOL OF ECONOMICS
COURSEWORK ASSESSMENT TEST
ANSWER ALL QUESTIONS TIME: 2 HRS.
QUESTION ONE
a) Suppose the quantity of good X demanded by individual 1 and 2 is given
X
1
= 10 2P
X
+ 0.1I
1
+ 0.5P
Y
X
2
= 17 P
X
+ 0.05I
2
+ 0.5P
Y
(i) What is the market demand function to total X (= X
1
+ X
2
) as a
function of P
X
, I
1
, I
2
and P
Y
.
(ii) Now given the values of some of the variables as follows: I
1
= 40,
I
2
= 20, P
Y
= 4
Give the algebraic equation for the market demand curve for total
X.
(b) (i) Calculate the point elasticity of demand from the demand functions
Q = 100 2P +
100
/
P
at P = 10 and Q = 90
(ii) Given a demand curve which is a rectangular hyperbola and with a
functional form Q =
1
/
P
. Show arithmetically that the point
elasticity of demand will be unitary throughout the demand curve.
(iii) Given the demand and supply functions shown below, calculate the
equilibrium price and quantity at which the market clears.
Q
d
= 90 2P
Q
s
= P 3
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QUESTION TWO
a) Suppose that goods X and Y are normal goods with prices P
x
and P
y
respectively. If the consumer has an income I initially, show how this
consumer will maximize his or her utility using the indifference curve
approach to utility maximization.
b) Suppose the price of good X now falls with all other variables above
remaining unchanged, show how we can clearly bring out the income
and substitution effects of the above change in the price of good X.
c) Using diagrammatic exposition show how a consumer reacts to an
inferior good as his or her income rises. In the process define both an
inferior and Giffen good.

Unformatted Attachment Preview

1 SCHOOL OF ECONOMICS COURSEWORK ASSESSMENT TEST ANSWER ALL QUESTIONS TIME: 2 HRS. QUESTION ONE a) Suppose the quantity of good X demanded by individual 1 and 2 is given X1 = 10 – 2PX + 0.1I1 + 0.5PY X2 = 17 – PX + 0.05I2 + 0.5PY (i) What is the market demand function to total X (= X1 + X2) as a function of PX, I1, I2 and PY. (ii) Now given the values of some of the variables as follows: I1 = 40, I2 = 20, PY = 4 Give the algebraic equation for the market demand curve for total X. (b) (i) Calculate the point elasticity of demand from the demand functions Q = 100 – 2P + 100/P at P = 10 and Q = 90 (ii) Given a demand curve which is a rectangular hyperbola and with a functional form Q = 1/P. Show arithmetically that the point elasticity of demand will be unitary throughout the demand curve. (iii) Given the demand and supply functions shown below, calculate the equilibrium price and quantity at which the market clears. Qd = 90 – 2P Qs = P – 3 2 QUESTION TWO a) Suppose that goods X and Y are normal goods with prices Px and Py respectively. If the consumer has an income I initially, show how this consumer will maximize his or her utility using the indifference curve approach to utility maximization. b) Suppose the price of good X now falls with all other variables above remaining unchanged, show how we can clearly bring out the income and substitution effects of the above change in the price of good X. c) Using diagrammatic exposition show how a consumer reacts to an inferior good as his or her income rises. In the process define both an inferior and Giffen good. Name: Description: ...
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