Assignment 1
1.
The demand and supply functions of a two commodity market model are as
follows:
Q
d1
= 18 – 3P
1
+P
2
Q
d2
= 12 + P
1
 2P
2
Q
s1
=  2 + 4P
1
Q
s2
=  2 + 3P
2
Find
P
i
*
and
Q
i
*
(
i
= 1, 2).
(Use fractions rather than decimals.)
2.
Solve the following national income model:
Y = C + I
0
+ G
0
C = a + b (Y – T)
(a > 0,
0 < b < 1)
[T: taxes]
T = d + t Y
(d > 0,
0 < t < 1)
[t: income tax rate]
a) By matrix inversion
b) By Cramer’s rule
(List the variables in the order
Y, C, T
.)
3.
Find the marginal and average functions for the following total cost function and
graph the result.
C = 3Q
2
+ 7Q +12
4.
Is the following function strictly monotonic?
y =  x
6
+ 5
(x > 0)
If it is strictly monotonic, find dx/dy by the inversefunction rule.
5.
Given the production function
Q = 96K
0.3
L
0.7
, find the
MPP
K
and
MPP
L
functions. Is
MPP
K
a function of
K
alone, or of both K and L? What about
MPP
L
?
6.
Examine the comparative static properties of the equilibrium quantity,
d
b
bc
ad
Q
+
−
=
*
and check your results by graphic analysis.
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 Fall '08
 TakrimaSyeda
 Economics, National Income, Supply And Demand, following national income, marginal function, following total cost

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