1
3 0 6  3 1 0
E N G I N E E R I N G
E C O N O M Y
SOLUTIONS TO PROBLEM SET #1 – INTRODUCTION
1.
i)
The initial demand and supply curves for the product are shown below.
The intersection of the demand and supply curves determines market equilibrium conditions,
which are at a price and quantity of approximately $41.60 per unit
and 20 600 units/month
, re
spectively.
ii)
Arc elasticity (AE) of demand:
AE
D
=  { [Q
2
 Q
1
] / [(Q
1
+ Q
2
) / 2] } / { [P
2
 P
1
] / [(P
1
+ P
2
) / 2] }
or,
AE
D
=  [ (Q
2
 Q
1
) / (Q
1
+ Q
2
) ] / [ (P
2
 P
1
) / (P
1
+ P
2
) ]
At P
1
=30, Q
1
=28 750, and at P
2
=35, Q
2
=25 000; thus AE
D
= 0.907
At P
1
=40, Q
1
=21 750, and at P
2
=45, Q
2
=18 750; thus AE
D
= 1.259
At P
1
=50, Q
1
=16 250, and at P
2
=55, Q
2
=14 250, thus AE
D
= 1.377
At P
1
=55, Q
1
=14 250, and at P
2
=60, Q
2
=12 500, thus AE
D
= 1.505
Arc elasticity of supply:
AE
S
= [ (Q
2
 Q
1
) / (Q
1
+ Q
2
) ] / [ (P
2
 P
1
) / (P
1
+ P
2
) ]
20
30
40
50
60
70
10000
15000
20000
25000
30000
35000
QUANTITY
(units/month)
PRICE
($/unit)
Demand
Supply
Shortage
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At P
1
=30, Q
1
=12 000, and at P
2
=35, Q
2
=16 000; thus AE
S
= 1.857
At P
1
=40, Q
1
=19 500, and at P
2
=45, Q
2
=22 500; thus AE
S
= 1.214
At P
1
=50, Q
1
=25 000, and at P
2
=55, Q
2
=27 000; thus AE
S
= 0.808
At P
1
=55, Q
1
=27 000, and at P
2
=60, Q
2
=28 500, thus AE
S
= 0.622
The price elasticity of demand tends to be higher at higher price levels.
This is typical of de
mand functions.
The opposite is observed with respect to the supply function, i.e. higher elastic
ities are obtained at lower price levels.
This is typical of supply functions.
iii)
The total consumer expenditure is the product of price and quantity
demanded
.
For the
demand schedule given, the values are:
Price
($/unit)
Total Consumer Expenditure
($)
60
750 000
55
783 750
50
812 500
45
843 750
40
870 000
35
875 000
30
862 500
The maximum total consumer expenditure is attained at a price of $35/unit.
The price elasticity
of demand is unitary at the price level at which total consumer expenditure is maximised.
As
indicated in part ii above, the elasticity of demand is unitary in either the upper portion of the
$3035 price interval or the lower portion of the $3540 interval, thus confirming our observation
in the table above.
iv)
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 Summer '08
 Bilido
 Supply And Demand, vca

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