EEP 101 Homework #1
Answer Key
1)
Let the market for SUVs be characterized by an Aggregate Utility Function equal to
US
S
S
()
=
100
2
2
, and a Cost of Production function equal to
CS
S
=
2
4
(where both U and C are
in $).
a)
Imagine that you are in charge of this economy, how many SUVs should be produced and
consumed? What is the net utility to society from this allocation?
If I were in charge of this economy, I would choose a quantity of SUVs to maximize the net
benefits of SUVs. That is, I would maximize U(S)C(S).
max
100
24
22
S
SS

so, take the first derivative, and set it equal to zero,
100
2
06
6
2
3
 =f=
S
S
S
.
The net utility can be found by putting 66 2/3 back into U(S)C(S),
100
200
3
200
3
2
200
3
4
10000
3
3333
1
3
*

Ê
Ë
Á
ˆ
¯
˜

Ê
Ë
Á
ˆ
¯
˜
==
Now imagine that the market for SUVs is competitive.
b)
Derive the Demand Curve for SUVs.
The Demand Curve is equivalent to the Marginal Benefit/Utility Curve, so simply take the first
derivative of the Utility Function to find that
PS
100
c)
Derive the Supply Curve for SUVs.
The Supply Curve is equivalent to the Marginal Cost Curve, so simply take the first derivative of
the Production Cost Function to find that
P
S
=
2
d)
What is the Competitive Equilibrium price and quantity sold?
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View Full DocumentWe find the competitive equilibrium by setting the demand equal to supply, which yields
100
2
66
2
3
= f=
S
S
S
, to find the price, we put this quantity back into either the supply or the
demand curve, to get P=$
33
1
3
.
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 Spring '07
 Wood
 Economics, Producer Surplus, Supply And Demand, Utility, producer, net utility

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