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QSRP Quiz: First Week
Name:
Date: 7/31/08
You may consult your class notes and the book
only
(i.e. no collaboration among peer
students)
, and you may also use a calculator if you wish.
Please show all of your work
.
Answers without justification will not receive credit.
The purpose of this test is to tell
you on which skills, if any, you need to improve.
Question 1:
In United States, the daily oil demand (in barrels per day) varies according
to the function d(P) = 10
7
– 200P
2
, where P is the oil price in dollars. The daily oil supply
(in barrels per day) varies linearly as a function of oil prices given by s(P) = k.P, where k
is a constant equal to 80,000.
a) Draw the graphs of the demand and supply functions (as a function of P). It may not be
to scale.
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View Full Documentb) What is the equilibrium spot price of the crude oil. Calculate the crude oil demand
and supply (in barrels per day) at this equilibrium price.
To calculate the equilibrium spot price of the crude oil, equate the demand and supply
functions –
d(P) = s(P)
10
7
– 200P
2
= 80,000*P
200P
2
+ 80000P  10
7
= 0
P
2
+ 400P  50000 = 0
P
2
+ 500P – 100P  50000 = 0
P(P+500) – 100 (P+500) = 0
(P100)(P+500)=0
P = 100 and P = 500
Ignoring P = 500, we get the equilibrium spot price of the crude oil to be equal to 100.
c)
Since hurricane dolly in South Texas unexpectedly did not affect the supply from
Gulf of Mexico, there is excess oil supply of 2.875 million barrels on the spot market.
What is the new equilibrium spot price of crude oil. (Note that this excess supply has
not been accounted in the original supply function).
New supply function s(P) = 80,000*P + 2.875x10
6
To calculate the equiliburium spot price of the crude oil, equate the demand and supply
functions –
d(P) = s(P)
10
7
– 200P
2
= 80,000*P + 2.875 x10
6
200P
2
+ 80000P – 7.125x10
6
= 0
P
2
+ 400P  35625 = 0
P
2
+ 475P – 75P  35625 = 0
P(P+475) – 75 (P+475) = 0
(P75)(P+475)=0
P = 75 and P = 475
Ignoring P = 475, we get the equilibrium spot price of the crude oil to be equal to 75.
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 Fall '10
 miller

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