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AAE 320 Spring 2007
Exam #1
Name: ____KEY
_____________________
1) (15 pts.)
You manage a berry farm and hire laborers.
The table below reports how many pints
of berries are picked, cleaned, and ready for sale in an hour with different numbers of laborers.
Laborers Hired
Pints of Berries
Marginal Product
Value of Marginal Product
3
50


5
70
10
$20
7
84
7
$14
9
94
5
$10
a)
Using numbers given in this table, show below how to calculate the Marginal Product for one
example, and then fill in the Marginal Product column in the table above.
MP =
∆
Q/
∆
X = (70 – 50)/(5 – 30 = 20/2 = 10
b)
Berries sell for $2.00/pint.
Using numbers from this table, show below how to calculate the
Value of Marginal Product for one example, and then fill in the Value of Marginal Product
column in the table above.
VMP = price
x
MP = 2
x
10 = $20
c)
What optimality condition defines the profit maximizing amount of the input to use?
(Be brief and to the point.)
VMP = input price r
d)
If wages, taxes, liability insurance, etc. cost $12/hour to hire a laborer, what is the profit
maximizing number of laborers to hire?
(You may need to interpolate between entries.)
We need VMP of $12.
In the table, this will occur somewhere between VMP of $14 and
$10.
Notice that $12 is halfway between $14 and $10, so go with
8 laborers
.
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Soybean yield as a function of potassium fertilizer is Y = 30 + 0.6K – 0.01K
2
, where
yield Y is bu/ac and the potassium rate K is lbs/ac.
The price of soybeans is $8.00/bu and the
price of potassium $0.20/lb.
a)
What is the economically optimal fertilizer rate? Set up and solve this economic problem
using calculus and the given information (Be sure to check the second order condition)
.
π
= 8(30 + 0.6K – 0.01K
2
) – 0.2K
FOC: d
π
/dK = 8(0.6 – 0.02K) – 0.2 = 0
Solve FOC to get K = 28.75 lbs/ac
Check SOC: d
2
π
/dK
2
= 8(– 0.02) = –0.16 < 0, satisfied for a maximum
b)
At the potassium rate you derived in part a, what is yield (bu/ac)?
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 Spring '08
 MITCHELL

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