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Economics 302
Summer 2007
Answers to Homework #2
Homework will be graded for content as well as neatness. Sloppy or illegible work will
not receive full credit. This homework requires the use of Excel which is a spreadsheet
program.
In your calculations, please round to the two places past the decimal wherever
necessary.
1.
Suppose that the production function for an economy is given by
Y = F(K, L) = AK
1/2
L
1/2
Where Y is output, A is the level of technology, K is capital and L is labor.
a.
Suppose that A has a value of 10, K has a value of 50, while L varies from 0
to 25 units. Using Excel prepare a spreadsheet showing the possible
combinations of labor, capital, technology and output that are possible for this
economy. Your table should include a column for labor, a column for capital,
and a column for output. I have included a sample of what the table should
look like below.
Technology
Labor
Capital
Output
10
0
50
0.00
10
1
50
70.71
10
2
50
100.00
10
3
50
122.47
10
4
50
141.42
10
5
50
158.11
10
6
50
173.21
10
7
50
187.08
10
8
50
200.00
10
9
50
212.13
10
10
50
223.61
10
11
50
234.52
10
12
50
244.95
10
13
50
254.95
10
14
50
264.58
10
15
50
273.86
10
16
50
282.84
10
17
50
291.55
10
18
50
300.00
10
19
50
308.22
10
20
50
316.23
10
21
50
324.04
10
22
50
331.66
10
23
50
339.12
10
24
50
346.41
10
25
50
353.55
1
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View Full Document b.
Now, use the data you generated in part (a) to draw the aggregate production
function where you will illustrate the relationship between aggregate output
on the vertical axis and labor on the horizontal axis. This graph will hold
technology and capital constant. Execute this graph using Excel.
Aggregate Production Function
0
50
100
150
200
250
300
350
400
1
3
5
7
9
11
13
15
17
19
21
23
25
Labor
Output
Output
c.
Now, suppose that this economy experiences a technological advance. A, the
measure of technology, now has a value of 12. Redo your calculations from
part (a) and with your new data, plot both the initial aggregate production
function (where A = 10) and the new aggregate production function (where A’
= 12).
Aggregate Production Function
0
100
200
300
400
500
1
3
5
7
9
11
13
15
17
19
21
23
25
Labor
Output
Output
d.
Now, this economy finds that the value of A is 12, but that its level of capital
has increased from 50 units to 60 units. Redo your calculations and generate a
new graph illustrating two different production functions: one with A’ = 12
2
and capital equal to 50 units; and the other with A’ = 12 and capital equal to
60 units. Use Excel to do this work.
Aggregate Production Function
0
100
200
300
400
500
600
1
3
5
7
9
11
13
15
17
19
21
23
25
Labor
Output
Output
Output
e.
Summarize briefly the effect of a change in technology or a change in capital
on the aggregate production function.
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This note was uploaded on 08/08/2008 for the course ECON 302 taught by Professor Gold during the Spring '07 term at Wisconsin.
 Spring '07
 GOLD
 Economics, Macroeconomics

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