ECON 221 Lecture Notes - Lecture 5: Standard Deviation
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First scenario: output price is given | ||||||||
The table (below) gives the total output, per hour, for anywhere from 0 to 17 workers. | ||||||||
You need to determine how many workers should be hired at five different wage rates, ranging from $13/hour up to $25/hour. The wage rate includes all relevant benefits. To get to this answer you will need to calculate the marginal product of labor and the marginal revenue product of labor. You will be entering the values you obtain for the boldy outlined celles into the Moodle submission area. | ||||||||
Cost of the other (non-labor) inputs that go into a case (and would need to be increased if more labor was hired and output increased) = | $13.00 | |||||||
Price received per case = | $15.00 | |||||||
Marginal product of labor is the change in total product when labor is increased by one. | ||||||||
Marginal Revenue Product (net of the cost of the other required inputs), when the output price is fixed) equals marginal product times the ((fixed) output price -$13) | ||||||||
Please note: A few of the table values are filled in. Use these to determine if your approach to the problem is correct. | ||||||||
Number of workers | Total product | Marginal product of labor | Marginal Revenue Product (net of the cost of the other required inputs) | |||||
0 | 0 | |||||||
1 | 10 | 10 | ||||||
2 | 21 | 11 | $22.00 | |||||
3 | 33 | 12 | $24.00 | |||||
4 | 46 | 13 | $26.00 | |||||
5 | 60 | 14 | $27.00 | |||||
6 | 75 | 15 | $30.00 | |||||
7 | 91 | 16 | $32.00 | |||||
8 | 106 | 15 | $30.00 | |||||
9 | 120 | 14 | $28.00 | |||||
10 | 133 | 13 | $26.00 | |||||
11 | 145 | 12 | $24.00 | |||||
12 | 156 | 11 | $21.00 | |||||
13 | 165 | 9 | $18.00 | |||||
14 | 172 | 7 | $14.00 | |||||
15 | 177 | 5 | $10.00 | |||||
16 | 179 | 2 | $4.00 | |||||
17 | 179 | 0 | $0.00 | |||||
Using the information from above, fill in the following 'derived demand' schedule: | ||||||||
Hourly wage | Number of workers to maximize profits | |||||||
$13.00 | 15 | |||||||
$17.00 | 13 | |||||||
$21.00 | 12 | |||||||
$23.00 | 11 | |||||||
$25.00 | 10 | |||||||
A |
B |
C |
D |
E |
|
1 |
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2 |
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3 |
Date |
Price of gas |
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4 |
Jan 07, 2008 |
325.3 |
|||
5 |
Jan 14, 2008 |
323.9 |
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6 |
Jan 21, 2008 |
320.1 |
|||
7 |
Jan 28, 2008 |
316.3 |
|||
8 |
Feb 04, 2008 |
313.5 |
|||
9 |
Feb 11, 2008 |
310.7 |
|||
10 |
Feb 18, 2008 |
315.4 |
|||
11 |
Feb 25, 2008 |
324.6 |
|||
12 |
Mar 03, 2008 |
325.2 |
|||
13 |
Mar 10, 2008 |
326.3 |
|||
14 |
Mar 17, 2008 |
333.7 |
|||
15 |
Mar 24, 2008 |
332.1 |
|||
16 |
Mar 31, 2008 |
334.8 |
|||
17 |
Apr 07, 2008 |
336.6 |
|||
18 |
Apr 14, 2008 |
341.6 |
|||
19 |
Apr 21, 2008 |
355 |
|||
20 |
Apr 28, 2008 |
366.9 |
|||
21 |
May 05, 2008 |
367.7 |
|||
22 |
May 12, 2008 |
376.4 |
|||
23 |
May 19, 2008 |
384.9 |
|||
24 |
May 26, 2008 |
397.5 |
|||
25 |
Jun 02, 2008 |
402.6 |
|||
26 |
Jun 09, 2008 |
407 |
|||
27 |
Jun 16, 2008 |
411.8 |
|||
28 |
Jun 23, 2008 |
411 |
|||
29 |
Jun 30, 2008 |
411.3 |
|||
30 |
Jul 07, 2008 |
412.3 |
|||
31 |
Jul 14, 2008 |
411.7 |
|||
32 |
Jul 21, 2008 |
408.4 |
|||
33 |
Jul 28, 2008 |
400.2 |
|||
34 |
Aug 04, 2008 |
393.9 |
|||
35 |
Aug 11, 2008 |
386.6 |
|||
36 |
Aug 18, 2008 |
376.4 |
|||
37 |
Aug 25, 2008 |
371.5 |
|||
38 |
Sep 01, 2008 |
369.8 |
|||
39 |
Sep 08, 2008 |
367.1 |
|||
40 |
Sep 15, 2008 |
373 |
|||
41 |
Sep 22, 2008 |
368 |
|||
42 |
Sep 29, 2008 |
362.7 |
|||
43 |
Oct 06, 2008 |
351.7 |
|||
44 |
Oct 13, 2008 |
323.9 |
|||
45 |
Oct 20, 2008 |
305 |
|||
46 |
Oct 27, 2008 |
286.1 |
|||
47 |
Nov 03, 2008 |
265.4 |
|||
48 |
Nov 10, 2008 |
247.7 |
|||
49 |
Nov 17, 2008 |
229.4 |
|||
50 |
Nov 24, 2008 |
212.8 |
|||
51 |
Dec 01, 2008 |
203 |
|||
52 |
Dec 08, 2008 |
191.8 |
|||
53 |
Dec 15, 2008 |
181 |
|||
54 |
Dec 22, 2008 |
178.1 |
|||
55 |
Dec 29, 2008 |
174.1 |
QUESTION 13
Label the next column (D) "6-month change." Here we will calculate how much prices have changed since the price six months ago. For example, if the price on January 1 were 224.1 and the price on July 1 is 324.1, the price change is 100. We can't calculate how much prices have changed over the past six months for the first half of 2008 because we don't know the price six months before. So, in column D, put an x in each cell for which we can't calculate the 6-month change. Starting in July, we can calculate the 6-month change. Using cell references, enter here the formula you should enter into cell D30 to calculate the 6-month change.
2 points
QUESTION 14
Copy and paste the formula from cell D30 (from the last question) into cells D31 to D55. What formula is now in cell D48?
2 points
QUESTION 15
What value is now in cell D50?
1 point
QUESTION 16
Label the next column (E) "% of Jan." In this column, we will divide every week's price by the price from January 7th. This will tell us as a percent how prices compare to their level at the start of the year. This time, we want an "absolute" reference so that it doesn't consider the position (i.e. "8 to the left and 2 down") but just locks in on B4 every time. To set up an absolute reference in a formula, we put the $ character into the reference, so instead of B4, we use $B$4. With the dollar signs in place, you can copy the formula and paste it, and in each case, it will go back to B4 regardless of where you are when you paste it. What formula should you type into cell E5 to get the "% of Jan" for January 14, 2008? Remember to use the absolute reference so it will be easy to copy later!
2 points
QUESTION 17
Copy and paste the formula from cell E5 into the rest of column E. (Well, at least from E6 down to E55.) What formula is now in cell E17?