Question

Summit Farms hires unskilled daily workers to pick strawberries in their fields. Output depends on the number of workers and on random factors such as weather. Summit Farms wishes to estimate itys short run production function and has collected the following data over 15 days on the number of workers. L and output, q, measured in pounds of strawberries.

a. Using Excel's regression tool to estimate a production function of the form q = aL^2 + bL^3 for Summit Farms. (Hint: This production function implies that output is zero when L=0. Therefore, you should set the constant term in the regression to zero, which is an option in the Regression tool.

b. Use the estimated function and Excel's charting tool to plot the estimated total product, average product of labor and marginal rpoduct of labor curves.

Day	L	Q
1	12.5	250
2	17.5	385
3	20	442
4	15	331
5	15	324
6	20	442
7	25	500
8	27.5	478
9	30	432
10	22.5	490
11	25	480
12	25	494
13	20	317
14	17.5	399
15	20	448

Answer 1

a.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.997
R Square	0.994
Adjusted R Square	0.917
Standard Error	34.613
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	2	2640453.561	1320226.781	1101.995	0.000
Residual	13	15574.439	1198.034
Total	15	2656028.000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.000	#N/A	#N/A	#N/A	#N/A	#N/A
L^2	2.293	0.107	21.407	0.000	2.061	2.524
L^3	-0.060	0.004	-14.148	0.000	-0.070	-0.051

So the estimated function is Q = 2.293*L^2-0.06*L^3

b.

Day	L	Q	L2	L3	Total Product	Average product = TP/L	marginal product =?L*(90*L-2293)/500
1	12.5	250	156	1953	240	19.21	29.2
2	17.5	385	306	5359	378	21.61	25.13
3	20	442	400	8000	433	21.67	19.72
4	15	331	225	3375	312	20.79	28.29
5	15	324	225	3375	312	20.79	28.29
6	20	442	400	8000	433	21.67	19.72
7	25	500	625	15625	488	19.53	2.15
8	27.5	478	756	20797	477	17.33	-10.01
9	30	432	900	27000	431	14.37	-24.42
10	22.5	490	506	11391	472	20.98	12.06
11	25	480	625	15625	488	19.53	2.15
12	25	494	625	15625	488	19.53	2.15
13	20	317	400	8000	433	21.67	19.72
14	17.5	399	306	5359	378	21.61	25.13
15	20	448	400	8000	433	21.67	19.72