I answered thsi very question back in July. Cutting and pasting my response back then:
(On July 23 to TrickyEconomics)
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You still have two values of 17 labor with different outputs. That said, here goes.
A) I wish there was more data, but a skatterplot kinda looks like an S-curve, which can be generated with a Cubic. So, yes.
B) for y= ax + bx^2 + cx^3 + d
I get (parameter and t-statistic):
a=-.81426 (-1.30)
b=0.10442 (2.46)
c=-.00183 (-2.17)
d=2.9235 (1.14)
Such parameters generate the shape shown in the skatter plot. With A cubic, its hard, a-priori to predict what the sign ought to be.
Only b is significant at the 5% level
C) the cubic is the total production function. Take the first dirivitive - this becomes the MP function. It has a maxima about 19. (check my math)
D) Plug 23 into the estimated cubic function and the derived MP function
E) since MP is falling at 23, SMC must be rising.
I hope this helps
Help me on this one please?
labor usage 3,7,9,11,17,17,20,24,26,28,30
output 1,2,3,5,8,10,15,18,22,21,23
a. does a cubic equation appear to be a suitable specification, given these data? You may construct a scatter
diagram to help with this question.
b.using the computer software for regression analysis, estimate your firm's short-run production function using thr data given here. Do the parameter estimates have the appropriate algebraic sighns? Are they statistically significant at the 5 percent level?
c.At what point do you estimate marginal product begins to fall?
D.calculate estimates of total, average, and marignal products when the firm employs 23 workers.
e.whenthe firm employs 23 workers, is short-run marginal cost (SMC) rising or falling? How can you tell.
2 answers
Output Labor X = L3 Y = L2
units/m hrs/m
1 3 27 9
2 7 343 49
3 9 729 81
5 11 1331 121
8 17 4913 289
10 17 4913 289
15 20 8000 400
18 24 13824 576
22 26 17576 676
21 28 21952 784
23 30 27000 900
a) Does a cubic euation appear to be a suitable specification, given these data? You may wish to construct a scatter diagram to help you answer
Yes a scatter diagram gives the s shape which is appropriate to indicate a cubic equation would be suitable.
b) Using a computer and software for regression analysis, estimate your firms's short-run production function using the data given here.
Do the parameter estimates have the appropriate algebraic signs? Are they statistically significant at the 5 percent level?
Yes the parameter estimates have the right algebraic signs
รข= -.00075 < 0 and b = .048731 > 0
k-1=2-1=1
n-k=11-2=9
Therefore the critical value of f is 5.12 at the 5% level as compared to the f ratio of 671.1836
The p values are insignificant and the chance of making a type 1 error are null.
The t values of -3.76916 and 9.238614 both exceed the critical t value for 9 degrees of freedom at the 5% level of 2.262 Regression Statistics
Multiple R 0.996664476
R Square 0.993340078
Adjusted R Square 0.881488976
Standard Error 1.277662242
Observations 11
ANOVA
df SS MS F Significance F
Regression 2 2191.308213 1095.654106 671.1836214 1.23183E-09
Residual 9 14.69178723 1.632420803
Total 11 2206
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
X Variable 2 -0.00074509 0.00019768 -3.769163007 0.004422153 -0.001192274 -0.000297906 -0.001192274 -0.000297906
X Variable 2 0.048730818 0.005274689 9.238614311 6.8893E-06 0.036798642 0.060662993 0.036798642 0.060662993
units/m hrs/m
1 3 27 9
2 7 343 49
3 9 729 81
5 11 1331 121
8 17 4913 289
10 17 4913 289
15 20 8000 400
18 24 13824 576
22 26 17576 676
21 28 21952 784
23 30 27000 900
a) Does a cubic euation appear to be a suitable specification, given these data? You may wish to construct a scatter diagram to help you answer
Yes a scatter diagram gives the s shape which is appropriate to indicate a cubic equation would be suitable.
b) Using a computer and software for regression analysis, estimate your firms's short-run production function using the data given here.
Do the parameter estimates have the appropriate algebraic signs? Are they statistically significant at the 5 percent level?
Yes the parameter estimates have the right algebraic signs
รข= -.00075 < 0 and b = .048731 > 0
k-1=2-1=1
n-k=11-2=9
Therefore the critical value of f is 5.12 at the 5% level as compared to the f ratio of 671.1836
The p values are insignificant and the chance of making a type 1 error are null.
The t values of -3.76916 and 9.238614 both exceed the critical t value for 9 degrees of freedom at the 5% level of 2.262 Regression Statistics
Multiple R 0.996664476
R Square 0.993340078
Adjusted R Square 0.881488976
Standard Error 1.277662242
Observations 11
ANOVA
df SS MS F Significance F
Regression 2 2191.308213 1095.654106 671.1836214 1.23183E-09
Residual 9 14.69178723 1.632420803
Total 11 2206
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
X Variable 2 -0.00074509 0.00019768 -3.769163007 0.004422153 -0.001192274 -0.000297906 -0.001192274 -0.000297906
X Variable 2 0.048730818 0.005274689 9.238614311 6.8893E-06 0.036798642 0.060662993 0.036798642 0.060662993
1 answer