If you differentiate the production function with respect to capital, the partial derivative with respect to K is found to be -9.5+6K, which has a positive slope, meaning the marginal product of capital is positive, whereas the the partial derivative of the given production function with respect to labor is 6-8L, which has a negative slope, i.e. the marginal product of labor is negative. It may be concluded, the production function is capital intensive.
FACTOR DEPENDENCE: @shahnawaz, after taking the derivative, now let's suppose that K(0) and L(1), then production is -11.5. This is prima facie evidence of capital dependence. Assume that L(0) and K(1), now the production is +2.5---for every unit of capital input with zero labor the system could still produce positive 2.3. Capital provides a carrying capacity for this economy (system). Now assume that K = 0 and L = 0, the production is -3.5---over all this is quiet vulnerable a system. If k = 0 and L = 0, the system cannot sustain itself. These "conclusions" are only preliminary. We need further tests in order to verify whether the relationship is significant.
INTENSITY VERIFICATION: In order to conclude about intensity, we need to verify by test statistic. here, production depends on capital (X1) and labor (X2). For multiple regression, this test statistic may be helpful:
(1) F = MSR / MSE
Use the F-table for critical value. The degrees of freedom: v1 = p; and v2 = n - p -1. The following definition applies:
(2) SST = sum(Yi - Y*)2 where df = n - 1 and Y* = mean Y
(3) SSE = sum(Yi - Y^)2 where df = n - p - 1 and p = number of independent factors and Y^ = Y hat.
(4) SSR = sum(Yi^ - Y*) where df = p
(5) MST = SST / n -1
(6) MSE = SSE / n - p - 1
(7) MSR = SSR / p
If the test confirms that the relationship is statistically significant than we can conclude about significant factor intensity.
I agree with Mr. Karim. Please see the attached graph. It would be helpful...
I agree with all the answers above. It simply means if we derive Q with respect to K; dQ/dK = -9.5+6K. So if K changes by 10 units, Q will change by 50.5 times. While derivative of Q with respect to L; dQ.dL = 6 -12L. Means that if L changes by 10 units, Q will change by -114. It's K intensive.
Normally the concept of "capital intensive" or "labor intensiv" production functions comes into play if you compare sectors. If you only have one production function, you cannot conclude that production is capital intensive or labor intensive.
Drs. karim, tasci and Hasam have explained it quite clrearly. I agree with them.
Hello, the way I understand it is as folloows: the production function is a catalog of possibilities all of which are equally viable, now what "is " intensive is the particular allocation or combination of factors, either in one end of the production function or the other, so we need to know the factor prices to determine where the actual production will take place and accordingly the characteristic of bias toward one factor or the other i.e. capital or labor intensity. Greetings
Some easier way to view it is to
1. Derive Y wrt K and L. Take same unit of K and L and trace the changes in output.
2. Assume K is (0) and L is (1). Do the exact opposite.
3. As Kamil has done it, plot the equation in a graph!....
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