Question 5 How does the interpretation of the B2 coefficient

Question 5 How does the interpretation of the B2 coefficient differ between the following two models? where - P-firm productivity K-total value of capital L-labor (number of workers in the firm)

Solution

Model 1:

In this model, B2 is the differentiation coefficient i.e. An increase in total value of capital by one unit will lead to a B2 times increase in firm productivity. Thus, B2 = dP/dK

Model 2:

However, in Model 2, since there is another variable - labour - that affects firm productivity, B2 is the partial differentiation coefficient i.e. an incraese in total value of capital by one unit will partially affect the firm productivity by B2 times.

Thus, B2 = Del(P)/Del(K)

where Del = partial differenciation symbol.