Assume that production is characterized by the CobbDouglas production function Q i = AK α i L
Question:
Qi = AKαi Lβi
Where
Q = output
K = capital input
L = labor input
A, α, and β = parameters
i = ith firm
Given the price of final output P, the price of labor W, and the price of capital R, and assuming profit maximization, we obtain the following empirical model of production:
Production function:
Marginal product of labor function:
Marginal product of capital function:
where u1, u2, and u3 are stochastic disturbances.
In the preceding model there are three equations in three endogenous variables Q, L, and K. P, R, and W are exogenous.
a. What problems do you encounter in estimating the model if α + β = 1, that is, when there are constant returns to scale?
b. Even if α + β ‰ 1, can you estimate the equations? Answer by considering the identifiability of the system.
c. If the system is not identified, what can be done to make it identifiable? Note: Equations (2) and (3) are obtained by differentiating Q with respect to labor and capital, respectively, setting them equal to W/P and R/P, transforming the resulting expressions into logarithms, and adding (the logarithm of) the disturbance terms.
Step by Step Answer:
a Writing the system in matrix notation we obtain which can be written in matrix notation as Ay x ...View the full answer
