Assume that production is characterized by the Cobb€“Douglas production function

Q_i = AK^α_i L^β_i

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.

In Q; = In A +a In K + In L + In u li (1) In Q; = In + In L + In + In u 21 (2)