A​ "Cobb-Douglas" production function relates production ​(Q​) to factors of​ production, capital ​(K​), labor ​(L​), raw materials ​(M​), and an error term u using the equation ​, Q= λK^β1L^β2M^βe^μ

where ​λ,β1,β2 ​and β2 and are production parameters. Suppose that you have data on production and the factors of production from a random sample of firms with the same​ Cobb-Douglas production function. Which of the following regression functions provides the most useful transformation to estimate the​ model?

a. A linear regression function.
b. A logarithmic regression function.
c. An exponential regression function.
d. A quadratic regression function.

The correct option is b. A logarithmic regression function.

Step-by-step explanation:

Given:

Q= λK^β1L^β2M^β3e^μ ………………………. (1)

Equation (1) can be transformed into a logarithmic regression function by taking natural log of both sides as follows:

lnQi = lnλ + β1lnKi + β2lnLi + β3lnMi + μInei ……………….. (2)

Where i = 0, 1, 2….n observations.

Let lnλ = β0 and let μIne = εi and then substituting them into equation (2), we have:

lnQi = β0 + β1lnKi + β2lnLi + β3lnMi + εi (3)

Equation (3) is the logarithmic regression function to estimate the model.

Therefore, the correct option is b. A logarithmic regression function.

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