Question

Excel

A factory owner wishes to estimate their firm's production function and provides you with data in problem 3 on “Homework 5 data".

A production function maps inputs-such as labor and capital-to the quantity of goods produced.Cobb-Douglas production function is a common way of characterizing this relationship and takes the form:

f(K, L)=Q=A K^{\alpha} L^{\beta}

where

*Q is the output (total production) *K is the capital input *L is the labor input *A is the total factor productivity (Think of this as technology) *a and B are the output elasticities of capital and labor, respectively

а.[2 Points] What assumptions are you implicitly making about the values of A, a, and ß-even the functional form of f (K,L)-during the data collection period?

b. [15 Points] Propose a model to estimate a and ß with OLS. Hint: Natural Log transformation on both sides of the production function

C. [3 Points] What restriction must we place on the values of Q, A, K, and L to make this transformation?

d. [5 Points] Estimate the values of a and B. Interpret the estimators from a statistical perspective.

e. The production function displays:

*constant returns to scale if a +ß = 1 *decreasing returns to scale if a +B <1 *increasing returns to scale if a +ß > 1

[5 Points] Does this factory experience constant, decreasing, or increasing returns to scale?

f.[3 Points] Perform a hypothesis test to see if it is feasible that this factory displays constant returns to scale. Assume Cov(â,ß) = 0.


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