Question

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.  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11  Fig: 12  Fig: 13