Cobb Douglas Production Function

" Write out exact expressions (in terms of Q, K, and L) for the OLS ‘normal equation’ (4 equations in 4 unknowns) for a data set with 50 observations. Returns to scale (RTS) in a 3-factor Cobb-Douglas production function are given by γ_1+γ_2+γ_3. If OLS is unbiased, will the sum of the OLS slopes in our model provide an unbiased estimator for returns to scale? Explain. Rewrite this model so that it will always exhibit constant RTS (i.e., γ_1+γ_2+γ_3=1). Simplify terms so that you end up with an equation of the form: Y_i=γ_0+γ_1 X_1i+γ_2 X_2i+u_i; Where Y, X1 and X2 are functions of the variables in the original variables Explain how you could use OLS regression results from the two versions of the model (with and without constant returns to scale) to formally test whether or not the true production function exhibits constant returns to scale. Specify null and alternative hypothesis, the exact form of the test statistic, and the exact degrees of freedom for the test. "