Can you please explain how questions 4 and 5 are solved? Thank you! Suppose we h

Question

Can you please explain how questions 4 and 5 are solved? Thank you!

Suppose we have observations on output (Q) and labor (L) for 32 firms with identical levels of capital. You estimate the following from these data: SSE = 80 sigma q_i^2 = 200 sigma l_i^2 = 100 sigma q_i l_i = 40 Average of Q_i = 40 Average of L_i = 80 where q_i and I_i are deviations of output and labor, respectively, from their means. What are the ordinary least squares estimates of alpha and beta, respectively, in the equation: Q_i = alpha + beta L_i + epsilon_i 24 and 0.20 -160 and 2.5 8 and 0.4 64 and 0.2 There's not enough information to estimate this regression What is the elasticity of output with respect to labor, evaluated at the mean output and labor input? 0.20 0.4 0.25 25.0 0.80

Explanation / Answer

4. beta= ssxy/ssxx = 40/100 = 0.4

alpha = ybar - beta*xbar = 40-80*0.4 = 8

5.elasticity = beta*(x/y) = 0.4*(80/40) = 0.8

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