Question:

Assume that y is explained by \(\ln y=\alpha +\beta \ln x\) where x is a positive variable.

1. Show that (2) implies
   \(y=A{{x}^{\beta }}\) (3)
   for an appropriately defined A.
2. Show that (3) implies
   \(\,\frac{x}{y}\frac{dy}{dx}=\beta \)
   Comment on this result.
3. Use the result in part (b) to develop an interpretation of a and b in the production function

\(q=x_{1}^{a}x_{2}^{b}\)

where x1 and x2 are input levels, q is output, and a and

b are positive parameters.

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