Suppose that labor input in total man hours(x) and total proiduction (y) follows

Question

Suppose that labor input in total man hours(x) and total proiduction (y) follows a single-input Cobb-Douglas production function:
Y= ß0X^(ß1) For each of the following pairs of variables, state whether the correlation coefficent is an appropriate summary (State yes or no) a) X and Y b) U and Y where U=X^ß1 c) X and V where V=Y^(1/ß1) d) log(X) and log(Y) could someone please explain this to me? Suppose that labor input in total man hours(x) and total proiduction (y) follows a single-input Cobb-Douglas production function:
Y= ß0X^(ß1) For each of the following pairs of variables, state whether the correlation coefficent is an appropriate summary (State yes or no) a) X and Y b) U and Y where U=X^ß1 c) X and V where V=Y^(1/ß1) d) log(X) and log(Y) could someone please explain this to me? c) X and V where V=Y^(1/ß1) d) log(X) and log(Y) could someone please explain this to me?

Explanation / Answer

a)
X and Y can not state the correlation coefficient to summarize the data.
b) U and Y where U=X^ß1. This may not represent correlation. c) X and V where V=Y^(1/ß1). This may not represent correlation. d) When we take logarithms for the given function y=ß0x^ß1. Then log(Y)=log(ß0)+ß1log(X) Now, we can determine the straight line relationship between the variables log (X) and log(Y). In this situtation correlation coefficient is the appropriate summary.

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