Economists often examine the relationship between the inputs of a production function and the resulting output. A common way of modeling this relationship is referred to as the Cobb-Douglas production function. This function can be expressed as ln(Q) = β0 + β1 ln(L) + β2 ln (K ) + ε, where Q stands for output, L for labor, and K for capital. The accompanying table lists a portion of data relating to the U.S. agricultural industry in the year 2004.

Estimate ln(Q) = β0 + β1 ln(L) + β2 ln(K ) + ε.
a. What is the predicted change in output if labor increases by 1%, holding capital constant?
b. Holding capital constant, can we conclude at the 5% level that a 1% increase in labor will increase the output by more than 0.5%?

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State AL AR Output 3.1973 7.7006 Labor 2.7682 4.9278 Capital 3.1315 4.7961 WY 1.2993 1.6525 1.5206