F I L E Economists often exam ine the relationship betw een th e inputs o f a production fu n ction and th e resulting o u tpu t. A com m on w ay o f m odeling this relationship is referred to as the Cobb-Douglas production function.

This function can be expressed as ln(Q) = β 0 + β 1 In(L) +

β 2 ln(K ) + ε . where Q stands fo r ou tpu t, L for labor, and K for capital. The fo llo w in g table lists a po rtio n o f data relating to th e U.S. agricultural industry in the year 2004;

the com plete data, labeled Production Function, are available on the te xt website.

State Output Labor Capital AL 3.1973 2.7682 3.1315 AR 7.7006 4.9278 4.7961 WY 1.2993 1.6525 1.5206 SOURCE: w w w .e r s .u s d a .g o v /D a ta /A g P r o d u c tiv ity ; s e e T a b le s 3 , 8 , 10. V a lu e s in ta b le a re in d ic e s .

E s tim a te ln (Q) = β 0 + β 1 In(L) + β 2 In(K ) + ε .

a. W h a t is th e p re d ic te d c h a n g e in o u t p u t if la b o r incre a ses b y 1 % , h o ld in g c a p ita l c o n s ta n t?

b . H o ld in g c a p ita l c o n s ta n t, ca n w e c o n c lu d e a t th e 5 %

le v e l th a t a 1% in c re a s e in la b o r w ill in cre a se th e o u t p u t b y m o re th a n 0.5% ?