Assuming that the United States' output is characterized by a Cobb-Douglas production function with constant returns to scale and that the elasticity of output with respect to the capital input equals 0.25, consider the following five cases, where n equals the growth rate of labor, k equals the growth rate of capital, and a equals the growth rate of the autonomous growth factor.

(a) In each case, what is the rate of growth of output?
(b) In each case, what is the rate of growth of per person output?
(c) Assuming that the autonomous growth factor is a €œneutral€ type of technological change, which case or cases are consistent with steady-state growth?

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Case 1: Case II: Case III: Case IV: n=1% n=2% n-1% n-3% k=3% k=3% k-4% k-3% a=2.5% a=0.75% a:2.4% a 0%