Suppose the production function is Y = AK0.3N0.7. Suppose in 2000, K = 1000, N = 100, and Y = 199.5. In 2010, capital, labor, and output have doubled, so K = 2000, N = 200, and Y = 399
(a) By what percentage did productivity grow from 2000 to 2010? (b) If output had risen to 798 instead of 399, and capital and labor doubled, by what percentage would productivity have grown from 2000 to 2010?
(a) From the production function, you can calculate that A = 1 in both 2000 and 2010, so A is unchanged.
(b) Since output doubles (relative to the case in which Y = 399 in 2010 ) with the same amounts of capital and labor, A doubled.
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