The following data give real GDP, Y, capital, \(K\), and labor, \(N\), for the U.S. economy in various years.

Units and sources are the same as in Table 3.1. Assume that the production function is \(Y=A K^{0.3} N^{0.7}\).

a. By what percentage did U.S. total factor productivity grow in each decade?

b. What happened to the marginal product of labor between 1960 and 2020? Calculate the marginal product numerically as the extra output gained by adding 1 million workers in each of the two years. The data for employment, \(N\), are measured in millions of workers, so an increase of 1 million workers is an increase of 1.0.

Table 3.1

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Year Y K N 1960 3262 3821 65 1970 4954 5767 78 1980 6764 8293 99 1990 9371 11,298 117 2000 13,138 15,887 134 2010 15,649 19,373 140 2020 18,385 23,539 158