Chapter 14.1, Problem 81E

(a) Show that, by taking logarithms, the general Cobb-Douglas function P = bL^αK^1−α can be expressed as

$\ln \frac{P}{K}=\ln b+\alpha \ln \frac{L}{K}$

(b) If we let x = ln(L/K) and y = ln(P/K), the equation in part (a) becomes the linear equation y = αx + ln b. Use Table 2 (in Example 3) to make a table of values of ln (L/K) and ln(P/K) for the years 1899–1922. Then use a graphing calculator or computer to find the least squares regression line through the points (ln(L/K), ln(P/K).

(c) Deduce that the Cobb-Douglas production function is P = 1.01L^0.75K^0.25.