(a) Show that, by taking logarithms, the general Cobb-Douglas function P = bL α K 1− α can be expressed as ln P K = ln b + α ln 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 = 1.01 L 0.75 K 0.25 .
(a) Show that, by taking logarithms, the general Cobb-Douglas function P = bL α K 1− α can be expressed as ln P K = ln b + α ln 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 = 1.01 L 0.75 K 0.25 .
Solution Summary: The author explains that the general Cobb-Douglas function P=bLalpha K1- alpha can be expressed as mathrmlnP
(a) Show that, by taking logarithms, the general Cobb-Douglas function P = bLαK1−α can be expressed as
ln
P
K
=
ln
b
+
α
ln
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 = 1.01L0.75K0.25.
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