For the production function Q = aL + bK,where a and b are constants,the
A) declines as the firm substitutes labor for capital.
B) remains constant as the firm substitutes labor for capital.
C) implies upward-sloping, straight-line isoquants.
D) is undefined.

Question

For the production function Q = aL + bK,where a and b are constants,the 
A) declines as the firm substitutes labor for capital. 
B) remains constant as the firm substitutes labor for capital. 
C) implies upward-sloping, straight-line isoquants. 
D) is undefined.

Quizplus · Accepted Answer

The marginal product of labor (MPL) is a, which is a constant, and the marginal product of capital (MPK) is b, which is also a constant. Therefore, the marginal product of labor does not change as the firm substitutes labor for capital, and the marginal product of capital does not change as the firm substitutes capital for labor. Thus, the total output (Q) increases linearly with the increase in the total input of either labor or capital, and the slope of the isoquants is constant. Therefore, the marginal rate of technical substitution (MRTS) between labor and capital remains constant, which implies that the total output does not change as the firm substitutes labor for capital.

For the Production Function Q = AL + BK,where a and B