Given the production function:
Q = 2L + 3K
The marginal products are derived as:
MPL (Marginal Product of Labor) = dQ/dL = 2
MPK (Marginal Product of Capital) = dQ/dK = 3
If we denote the price of labor as w and the price of capital as r (where r = 6), then the marginal product per dollar for each input is:
Marginal product of labor per dollar spent = MPL/w = 2/w
Marginal product of capital per dollar spent = MPK/r = 3/6 = 0.5
For efficient production, you'd want:
MPL/w = MPK/r
2/w = 0.5
But this equation does not suggest that 2L = 3K. Thus, the statement "it should always set 2L = 3K" is false.
