The correct answer is: C. Statement I is true while Statement II is false.
Statement I is true. The least-cost or optimal input combination of labour capital requires that the marginal revenue productivity ratio of the two inputs should be equal to their price ration. This is known as the marginal productivity theory of factor demand. It states that a firm will hire workers up to the point where the marginal revenue product of labor equals the wage rate. Similarly, a firm will rent capital up to the point where the marginal revenue product of capital equals the rental rate.
Statement II is false. The marginal physical productivity of labor is not equal to $L^2 + 15L + 10$ in the hypothetical production function $Q = L^3 + 15L^2 + 10$. The marginal physical productivity of labor is the change in output that results from a one-unit change in labor input, holding all other inputs constant. In this case, the marginal physical productivity of labor is $3L^2 + 15L$.
To see this, let’s consider the following table:
| Labor input (L)| Output (Q)| Marginal physical productivity of labor (MP) |
|—|—|—|
| 0 | 0 | 0 |
| 1 | 10 | 10 |
| 2 | 35 | 25 |
| 3 | 70 | 35 |
| 4 | 115 | 45 |
| 5 | 165 | 50 |
As you can see, the marginal physical productivity of labor is increasing at first, but then it starts to decrease. This is because as we add more and more labor, each additional worker produces less and less output. This is because the workers start to get in each other’s way and there are diminishing returns to labor.
In conclusion, Statement I is true while Statement II is false.