The correct answer is: Only 1.
The point of inflexion exists where the first stage of the law of variable proportions ends. In the first stage, the total product increases at an increasing rate as more and more units of the variable input are added to a fixed amount of the fixed input. However, after a certain point, the total product starts to increase at a decreasing rate. This is because the law of diminishing returns has set in. The point at which the total product starts to increase at a decreasing rate is called the point of inflexion.
The total product can increase even when the marginal product is decreasing. This is because the total product is the sum of the marginal products of all the units of the variable input that have been used. So, even if the marginal product of each additional unit of the variable input is decreasing, the total product can still increase if the number of units of the variable input is large enough.
The producer will not stop only at the second stage of variable proportions. The producer will continue to add units of the variable input until the marginal product of the variable input is equal to the marginal cost of the variable input. This is because the producer wants to maximize profits, and the marginal product of the variable input is equal to the marginal cost of the variable input at the point of optimal output.
Therefore, only statement 1 is correct.