Question

Complete the following table and answer the accompanying questions.

1. At what level of the control variable are net benefits maximized?

2. What is the relation between marginal benefit and marginal cost at this level of the variable?

Short answer

1. The net benefits are maximized when the control variable is 107.

2. The relation between the marginal benefit and marginal cost at that level of variable is that the marginal benefit is greater than the marginal cost.

Step-by-step solution

(a) Finding level of the control variable where net benefit is maximized.

We use the following equations to complete the table. Thus,

Net benefit = Total benefit-Total cost

$$\begin{gathered} =1,200-950 \\ =250. \end{gathered}$$

After calculating every row for the net benefits $N\left(Q\right)$using the same method, we can complete the table by the following way.

Net benefit = Total benefit-Total cost

$$\begin{gathered} =250-60 \\ =190 \end{gathered}$$

After calculating every row for the marginal benefits $MNB\left(Q\right)$using the same method, we can complete the table as the following way.

Total cost = total benefits-net benefits

$$\begin{gathered} =1,200-250 \\ =950 \end{gathered}$$

Therefore, based on the completed table, net benefits are maximized when the control variables is $107$.

(b) Relation between marginal benefits and marginal costs.

The relation between the marginal benefit and the marginal cost at that level of variable is that the marginal benefit is greater that the marginal cost.

If one more unit is added, the marginal cost will be greater than the marginal benefits. However, the marginal net benefit will be negative. Therefore, it is the most favorable point of the control variable.