The problem states that a farmer's total cost (TC) function is given by $TC = 0.1q^2 + 2q + 30$ and the marginal cost (MC) function is $MC = 0.2q + 2$. The farmer has to purchase a license for $50 per period. The question asks for the farmer's new total cost function.

1. Problem Description

The problem states that a farmer's total cost (TC) function is given by $TC = 0.1q^2 + 2q + 30$ and the marginal cost (MC) function is $MC = 0.2q + 2$. The farmer has to purchase a license for $50 per period. The question asks for the farmer's new total cost function.

2. Solution Steps

Since the license cost is a fixed cost, it is simply added to the existing total cost function.

The original total cost function is:

$TC = 0.1q^2 + 2q + 30$

The cost of the license is $50$.

Therefore, the new total cost function is:

$New TC = 0.1q^2 + 2q + 30 + 50$

$New TC = 0.1q^2 + 2q + 80$

3. Final Answer

The new total cost function is $TC = 0.1q^2 + 2q + 80$. However, the available options contain a typographical error where "2q" is written as ".2q". Assuming that "2q" should be "2q", the closest answer is $TC = 0.1q^2 + 2q + 80$ if the typo is understood.

The answer is (b). $TC = 0.1(q^2) + .2q + 80$ if we take the options literally.

However, I will assume it should be read as TC = 0.1(q^2) + 2q +

8

0. Since option (a) has 50, we add

2

0. Assuming the question means $TC = 0.1q^2 + 2q + 30$, then $New TC = 0.1q^2 + 2q + 30 + 50 = 0.1q^2 + 2q + 80$.

Final Answer: $TC = .1 (q^2) + 2q + 80$, however, it appears that the "2q" term has been typoed to be ".2q" in the given answers. Assuming this typo and based on the problem statement, the answer is:

b. $TC = .1 (q^2) + .2q + 80$