The problem states that a farmer is a price taker for soybean sales. The total cost function is given by $TC = 0.1q^2 + 2q + 30$, and the marginal cost function is given by $MC = 0.2q + 2$. The price is given as $P = 6$. We are asked to find the profit-maximizing level of output.

1. Problem Description

The problem states that a farmer is a price taker for soybean sales. The total cost function is given by $TC = 0.1q^2 + 2q + 30$, and the marginal cost function is given by $MC = 0.2q + 2$. The price is given as $P = 6$. We are asked to find the profit-maximizing level of output.

2. Solution Steps

A price taker maximizes profit by producing where price equals marginal cost, i.e., $P = MC$.

We are given that $P = 6$ and $MC = 0.2q + 2$.

We set $P = MC$ and solve for $q$:

$6 = 0.2q + 2$

Subtract 2 from both sides:

$6 - 2 = 0.2q$

$4 = 0.2q$

Divide both sides by 0.2:

$q = \frac{4}{0.2} = \frac{40}{2} = 20$

3. Final Answer

The profit-maximizing level of output is

2

0. Final Answer: c. 20