Final answer:
When finding the profit-maximizing output for a price-taking farmer in a perfectly competitive market, the Marginal Cost (MC) must be set equal to the market Price (P). However, according to the MC function provided, the calculated output level for profit maximization is 2, not any of the provided options. A clarification or correction in the question or the provided functions might be necessary.
Step-by-step explanation:
The question involves determining the profit-maximizing level of output for a farmer who is a price taker in a perfectly competitive market for soybean sales. Given the cost functions TC = .1q2 + 2q + 30 and MC = 2q + 2, and a market price (P) of $6, we apply the economic principle that a firm maximizes profit by producing at the level where Price (P) equals Marginal Cost (MC). To find the profit-maximizing output level, we set MC equal to P and solve for q:
6 = 2q + 2
q = (6 - 2) / 2
q = 2
So, the correct answer is not listed in the options given, as the calculation above shows profit-maximization occurs at q = 2. A correction might be necessary because according to the provided reference information, MR and MC intersect at a quantity of 40, which would suggest that the profit-maximizing output level could be 40, assuming MR = P in a perfectly competitive market. However, with the provided equation, this is not the case. Therefore, clarification is recommended.