Final answer:
In a competitive market where the market price is $100, the firm should also charge $100 for the product to maximize profit, as this is where marginal revenue equals marginal cost.Option B is the correct answer.
Step-by-step explanation:
In a competitive market, firms are price takers, meaning they must accept the market price. Since the market price is given as $100, to maximize profit, your firm should also charge $100 for the product.
Profit maximization in a perfectly competitive market occurs where marginal revenue (MR) equals marginal cost (MC). In this case, since each additional unit is sold at the market price ($100), the MR is $100. Therefore, you want to produce where your MC is also $100 to maximize profits. However, your cost function is c(q)=100+0.5q2, here q represents the quantity produced and the marginal cost would be the derivative of this function with respect to q. To find q which makes MC = MR, we would set MR equal to MC and solve for q, then plug this q back into our pricing strategy. But since it's a competitive market, the firm cannot choose the price, it can only decide on the quantity to produce, so it will produce up to the point where the market price equals marginal cost.
As in the scenario given, the market price the firm should accept is $100 (B), which is also the correct answer to your multiple choice question.