Suppose TC = 10 + (0.1 ∗ q²).If p = 10,the firm's profit-maximizing level of output is

Question

Quizplus · Accepted Answer

In order to maximize profit, the firm should produce where Marginal Cost (MC) is equal to Marginal Revenue (MR). We can derive the firm's MC equation by taking the derivative of TC with respect to q and setting it equal to the fixed cost (10), as the variable cost is 0.1q. Therefore,
MC = 10 + 0.1q
We can derive the firm's MR equation from the demand equation, which is given implicitly as p = 10. Therefore,
MR = 10
Setting MC = MR and solving for q, we get
10 + 0.1q = 10
0.1q = 0
q = 0
However, producing 0 output will result in negative profit since Total Revenue will also be 0. Therefore, the firm's profit-maximizing level of output is the one before the point where the MC curve crosses the MR curve, which is at q = 50. Thus, the answer is B.