The total costs of a firm under perfect competition is given by the equation
TC = 5, 000 + 4Q + 2Q2 and the market price is $100 per unit.
What is the profit maximizing level of output?
Always Always Always. Set MC=MR. MC is the first derivitive of the TC function. So, MC=4+4Q. Solve for Q.
Equating MR=MC and solving for Q is this the answer?
part b to the question says to calculate the total revenue at the profit maximizing level. I'm not sure how to do this
To find the profit-maximizing level of output, we need to determine the quantity at which the firm's marginal cost (MC) equals the market price (P).
In perfect competition, the profit-maximizing level of output occurs where MC = P. We can find the marginal cost by taking the derivative of the total cost equation with respect to Q.
TC = 5,000 + 4Q + 2Q^2
Taking the derivative:
MC = d(TC)/dQ = 4 + 4Q
Setting MC equal to the market price of $100:
4 + 4Q = 100
Solving for Q:
4Q = 100 - 4
4Q = 96
Q = 96/4
Q = 24
Therefore, the profit-maximizing level of output is 24 units.