A profit-maximizing firm in a competitive market has total costs TC(q) = 10 + 4q + q2 and marginal costs are MC(q) = 4 + 2q. What are its total costs if it faces a market price of £24?

Round to two decimal places and do not enter the currency symbol. If your answer is £1.125, enter 1.13.

Question

A profit-maximizing firm in a competitive market has total costs TC(q) = 10 + 4q + q2 and marginal costs are MC(q) = 4 + 2q. What are its total costs if it faces a market price of £24?

Round to two decimal places and do not enter the currency symbol. If your answer is £1.125, enter 1.13.

BlackTom AI · Accepted Answer

In a perfectly competitive market, a profit-maximizing firm chooses output where price equals marginal cost (P = MC), provided it covers average variable costs in the short run. Here, the given MC function is MC(q) = 4 + 2q and the market price is P = 24. 
To find the profit-maximizing quantity, set MC equal to P: 4 + 2q = 24. 
Solving for q gives 2q = 20, so q = 10. 
Next, compute total costs at this quantity using the provided total cost function TC(q) = 10 + 4q + q^2. 
Plugging in q = 10 yields TC(10) = 10 + 4(10) + (10)^2 = 10 + 40 + 100 = 150. 
Since the instruction asks for two decimal places and without currency symbols, the final numerical total cost to report is 150.00. 
Note that if one tried a different rule, such as setting P equal to average total cost or evaluating at a different q, the result would not reflect profit maximization under price-taking behavior with the given TC and MC functions. Also, remember that fixed costs are included in TC, but the decision rule for output hinges on MC versus P rather than TC directly. In this problem, the key steps were identifying q via P = MC and then substituting into TC to obtain the total cost.

A profit-maximizing firm in a competitive market has total costs TC(q) = 10 + 4q + q2 and marginal costs are MC(q) = 4 + 2q. What are its total costs if it faces a market price of £24? Round to two decimal places and do not enter the currency symbol. If your answer is £1.125, enter 1.13.Numerical

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