What is the total profit earned by the firm?

Question

Given a perfectly competitive market structure at the profit-maximizing output level, a firm's average fixed costs are $3, total variable costs are $137, marginal revenue is $4, and the quantity demanded is 65.

 

a)$123

b) -$15

c) $195

d) -$72

e) $245

Answer 1

We can look at two different ways to answer this question, using Total Costs or Average Costs. The math is basic addition, subtraction, and division. The tricky part is making sure you use the correct equations and understand the relationship between all the values.

If we calculate profits using total costs, we can use the equation: Total Profit = Total Revenue – Total Cost.

Now we can calculate each part of that equation.

How to Calculate Total Revenue: TR = Price x Quantity

$4 x 65 = $260

How to Calculate Total Cost: TC = Total Fixed Costs + Total Variable Costs

The question doesn’t explicitly tell us what Total Fixed Costs are, so we will have to find that using Average Fixed costs.

Average Fixed Costs = Total Fixed Costs/Quantity

$3 = TFC/65

TFC = $195

Now we can plug that back into our equation for Total Cost

TC = TFC + TVC

TC = $195 + $137

TC = $332

Now we can plug that number back into our original equation for Total Profit.

Total Profit = TR – TC

Total Profit = $260 - $332

Total Profit = -$72

The answer is D.

Alternative explanation: You can also answer this question using average costs instead of total costs. It’s less likely that you would see a question framed this way on the AP Exam, but the math comes out the same and it might help to see how these numbers relate to each other in a different way.

To answer the question this way, we can use this equation:

Average Profit = Average Revenue – Average Total Cost.

Just like before we need to calculate each part of the equation first.

In a perfectly competitive market, Marginal Revenue = Average Revenue. So in this question, Average Revenue is $4.

How to Calculate ATC: Average Total Costs = AFC + AVC

Average Fixed Costs (Total Fixed Costs/Quantity) are $3 and Average Variable Costs (Total Variable Costs/Quantity) are $2.10 .

So, ATC = $5.10

Just like before we can take that number and plug it back into our original profit equation:

Average Profit = AR – ATC

Average Profit = $4 - $5.10

Average Profit = -$1.10

So....

Total Profit = Average Profit x Quantity

Total Profit = 65 x -$1.10

Total Profit = -$71.5

Again, the answer is D.

Extra-credit review question: Why does MR = AR in a perfectly competitive market?