Tutorial 5 (specific solutions):
April 18, 2026
Problem 2: Profit Maximization
Note: Kindly note everyone that there is a definite/methodical way from
exam’s point of view to solve question 2, we discussed during the tut today
which is given below:
Q2. A firm produces a product in a competitive industry and has a total
cost function
T C = 50 + 4q + 2q 2
and a marginal cost function
M C = 4 + 4q.
At the given market price of $20, the firm is producing 5 units of output.
Is the firm maximizing profit? What quantity of output should the firm
produce in the long run?
Solution
• If the firm is maximizing profit, then price will be equal to marginal
cost:
P = M C.
Setting price equal to marginal cost:
20 = 4 + 4q ⇒ q = 4.
We didn’t solve for this quantity in the tutorial which is the
profit maximization quantity to be produced in short-run under profit maximization. Hence1
• The firm is not maximizing profit, since it is producing more than the
optimal level.
• Current profit at q = 5:
π = T R − T C = 20 · 5 − (50 + 4 · 5 + 2 · 52 )
= 100 − (50 + 20 + 50) = 100 − 120 = −20.
• Profit at profit-maximizing output q = 4:
π = 20 · 4 − (50 + 4 · 4 + 2 · 42 )
= 80 − (50 + 16 + 32) = 80 − 98 = −18.
Note: You don’t need the shutdown condition in this question• Since profit is negative even at the optimal output level, in the long
run the firm should shut down production:
q = 0.
• Therefore, the firm should exit the industry.
Shutdown vs Exit:
• Shutdown (Short Run): Occurs when P < AV Cmin . The firm
stops production temporarily but still incurs fixed costs.
• Exit (Long Run): Occurs when P < AT Cmin . The firm leaves the
industry permanently as it cannot cover total costs.
In this problem, if you use the shutdown condition, note that:
Although P > AV C, profit is negative at the optimal output level, so the
firm will exit in the long run.
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