A firm in a competitive market has the following cost structure: If the market price is $8, how many units of output should the firm produce to maximize profit?
A)5 units
B)6 units
C)7 units
D)8 units

Question

A firm in a competitive market has the following cost structure:  If the market price is $8, how many units of output should the firm produce to maximize profit?
A)5 units 
B)6 units 
C)7 units 
D)8 units

Quizplus · Accepted Answer

To maximize profit, the firm should produce where MC = MR. From the given cost structure, we can calculate the marginal cost as:
MC = $6 + $0.5Q
Where Q is the quantity produced. 
The market price is given as $8, which is also the firm's marginal revenue. 
Set MC = MR: 
$6 + $0.5Q = $8
$0.5Q = $2
Q = 4
So, the firm should produce 4 units of output to break even. To maximize profit, the firm should produce where MC = MR and where MR > AVC (otherwise, the firm should shut down in the short run). From the above equation, we can see that if the firm produces 4 units, it will not cover its variable costs ($6 + $0.5(4) = $8, which is equal to the market price). Therefore, the firm should produce more than 4 units. 
At Q=5, Total Revenue (TR) = $8*5 = $40, 
Total Cost (TC) = $49 ($20 + $6*5 + $0.25*5^2)
Profit (π) = $40 - $49 = -$9
At Q=6, TR = $48, 
TC = $56 ($20 + $6*6 + $0.25*6^2)
π = $48 - $56 = -$8
At Q=7, TR = $56, 
TC = $63 ($20 + $6*7 + $0.25*7^2)
π = $56 - $63 = -$7
At Q=8, TR = $64, 
TC = $72 ($20 + $6*8 + $0.25*8^2)
π = $64 - $72 = -$8
Therefore, the maximum profit is obtained at Q=5, and the firm should produce 5 units of output.

A Firm in a Competitive Market Has the Following Cost