A firm operating in a perfectly competitive market has a

Solution

Find Marginal Cost (MC):

• Profit maximization requires MC(Q)=P for a perfectly competitive firm.
• MC is the derivative of the Total Cost (TC) function with respect to Q:

• Set MC equal to the market price (P=10):

• Profit is Total Revenue (TR) minus Total Cost (TC): π=TR−TC.
• TR(Q)=P×Q

• TC(Q)=20+2Q+0.5Q2

• π=TR−TC

• The firm should only produce if P≥AVC.

• VC(Q)=2Q+0.5Q2. AVC(Q)=QVC(Q)=2+0.5Q.

• AVC(8)=2+0.5(8)=6. Since P=10>AVC=6, the firm should continue to operate.