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Rule The firm should produce where MR = MC PROVIDED that above that output MC exceeds MR and below that output MR exceeds MC. MC, MR. MC. Q. O. Q 1. Q 2. MR. Shut down point. Costs, revenue. AC. P = AVC. AVC. AR = D. Q. O. Q. Using calculus to find maximum profit output.
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Rule The firm should produce where MR = MC PROVIDED that above that output MC exceeds MR and below that output MR exceeds MC. MC, MR MC Q O Q1 Q2 MR
Shut down point Costs, revenue AC P = AVC AVC AR = D Q O Q
Using calculus to find maximum profit output • TR = 48Q – Q2 • TC = 12 + 16Q + 3Q2
FINDING WHERE MR = MC • MR = dTR dQ MC = dTC dQ • Differentiating the TR and TC gives dTR = 48 – 2Q = MR dQ dTC = 16 + 6Q = MC dQ
Profit is maximized where MR = MC: 48 – 2Q = 16 + 6Q • Solving this for Q gives: 32 = 8Q Q = 4 • The equation for total profit is Tπ = TR –TC = 48Q – Q2 – (12 + 16Q + 3Q2) = -12 + 32Q – 4Q2 Putting Q = 4 Tπ = 52
Slope = – 1 Slope = – 2 AR Q MR
A price taking firm (a) The market (b) The firm P S AR,MR (RS) D=AR = MR P* D O Q O Q (millions)
Firm makes super normal profits Costs, revenue MC AC D=AR = MR AR T V AC L K Q O Q*
Firm makes normal profits Costs, revenue MC AC` T D=AR = MR V AR Q O Q*
Firm makes loss Costs, revenue MC AC`` S AC U D=AR = MR AR V T Q O Q*