Profit Analysis of the Firm Profit Maximization for

Profit Analysis of the Firm

Profit Maximization for Total Measures T is maximized: • Where the slope of T is 0 (TR and TC are parallel or their slopes are equal). d. T / d. Q = M = 0 2 such points (Q 1, Q 3) require: 2. d 2 T / d. Q 2 is negative or max TR - TC => Q* = Q 3.

Profit Maximization for per Unit Measures T is maximized: • At Q where MR = MC. 2 such points require: • MR < MC for any Q > Q* = Q 3 (Q* is one of FONC candidates) or when MC is increasing. T = [(TR – TC)/Q]Q = (AR – AC)Q = (P – AC)Q Max T = area of the rectangle = (AR|Q* - AC|Q*)Q* = (P|Q* - AC|Q*)Q*

A Numerical Example • Given estimates of • P = 10 - Q • C(Q) = 6 + 2 Q • Optimal output? • MR = 10 - 2 Q = 2 = MC • Q = 4 units • Optimal price? • P = 10 - (4) = $6 • Maximum profits? • PQ - C(Q) = 6(4) - (6 + 8) = $10

Shut-Down Point • In the long run all cost must be recovered. • In the short run fixed cost incurred before production begins and do not change regardless of the level of production (even for Q = 0). • Shut down only if: –TFC > max T (total) P < AVC (per unit). • TFC = AFC*Q = (SAC – AVC)*Q • Operate with loss if: max T > –TFC (total) SAC > P AVC (per unit). – This is the third T maximizing condition.

Break-Even Analysis Approximation in absence of detailed data on revenue & cost. Assume both TR & TC are linear. At the Break-even: TR = TC = TVC + TFC P*QBE = AVC*QBE + TFC (P – AVC)*QBE = TFC / (P – AVC) P = $6, AVC = $3. 6, TFC = $60 K QBE = 60, 000 / (6 – 3. 6) QBE = $25, 000 (P – AVC) unit contribution margin. 1 – P/AVC contribution margin ratio (fraction of P to recover TFC)

Types of Business Analysis • Profit Maximization – Requires complete knowledge of Revenue and Cost Functions. • Break-Even Analysis – Simplified profit maximization analysis with limited applications • Incremental Profit Analysis – Variation of profit maximization analysis used to evaluate proposed projects by comparing incremental revenues and cost associated with project