Profit Analysis of the Firm

1. Profit Analysis of the Firm

2. 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). dT / dQ = M = 0 • 2 such points (Q1, Q3) require: • 2. d2T / dQ2 is negative ormax TR - TC => Q* = Q3.

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* = Q3(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*

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

6. 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.

7. 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 QBE = TFC / (P – AVC)P = $6, AVC = $3.6, TFC = $60KQBE = 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)

8. 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