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 (Q 1, Q 3 ) require: 2.d 2 T  / dQ 2 is negative or max TR - TC => Q* = Q 3.

3. Profit Maximization for per Unit Measures T  is maximized: At Q where MR = MC. 2 such points require: MR 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*

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*Q BE = AVC*Q BE + TFC (P – AVC)*Q BE = TFC Q BE = TFC / (P – AVC) P = $ 6, AVC = $ 3.6, TFC = $ 60K Q BE = 60,000 / (6 – 3.6) Q BE = $ 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