Chapter 6: Introduction to Differentiation and Applications Worked Example 6.25 Figure 6.27 Profit Maximization for perfect competition: Slide 2 Worked Example 6.26 Figure 6.28 Profit Maximization for a monopolist: Slide 3 Worked Example 6.31, Figure 6.37: Total Cost, Fixed Cost, Marginal Cost and Variable Cost: Slide 3 Worked Example 6.32: Figure 6.38 TC, TVC, MC, AVC, AC: Slide 4 Worked Example 6.32: Figure 6.38 (b) Points of intersection for MC, AC, AVC: Slide 5 Worked Example 6.29/6.30: Figure 6.36 Short run Production function and MPL, and APL: Slide 6 Worked Example 6.42, Figure 6.41: The relationship between TR, MR and elasticity of demand: Slide 7

Profit Maximization for perfect competition Worked Example 6.25 6000 TC (a) 5000 4000 TR 3000 2000 1000 Q 5 10 15 20 25 30 -1000 Q = 2 Q = 18 p -2000 -3000 700 (b) 600 Profit maximization MC 500 400 300 Profit minimization 200 MR 100 Q 5 10 15 20 25 30 Figure 6.27

Profit Maximization for a monopolist Worked Example 6.26 3500 (a) TC 3000 2500 TR 2000 1500 1000 Q = 15 500 Q = 1 Q 5 10 15 20 25 -500 p -1000 400 (b) Profit maximization 350 MC 300 250 Profit minimization 200 150 100 MR 50 Q 5 10 15 20 25 Figure 6.28

Total Cost, Fixed Cost, Marginal Cost and Variable Cost Figure 6.37 C (a) TC TVC Points of inflection Q (b) C Minimum MC = 25 MC Q Figure 6.37

Relationship between TC, MC, AVC, AC (a) Figure 6.38: Worked Example 6.32 C (a) TC , TVC , TFC functions TC TVC Points of inflexion TFC Q C (b) AC , AVC , MC functions Minimum AC MC Minimum AVC Minimum MC AC AVC Q

Points of intersection for MC, AC, AVC Graph MC. AC. AVC as given in Worked Example 6.32 C (b) AC , AVC , MC functions Minimum MC AC Minimum Minimum AVC MC AC AVC Q Figure 6.38(b): Worked Example 6.32

Point of inflexion on the production function Worked Example 6.29 / 6.30 Point of inflexion on the production function Q (a) Short-run production function 400 350 Q = f ( L ) 300 250 200 Point of inflexion 150 100 50 L 2 4 6 8 10 12 14 16 18 20 22 Maximum MP L MP L 30 APL Maximum APL 25 20 APL 15 10 5 L 2 4 6 8 10 12 14 16 18 20 22 -5 -10 (b) MP L , APL functions -15 Figure 6.36 Short-run production function, and APL functions MP L

The relationship between TR, MR and elasticity of demand Figure 6.41: Worked Example 6.42 P MR MR = 60 - 1.2 Q (MR = a -2bQ) P = 60 - 0.6 Q (P = a - bQ) Q TR e d < > - 1 e d > < - 1 e d = - 1 TR Q = - 60 6 2 . a Q = a/b Q = 2 b Q