1. Slide 17.1 Microeconomics MathematicalMarketing Chapter 17 Econometrics This series of slides will cover two aspects of Chapter 17  Elasticity  Optimizing Decisions

2. Slide 17.2 Microeconomics MathematicalMarketing The Demand Curve p1p1 p2p2 q1q1 q2q2 p q

3. Slide 17.3 Microeconomics MathematicalMarketing Revenue Visualized p1p1 p2p2 q1q1 q2q2 p q Can we see revenue on this curve?

4. Slide 17.4 Microeconomics MathematicalMarketing Change in Demand, Change in Price p1p1 p2p2 q1q1 q2q2 p q  q = q 1 – q 2  p = p 1 – p 2

5. Slide 17.5 Microeconomics MathematicalMarketing Algebra → Calculus p1p1 p2p2 q1q1 q2q2 p q

6. Slide 17.6 Microeconomics MathematicalMarketing Elasticity Under the Linear Model q i =  0 + p i  1 so that but since q =  0 + p  1 then Elasticity depends on p

7. Slide 17.7 Microeconomics MathematicalMarketing The Cobb-Douglas Function ln q i = ln  0 +  1 ln p i

8. Slide 17.8 Microeconomics MathematicalMarketing Cobb-Douglas Elasticity

9. Slide 17.9 Microeconomics MathematicalMarketing Cobb-Douglas Is a Constant Elasticity Model but since e =  1

10. Slide 17.10 Microeconomics MathematicalMarketing The Breakeven Point Demand q = f(p) Revenue = pq Cost = g(q) Profit  = revenue - cost = pf(p) – g(q) = pq - g(q) Breakeven point occurs when pq = g(q) or

11. Slide 17.11 Microeconomics MathematicalMarketing Optimization

12. Slide 17.12 Microeconomics MathematicalMarketing Optimal Point Is Here The Chain Rule (3.14) has been employed