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Topic 10: Integration

Topic 10: Integration. Jacques Indefinate Integration 6.1 Definate Integration 6.2. Intuition. Definition. Rule 3 of Integration: Example. Marginal Cost Function. Another Example. Another Example. Some general points for answering these types of questions. Definite Integration.

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Topic 10: Integration

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  1. Topic 10: Integration Jacques Indefinate Integration 6.1 Definate Integration 6.2

  2. Intuition

  3. Definition

  4. Rule 3 of Integration: • Example

  5. Marginal Cost Function

  6. Another Example

  7. Another Example

  8. Some general points for answering these types of questions

  9. Definite Integration

  10. Example

  11. Definition

  12. Consumer Surplus Difference between value to consumers and to the market…. Represented by the area under the Demand curve and over the Price line…..

  13. Or more formally….

  14. Producer Surplus Difference between market value and total cost to producers…. Represented by the area over the Supply curve and under the Price line…..

  15. Or more formally….

  16. Example 1…..

  17. The picture…. 2) ‘sketch’ diagram P = 30 – 4Q intercepts: (0, 30) and (7.5, 0) At Q = 5, we have P = 10 ….. Draw in price line….

  18. Calculation…

  19. Example 2

  20. The picture…. 2) ‘Sketch’ the diagram P = 3 + Q2 intercept: (0, 3) Price line at Q = 4, P = 19

  21. Calculation…

  22. Example 3 • The inverse demand and supply functions for a good are, respectively: • and • Find the market equilibrium values of P and Q. • Find the Total surplus (CS + PS) when the market is in equilibrium.

  23. Find market equilibrium….

  24. ‘sketch’ the diagram

  25. Consumer surplus…

  26. Producer Surplus…

  27. Total Surplus • Total surplus = CS + PS = 16 + 8 = 24

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