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

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Presentation transcript:

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

2 Intuition

3 Definition

4

5

6 Rule 3 of Integration: Example

7

8 Marginal Cost Function

9 Another Example

10 Another Example

11

12

13

14 Some general points for answering these types of questions

15 Definite Integration

16 Example

17 Definition

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

19 Or more formally….

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

21 Or more formally….

22 Example 1…..

23 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….

24 Calculation…

25 Example 2

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

27 Calculation…

28 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.

29 Find market equilibrium….

30 ‘sketch’ the diagram

31 Consumer surplus…

32 Producer Surplus…

33 Total Surplus Total surplus = CS + PS = = 24