Section+handout+1_Fei+Han - Section Handout 1. Bivariate...

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Section Handout 1. Bivariate linear equation & 2D graph 1.1. Bivariate linear equation Example 1: univariate function 42 qp Demand function = Example 2: Inverse Demand function of example 1 20 . 5 pq =− p Example 3: 12 24 qq += Every bivariate linear equation represents a straight line in a 2D diagram. 1.2. 2D graph of a bivariate linear equation The graph depends on the horizontal/vertical axis. Step 1. What is on the horizontal axis? What is on the vertical axis? Step 2. What are the horizontal intercept and the vertical intercept of the straight line? Step 3. Join the two intersection points to form a straight line. If q is on the horizontal axis, and p is on the vertical axis, then the 2D graphs are: Example 1: Example 2: q . 5 = 2 p q 2 0 4 p q 0 4 Example 1 & 2 tell us: The graph of the inverse function is the same as the graph of the original function in the same 2D diagram. 1
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Example 3: 12 24 qq += In a 2D diagram with q 1 on the horizontal axis and q 2 on the vertical axis, the graph is: q 2 4 0 q 1 2 While in a 2D diagram with q 2 on the horizontal axis and q 1 on the vertical axis, the graph is: 2 q 1 q 2 0 4 1.3. 2D graph of a bivariate linear equation with exogenous parameters What is an exogenous parameter? (see section 3.1) Example: Demand function 10 2 CS qp p p = −− + , where: S p is the price of a substitute, and is the price of a complement, and they are both exogenous parameters. Draw the graph of the demand function in a 2D diagram with quantity on the horizontal axis and price on the vertical axis. (An equivalent saying is: “draw the graph of the inverse demand function”.) C p 2
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p 50 . 5 0 . 5 CS pp −+ Now suppose that the substitute price is 2, and the complement price is 1, then the graph becomes: 1.4. Slope of the graph What is the slope of the demand curve in the example in section 1.3?
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This note was uploaded on 02/04/2011 for the course EEP 100 taught by Professor Perloff during the Spring '10 term at University of California, Berkeley.

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Section+handout+1_Fei+Han - Section Handout 1. Bivariate...

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