ch04.1-systems-of-equations-comparative-statics

# ch04.1-systems-of-equations-comparative-statics - G = G 1...

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Systems of Equations and Comparative Statics Professor Erkut Ozbay Economics 300

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Systems of equations Model many participants Model many markets Model many related variables Solving systems of equations Comparative statics Find impact of change in exogenous variable on endogenous variables
Supply and demand 2 4 6 8 1 0 2 10 S D S D Q P Q P Q Q = - = - = Q P 2 10 2 12 6 4 S D P P P P Q Q - = - = = = =

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Supply and Demand Demand equation Q D = a – bP + cG G = price of substitute good a, b, c > 0 are parameters Supply equation Q S = d + eP Balance equation Q D = Q S = Q Substitute into balance equation d + eP = a – bP + cG Solve for P (b + e)P = a – d +cG P = (a – d +cG)/(b+e) Plug P into Q S or Q D Q = d + e(a – d +cG)/(b+e)
Comparative statics: Increase in price of substitute, G P P 1 P 0 Q Q 0 S D 0 D 1 P Q D = a – bP + cG Q S = d + eP c G Q 1 Q

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Comparative statics How does change in exogenous variable G impact endogenous variables P and Q? P = (a – d +cG)/(b+e) Q = d + e(a – d +cG)/(b+e) 2200 ∆

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Unformatted text preview: G = G 1 – G ; ∆ P = P 1 – P ; ∆ Q = Q 1 – Q • P 1 = (a – d +cG 1 )/(b+e) P = (a – d +cG )/(b+e) 2200 ∆ P = ∆ G c/(b + e) • Q 1 = d + e(a – d +cG 1 )/(b+e) Q = d + e(a – d +cG )/(b+e) 2200 ∆ Q = ∆ G ec/(b + e) Exercise: Solve for x, y, z • x = 6z + 3h – 4a + 10 • y = 4z – h + 6 • x = y • Substitute 1 st and 2 nd into 3 rd 6z + 3h – 4a + 10 = 4z – h + 6 • Solve for z 2z = 4a – 4h – 4 ⇒ z = 2a – 2h – 2 • Substitute z into 1 st and 2 nd x = 12a – 12h – 12 + 3h – 4a + 10 = 8a – 9h – 2 y = 8a – 8h – 8 – h + 6 = 8a – 9h – 2 Exercise: Impact of ∆ h = 3 • x = 8a – 9h – 2 • y = 8a – 9h – 2 • z = 2a – 2h – 2 2200 ∆ x = – 9 ∆ h = – 27 2200 ∆ y = – 9 ∆ h = – 27 2200 ∆ z = – 2 ∆ h = – 6...
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