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
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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)
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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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