ajaz_204_2009_lecture_6

ajaz_204_2009_lecture_6 - University of Toronto Department...

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University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 6 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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Today ± Utility Maximization Problem (UMP) ² Perfect Substitutes ² Complements ± Perfect Substitutes Applications ² ² ² McDonald’s and Starbucks ² iPhones in Japan ± Incentives Application ² Marketing ² Teenage sexual behavior ² Subsidized education ² Declining Birth Rates Ajaz Hussain. Department of Economics. University of Toronto (St. George) 2
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Perfect Substitutes UMP Max U = α Q 1 + β Q 2 s.t. P 1 Q 1 + P 2 Q 2 = Y L = α Q 1 + β Q 2 λ [P 1 Q 1 + P 2 Q 2 –Y] L/ Q 1 = 0 L/ Q 2 = 0 L/ ∂λ = 0 P 1 Q 1 + P 2 Q 2 = Y Ajaz Hussain. Department of Economics. University of Toronto (St. George) 3
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Perfect Substitutes UMP: Case 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 4 Q 2 Q 1 P 1 = P 2 At optimal solution, note how MRS = P 1 /P 2 Optimal Solution: any bundle along: P 1 Q 1 + P 2 Q 2 = Y Slope = 1 U = α Q 1 + β Q 2 For simplicity, assume α = β = 1 MRS = 1 Budget Line Slope = P 1 /P 2
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Perfect Substitutes UMP: Case 2 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 5 Q 2 Q 1 P 1 > P 2 Slope = 1 U = α Q 1 + β Q 2 For simplicity, assume α = β = 1 MRS = 1 Budget Line Slope = P 1 /P 2 At optimal solution, note how MRS < P 1 /P 2 Optimal Solution: Q 1 = 0, Q 2 = Y/P 2
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Perfect Substitutes UMP: Case 3 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 6 Q 2 Q 1 P 1 < P 2 Slope = 1 U = α Q 1 + β Q 2 For simplicity, assume α = β = 1 MRS = 1 Budget Line Slope = P 1 /P 2 At optimal solution, note how MRS > P 1 /P 2 Optimal Solution: Q 1 = Y/P 1 , Q 2 = 0
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Perfect Substitutes: “Competition” MRS = P 1 /P 2 P 1 Q 1 + P 2 Q 2 = Y MRS < P 1 /P 2 Q 1 = 0, Q 2 = Y/ P 2 MRS > P 1 /P 2 Q 1 = Y/P 1 , Q 1 = 0 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 7 If consumers perceive goods as “perfect substitutes” Implications for pricing? How is pricing different from “perfect competition”?
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Max U = min( α Q 1 , β Q 2 ) s.t. P 1 Q 1 + P 2 Q 2 = Y L = min( α Q 1 , β Q 2 ) – λ [P 1 Q 1 + P 2 Q 2 –Y] Cannot solve by taking FOCs because the utility function is not differentiable everywhere Exploit graphical analysis
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ajaz_204_2009_lecture_6 - University of Toronto Department...

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