ajaz_204_2009_lecture_8

ajaz_204_2009_lecture_8 - University of Toronto Department...

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University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 8 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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Today ± Consumption & savings: one period model ² UMP: one vs. two options for savings ± Consumption & savings: two period model ² Real Price and Real Income ² Consumption and savings without capital markets ² Consumption and savings with capital markets ² Intertemporal budget constraint o Present value (PV) vs. Future value (FV) constraint ² Graphical UMP for zero inflation economy Ajaz Hussain. Department of Economics. University of Toronto (St. George) 2
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Consumption & Savings: One Period Model Y = Income in dollars C = Consumption in dollars S = Savings in dollars UMP: Choose C, S to max Utility such that C + S Y When can you solve UMP by Lagrangean? Ajaz Hussain. Department of Economics. University of Toronto (St. George) 3 Assume there’s only one savings option (ECO 100 “loanable funds”)
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C and S: One Period Model Cobb Douglas Utility Function UMP : choose C, S to Max U = S α C β s.t. S + C = Y L = S α C β ‐λ [S + C Y] L = λ [S + C Y] Optimal S = [ α /( α + β )]Y Optimal C = [ β /( α + β )]Y Optimal λ = ( α + β )/Y Will consumer always save? When is consumer a borrower ? Impact on optimal utility due to higher income? Ajaz Hussain. Department of Economics. University of Toronto (St. George) 4 In test & exam, derive these
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Example: One Period Model Cobb Douglas Utility Function α = β = ¼, Y = $16,000 Optimal S = [ α /( α + β )]Y = Optimal C = [ β /( α + β )]Y = Optimal λ = ( α + β )/Y = Ajaz Hussain. Department of Economics. University of Toronto (St. George) 5
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C and S: One Period Model Tax Free Saving Account In 2008, Canada introduced You can deposit up to $5,000/year into TFSA account TFSA Limit = L (currently $5,000) Ignore tax treatment and impact on income (RSM 332) S 1 = TFSA savings, S 2 = Other savings, C = Consumption Suppose U = S 1 α S 2 β C γ Let: α + β + γ = 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 6
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UMP for Individual with Annual TFSA Contribution < Limit UMP : choose S 1 , S 2 ,C to Max U = S 1 α S 2 β C γ s.t. S 1 + S 2 + C = Y L = S 1 α S 2 β C γ ‐λ [S 1 + S 2 + C Y] L = λ [S 1 + S 2 + C Y] Optimal S 1 = [ α /( α + β + γ )] Y Optimal S 2 = [ β /( α + β + γ )] Y Optimal C = [ γ /( α + β + γ )] Y Optimal λ = ( α + β + γ )/Y Ajaz Hussain. Department of Economics. University of Toronto (St. George) 7 Interpretation? In test & exam, derive these
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UMP for Individual with Annual TFSA Contribution = Limit UMP : choose S 1 , S 2 ,C to Max U = S 1 α S 2 β C γ s.t. S 1 + S 2 + C = Y and S 1 = L = Limit L = L α S 2 β C γ ‐λ [L + S 2 + C Y] = L α S 2 β C γ [S 2 + C (Y L )] L = α ln L + β ln S 2 + γ ln C ‐ λ [ L + S 2 + C Y] Optimal S 1 = L (Currently $5,000)
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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ajaz_204_2009_lecture_8 - University of Toronto Department...

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