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ajaz_204_2009_lecture_9 - University of Toronto Department...

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University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 9 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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Today Consumption/Savings Two period model with capital markets Intertemporal budget constraint Present value (PV) vs. Future value (FV) constraint Real interest rates Fisher approximation Intertemporal consumption: complements utility Intertemporal consumption: Cobb Douglas utility Ajaz Hussain. Department of Economics. University of Toronto (St. George) 2
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T = 2 Model With Capital Markets Ajaz Hussain. Department of Economics. University of Toronto (St. George) 3 T = 1 “Young” T = 2 “Old” Receive “Endowment” Y 1 (real terms) Consume < “Endowment” C 1 < Y 1 “Save” Save = Y 1 C 1 Consume > “Endowment” C1 > Y1 “Borrow” Borrow = C1 Y1 Receive “Endowment” Y2 and Receive Principal + interest on Savings Receive “Endowment” Y2 but Pay Back Loan +interest
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Assumptions Consumer receives ( real ) incomes Y 1 and Y 2 Incomes are independent Price level in T = 1, P 1 = 1 Price level in T = 2, P 2 Nominal interest rate = i Ajaz Hussain. Department of Economics. University of Toronto (St. George) 4 T = 1 “base period”
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Inter temporal Consumption Set Ajaz Hussain. Department of Economics. University of Toronto (St. George) 5 C 2 C 1 C 2 = C 1 C 2 < C 1 C 2 > C 1 Consumption Smoothing
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Intertemporal Budget Constraint P 2 C 2 = P 2 Y 2 + “Savings” P 2 C 2 = P 2 Y 2 + (P 1 Y 1 P 1 C 1 )(1 + i) P 1 C 1 (1 + i) + P 2 C 2 = P 1 Y 1 (1 + i) + P 2 Y 2 P 1 C 1 + P 2 C 2 /(1 + i) = P 1 Y 1 + P 2 Y 2 /(1 + i) Ajaz Hussain. Department of Economics. University of Toronto (St. George) 6 If Savings > 0 “saving” If Savings < 0 “borrowing” Future Value Constraint Present Value Constraint Interpretation? Backward Induction: In T = 2 it must be:
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Endowment Point and Constraint Does constraint passes through endowment point? Yes. P 1 C 1 (1 + i) + P 2 C 2 = P 1 Y 1 (1 + i) + P 2 Y 2 Endowment point is C 1 = Y 1 and C 2 = Y 2 P 1 Y 1 (1 + i) + P 2 Y 2 = P 1 Y 1 (1 + i) + P 2 Y 2 = Ajaz Hussain. Department of Economics. University of Toronto (St. George) 7 Future Value Constraint
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Plotting Inter temporal Budget Constraint No Inflation P 1 C 1 (1 + i) + P 2 C 2 = P 1 Y 1 (1 + i) + P 2 Y 2 Suppose no inflation: P 1 = P 2 = 1 C 1 (1 + i) + C 2 = Y 1 (1 + i) + Y 2 To plot, note C 2 on y axis C 2 = Y 1 (1 + i) + Y 2 (1 + i) C 1 Ajaz Hussain. Department of Economics.
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