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Unformatted text preview: 1 14.02. Recitation 3. Consumption and Investment 1.1 Consumption & Consider an agent who lives for two periods. In the &rst period she has an endowment of y + a goods(where a are assets, and y is current income). In the second period (future) she has an endowment of y f goods. & Flow budget constraints c + s = y + a ; c f = s (1 + r ) + y f & Combining these two ¡ow budget constraints into a single one: PV LC ¡ c + c f 1 + r = y + a + y f 1 + r ¡ PV LR & Note: relative price of c f is 1 = (1 + r ) ; relative price of c is 1 + r . & Preferences given by U & c;c f ¡ = ln( c ) + & ln & c f ¡ ¡ u ( c ) + &u & c f ¡ & Agent¢s problem: current vs. future consumption max c;c f ln( c ) + & ln & c f ¡ s.t. c + c f 1 + r = y + a + y f 1 + r & Ratio of FOCs (called Euler equation) Mu ( c ) = & (1 + r ) Mu & c f ¡ () (1 + r ) &c = c f & Combine with intertemporal budget constraint to &nd solutions c = 1 1 + & ¢ y + a + y f 1 + r £ ; c f = & 1 + & ¤ (1 + r ) ( y + a ) + y f ¥ & If & (1 +...
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This note was uploaded on 10/25/2009 for the course 14 14.02 taught by Professor Geurrieri during the Fall '09 term at MIT.
- Fall '09