ECO
Macro1_PS4sol

# Provide details of your use of the envelope theorem

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Unformatted text preview: Provide details of your use of the Envelope Theorem. Interpret the Euler equation. s t +1 = (1 + r t ) s t + y t- c t is the transition equation : that is the relationship between the 2 states of the economy ( t and t + 1 ) ; it summarizes information from the past that is needed for the forward looking optimization problem. Thus, s t ( nancial savings between t and t + 1 ) is the state variable of the problem. The control variable (or decision variable) is c t , it is the variable that is being chosen by the representative agent and that enter into the transition equation. 1 Macroeconomics 1. Master APE. 2010-2011. PS4 Prof. Xavier Ragot / T.A : Eric Monnet Hence, the Bellman equation of this problem : V ( s t ) = Max c t [ u ( c t ) + βV ( s t +1 )] The 'value' of the state variable at time t is the maximization of the discounted 'value' of this variable at the following period, given that the individual chooses the optimal c at time t (this choice then in uences the value of s t and s t +1 ). Instead of choosing today's consumption, we choose tomorrow's state (equivalent because of the transition equation), so s t +1...
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