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Hi, I need your answer for both part A and B this question very  quickly.Br/H Consider a...

Hi, I need your answer for both part A and B this question very  quickly.Br/H

Consider a household living for two periods. The intertemporal budget constraint is given by:

?1 + ?2 /1 + r = ?1 + y2/1+r ,

where C is consumption, ? is income and ? is the interest rate. The household’s preferences are characterised by the utility function:

?(?1, ?2 ) = ?(?1) + ??(?2)

where ?(?t) is the period utility function and ? < 1 is the discount factor.

a. Formulate the household’s optimisation problem and derive the Euler equation.

b. Suppose that ?(?t ) = ln ?t , that ? = 0 and ? = 1. Solve for the levels of optimal consumption, i.e. ?1 and ?2.

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