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Consider a household living for two periods

Consider a household living for two periods, t = 1, 2.  Let ct and yt denote consumption and income in period t. s denotes saving in period 1, r is the real interest rate and β the weight the household places on future utility.  The following must be true about the household’s consumption in the two periods:


c1 = y1 − s


and


c2 = (1 + r)s + y2


a.  Derive the household’s intertemporal budget constraint.


b.  Assume that the preferences of the household can be represented by a log utility function so that u(ct)  =  ln ct.   Formulate the household’s maximisation problem and derive the Euler equation.


c.  Suppose that the real interest rate decreases. How will this affect the household’s consumption decision?


d.  Suppose that β = 1 and r = 0.  Solve for c1 and c2 and interpret your results.


economics   Intermediate-Macroeconomics   
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Answer #1

Max u st Interstempal B cl a ) IHP ausent Cons falls&future Gons tes.A thus No futuse discounting Nointeaßt on Bavings

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