²(₂): 1. Consider a deterministic DGE model where time lasts for two periods. The representative consumer has the utility function U₂ = faces the budget constraint c, +a, -y,+(1+r), for t= 0,1; and has an initial assets position given by a., <0. a) Specify the maximization problem of the representative consumer and provide its economic interpretation. b) Assume (1) and (i) y, for t=0,1, with >0. Derive analytically the optimal consumption and assets holding plan and provide an economic interpretation. c) Explain how your result in part (b) changes if the initial asset position is positive.
²(₂): 1. Consider a deterministic DGE model where time lasts for two periods. The representative consumer has the utility function U₂ = faces the budget constraint c, +a, -y,+(1+r), for t= 0,1; and has an initial assets position given by a., <0. a) Specify the maximization problem of the representative consumer and provide its economic interpretation. b) Assume (1) and (i) y, for t=0,1, with >0. Derive analytically the optimal consumption and assets holding plan and provide an economic interpretation. c) Explain how your result in part (b) changes if the initial asset position is positive.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:u();
1. Consider a deterministic DGE model where time lasts for two periods.
The representative consumer has the utility function U₁ =
faces the budget constraint c, +a, -y, +(1+r), for t=0,1; and has an
initial assets position given by a., <0.
a) Specify the maximization problem of the representative consumer
and provide its economic interpretation.
b) Assume (1)= and (ii) y, for t=0,1, with y>0. Derive
1+r
analytically the optimal consumption and assets holding plan and
provide an economic interpretation.
c) Explain how your result in part (b) changes if the initial asset
position is positive.
2. Consider a stochastic DGE model with uncertainty about future income.
The representative consumer has the utility function U,E,'(c.).
faces the budget constraint c, +a, = y, +(1+r),.,. for 120, and has an
initial assets position given by a...
a) Derive analytically the consumption function under the permanent
income hypothesis.
b) Use your result to illustrate analytically how income shocks affect
consumption and provide an economic interpretation.
c) Show analytically how increase in income volatility affects current
consumption and provide an economic interpretation.
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