Consider the two-period household-maximization model discussed inclass. The model is modified in order to look at applications including credit constraints,interest-rate markups, and taxation. A representative household lives for two periods andmaximizes utility of consumption in period 1 and in period 2. The utility is represented bylog(c) where c denotes consumption. Assuming no discounting between period 1 and period 2. The maximization problem for the representative household can be written asmax{log c1 + log c2}c1 + a1 = y1 − τ1 + (1 + r)a0c2 = y2 − τ2 + (1 + r)a1where y1 and y2 denote income levels in period 1 and period 2, τ1 and τ2 are taxes in the twoperiods, and a0 and a1 denote the assets of the households in each period. a0 is exogenouslygiven. Assume the interest rate r = 0, and the government can borrow or save at the sameinterest rate so that its present-value budget constraint is given byg1 + g2 = τ1 + τ2where g1 and g2 are exogenous government expenditures in the two periods. Question: Show consumption c1 and c2 (you can use algebraic or graphical methods). In theanswer, you should discuss whether a1 ≥ 0 or a1 < 0 and provide an economic interpretation.What determine(s) the sign of a1 and why?
Consider the two-period household-maximization model discussed in
class.
The model is modified in order to look at applications including credit constraints,
interest-rate markups, and
maximizes utility of consumption in period 1 and in period 2. The utility is represented by
log(c) where c denotes consumption. Assuming no discounting between period 1 and period 2.
The maximization problem for the representative household can be written as
max{log c1 + log c2}
c1 + a1 = y1 − τ1 + (1 + r)a0
c2 = y2 − τ2 + (1 + r)a1
where y1 and y2 denote income levels in period 1 and period 2, τ1 and τ2 are taxes in the two
periods, and a0 and a1 denote the assets of the households in each period. a0 is exogenously
given. Assume the interest rate r = 0, and the government can borrow or save at the same
interest rate so that its present-value budget constraint is given by
g1 + g2 = τ1 + τ2
where g1 and g2 are exogenous government expenditures in the two periods.
Question: Show consumption c1 and c2 (you can use algebraic or graphical methods). In the
answer, you should discuss whether a1 ≥ 0 or a1 < 0 and provide an economic interpretation.
What determine(s) the sign of a1 and why?
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