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 taxation. A representative household lives for two periods 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. (a). Explain what is meant by a representative household. Briefly explain the budgetconstraints of the representative households and of the government. Explain the role played by the assumption that the representative households lives for only two periods and the assumption of “no discounting” (b). 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?
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
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.
(a). Explain what is meant by a representative household. Briefly explain the budgetconstraints of the representative households and of the government. Explain the role played by the assumption that the representative households lives for only two periods and the assumption of “no discounting”
(b). 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?
Step by step
Solved in 4 steps with 2 images
