Consider the two-period endowment economy discussed in class. The economy is populated by m consumers. The lifetime utility function of each consumer is time separable and is given by U(c, c') = u(c) + Bu(c) 0
Consider the two-period endowment economy discussed in class. The economy is populated by m consumers. The lifetime utility function of each consumer is time separable and is given by U(c, c') = u(c) + Bu(c) 0
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Consider the two-period endowment economy discussed in class.
The economy is populated by m consumers. The lifetime utility
function of each consumer is time separable and is given by
U (c, c') = u(c) + Bu(c) 0<B<1
where c is current consumption, d' is future consumption and 3 is
the subjective discount factor. Suppose that the per-period utility
function is such that u(c) = log c. The consumer budget constraint
in the current period is given by:
c+s=y-t
where s is savings, y current income and t lump-sum taxes in the
current period. The future period budget constraint can be written
as:
c=yt+ (1+r)s
r is the real interest rate, y' future income and t' lump-sum taxes
in the future period. Suppose there two groups of consumers who
differ in their income profiles. Half of the consumers (indicated with
1) have income y = y in the current period and y' = 0 in the future
period. The other half (indicated with b) have income y = 0 in the
current period and y = y in the future period. Finally, there is no
government spending in both periods.
(a) For the moment being, suppose there are no lump-sum taxes.
Find the equilibrium level of the real interest rate r (i.e., express
r as a function of the exogenous parameters of the model).
(b) Given the answer on point (a), calculate the equilibrium level
of savings for each group. Is there any lending in equilibrium?
Explain your results intuitively.
Transcribed Image Text:(c) Suppose the government runs a redistributive tax scheme. That
is, the government redistributes income across the two groups
by setting t₁ = = ¹ and to = −ÿ in the current period and
t' = and t₁ = y in the future period. Find the equilibrium
level of the real interest rate under this tax scheme. Is there any
lending in equilibrium? Explain your results intuitively.
(d) Use a graphical analysis to analyse the effects of the introduction
of the new tax scheme on the consumer choice of group b.
(e) Does the new tax scheme imply a Pareto improvement compared
to the initial situation with no taxes? Explain, also intuitively,
why or why not.
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