3. Can a government run persistent budget deficit? Can national debt growforever without bankrupting the nation? Let D(t), y(t), and r be theamount of debt at year t, national income at year t, and interest rate ondebt per-year, respectively, with D(0) = 0 and y(0) = 1. Here bankruptcymeans whether the ratio of interest payment to national income will exceedone i.e. rD(t)/y(t) > 1 at some year. Suppose that time path of debt isgiven byD = by(t), b > 0||and the time path of income is given byģ = gy(t), g > 0.(a) How does the time path of rD(t)/y(t) look like?(b) What is the steady-state value of rD(t)/y(t)?(c) Does it exceed one? Interpret your result.

Budget deficit refers to a condition that occurs when a government's expenditures exceed its…

Answered: (a) How does the time path of…

(a) How does the time path of rD(t)/y(t) look like? (b) What is the steady-state value of rD(t)/y(t)? (c) Does it exceed one? Interpret your result.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

3. Can a government run persistent budget deficit? Can national debt grow
forever without bankrupting the nation? Let D(t), y(t), and r be the
amount of debt at year t, national income at year t, and interest rate on
debt per-year, respectively, with D(0) = 0 and y(0) = 1. Here bankruptcy
means whether the ratio of interest payment to national income will exceed
one i.e. rD(t)/y(t) > 1 at some year. Suppose that time path of debt is
given by
D = by(t), b > 0
||
and the time path of income is given by
ģ = gy(t), g > 0.
(a) How does the time path of rD(t)/y(t) look like?
(b) What is the steady-state value of rD(t)/y(t)?
(c) Does it exceed one? Interpret your result.

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