Given that nothing else is borrowed in the near future, the length of time it will take a government to completely eliminate its stock of debt will be entirely dependent on how much more annual repayments exceed the annual interest expenses. The interest expense portion of the debt is a function of the present stock of debt, y, and is given by i(y) %3D у — у? The amount of money that the government repays to reduce its debt stock is assumed to be a fraction, a, of the present stock of debt. Repayment is done at the end of each financial vear

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.5P
icon
Related questions
Question

For part (i), it is required to identify the differential equation

Given that nothing else is borrowed in the near future, the length of time it will take
a government to completely eliminate its stock of debt will be entirely dependent on
how much more annual repayments exceed the annual interest expenses. The
interest expense portion of the debt is a function of the present stock of debt, y, and
is given by
i(y) = y – y?
The amount of money that the government repays to reduce its debt stock is
assumed to be a fraction, a, of the present stock of debt. Repayment is done at the
end of each financial year.
(i)
(ii)
Solve for the present stock of debt, y, as a function of t.
What will happen to government debt ast → o? Justify your response.
Transcribed Image Text:Given that nothing else is borrowed in the near future, the length of time it will take a government to completely eliminate its stock of debt will be entirely dependent on how much more annual repayments exceed the annual interest expenses. The interest expense portion of the debt is a function of the present stock of debt, y, and is given by i(y) = y – y? The amount of money that the government repays to reduce its debt stock is assumed to be a fraction, a, of the present stock of debt. Repayment is done at the end of each financial year. (i) (ii) Solve for the present stock of debt, y, as a function of t. What will happen to government debt ast → o? Justify your response.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Property Rights, Bargaining And The Coase Theorem
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Microeconomic Theory
Microeconomic Theory
Economics
ISBN:
9781337517942
Author:
NICHOLSON
Publisher:
Cengage