b) 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

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter17: Long-term Investment Analysis
Section: Chapter Questions
Problem 7E
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b) 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) Solve for the present stock of debt, y, as a function of t.
(ii) What will happen to government debt as t → 00? Justify your response.
Transcribed Image Text:b) 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) Solve for the present stock of debt, y, as a function of t. (ii) What will happen to government debt as t → 00? Justify your response.
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