BS1780 Macroeconomics for Business Problem Set 3 Group Assignment February 2016

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Assuming that the nominal interest rate, the inflation rate, the real GDP growth and primary deficit remain constant for the next year, we can compute the projected next year end debt as a percentage of GDP by using the equation: dt+1=dt+i-πdt-grdt-st+1 In this case, dt is the public debt (as % of GDP) of 2011, which is 88%; i is the government interest rate 7% according to our assumption; π is the inflation rate, which was 2% if it is held constant constant in the next year; gr is -1%, the real GDP growth; and -st+1 is the primary deficit, which is 3%. Therefore: dt+1=88%+7%-2%×88%--1%×88%+3%=96.28% Thus, the projected next year-end debt (as % of GDP), based upon our assumptions, would be 96.28%. If we decompose the changes in debt-to-GDP ratio into three components, among the 8.28% of debt changes (as % of GDP), 4.4% is due to the real interest rate, 0.88% is coming from the growth, and primary deficit makes a contribution of 3%. The above calculation is shown in Table 1 below.
Table 1: Debt to GDP ratio forecast | t=2012 | t=2013 | t=2014 | t=2015 | Inputs | | | | | Primary deficit (% of GDP) | 3 | 3 | 3 | 3 | Interest rate (money market, %) | 7 | 7 | 7 | 7 | Inflation (%) | 2 | 2 | 2 | 2 | Real GDP growth (%) | -1 | -1 | -1 | -1 | Public debt (% of GDP, end of t-1) | 88 | 96.28 | 105.06 | 90.66 | | | | | | Miscellaneous calculations | | | | | Real interest rate (%) | 5.00 | 5.00 | 5.00 | 5.00 | | | | | | Components of change in B/Y | | | | | (A) Real interest | 4.40 | 4.81 | 5.25 | 5.72 | (B) Growth | 0.88 | 0.96 | 1.05 | 1.14 | (C) Primary deficit | 3.00 | 3.00 | 3.00 | 3.00 | Total | 8.28 | 8.78 | 9.30 | 9.86 | | | | | | Year end debt (% of GDP) | 96.28 | 105.06 | 114.36 | 124.22 |