Imagine a country that has never issued debt prior to year = 1980. Every year prior to 1980, GDP or income was equal to $100. Given a 20% tax rate government revenue were constant at $20 ( = 20) and government expenditures were also constant at $20 ( = 20).

At the beginning of year 1980, the government announced a new health care program that increased expenditures to $22 per year which will result in primary deficits equal to 2% of GDP in 1980 and for the foreseeable futureassume that at a 20% tax rate, this country has reached the maximum tax revenue it can raise from its citizens (top of the Laffer curve).

For simplicity, assume that all debt issued comes due one year later and that the yearly interest rate is 5%. For example, if the government issued $100 of debt in period 1 (_t= 100), then it needs to pay $105 in period ((1 + )_t= 105). Also assume that the money supply is constant and there are no transfers.

1. In what year will this country's debt issued (_t+1) surpass 50% of GDP?
2. Suppose that in some year, say = 2000, debt is exactly equal to 50% of GDP (₂₀₀₀ = 50). In that year, the government permanently cuts its expenditures by $5 ( = 17) and will therefore generate a primary surplus of 3% of GDP on a yearly basis in 2000 and for the foreseeable future. How much debt will this country issue in year = 2015 (₂₀₁₅)? [Note: you do not need to know the answer to question a) to answer this question.]
3. Suppose that in some year, say = 2020, debt is exactly equal to 50% of GDP (₂₀₂₀= 50). In that year, instead of cutting its expenditures (which remain at $22), the government funds an initiative which will help the private sector increase productivity at a rate of 5% per year starting in 2021 and for the foreseeable future. As a results of this increased productivity, GDP/income and therefore government tax revenues will all increase at a yearly rate of 5% per year starting in 2021. How much debt will this country issue in year = 2035 (₂₀₃₅)?

[Note: you do not need to know the answers to question a) nor b) to answer this question.]