Description of the economy

Government. The economy lives for two periods: t = 1 and t = 2 (we can interpret t = 1 as being today and t = 2 as being some fairly distant future). In each period, the government must make purchases: G1 = 10 and G2 = 10. At t = 1 the government is able to collect taxes T1 = 5 and can sell bonds (i.e. issue debt) B1 to cover the remaining part of the expenditure. That debt will have to repaid in period t = 2 with interest r. There is a large number of risk-neutral investors that buy the government debt. These investors have access to some risk-free bond (e.g. a German T-bill) that yields a net return r.

Exercises

Question 1. Write down the budget constraint the government faces in period 1. Write down the separate budget constraint the government will face in period t = 2. What is the level of borrowing in t = 1 (i.e. what is B1)?

Question 2. Suppose the government can commit to repaying the debt in period t = 2. What is the interest rate it will have to pay on the debt issued in t = 1 (explain)?

Question 3. At the interest rate you calculated in the previous part, what will be level of taxes at t = 2?

Question 4. Suppose that due to a political conflict inside the country, there is a risk the government will default in its debt in t = 2. The investors perceive the probability of that default to be = 0:10. What interest will they demand? (HINT: because investors are risk-neutral, they only require that the expected return on the risk-free bond and on the government be equal).

Question 5. At the interest rate you calculated in the previous part, what will be level of taxes at t = 2, if we assume the government actually does repay the debt?
What will be the level of taxes at t = 2, if the government in fact defaults on the debt?