.The government budget constraint. In each period, the government must satisfy the budget constraint Bt+1 = (1 + i)Bt + Gt – Tt (1)
Please answer the following questions and show me how to do.
1.The government budget constraint. In each period, the government must satisfy the budget constraint Bt+1 = (1 + i)Bt + Gt – Tt (1)
Consider first an economy that exists for three periods: period 1, period 2, and period 3.
(a) Write this budget constraint for each period
(b) Since the economy only exists for three periods, B4 = 0. Use this fact and solve the period 3 budget constraint for B3 and substitute this back into the period 2 budget constraint.
(c) Solve this new version of the period 2 budget constraints and substitute the result back into the period 1 budget constraint.
(d) You have the inter temporal budget constraint. Interpret this equation.
Consider then how the debt-to-GDP ratio evolves over time in an n period economy.
Suppose a government has an initial debt of $ 5 trillion and the nominal interest rate is 5%.
(e) If the government keeps its primary budget in balance (Gt -Tt), what is the growth rate of its debt? Why?
(f) If the government keeps its total budget in balance, what is the growth rate of its debt. Why?
(g) Suppose the country’s GDP grows at 4% per year. What happens to the debt-to-GDP ratio in the two cases in parts (e) and (f)?
(h) Does the situations in part (g) satisfy the government’s long-run inter temporal budget constraint? Why or why not?
2. (a) Can a country run a fiscal deficit forever? Why or why not?
(b) True or false (explain why): To minimize the burden of taxation, it is always better to levy large taxes on a small number of goods and services, than small taxes more universally.
(c) True or false (explain why): When a country must make an unusually large one-time outlay – say, for the cost of conducting a war { it is optimal from the perspective of tax efficiency to spread that cost over many years by running deficits and borrowing.
3. Describe how, if at all, each of the following developments affects the real interest rate and output in the short run (or whether it is not possible to tell). In parts
(a) and (b), assume that the central bank is following a monetary policy rule; in parts (c), use the information in the question to decide what assumption to make about how monetary policy is being conducted.
(a) The government cuts taxes.
(b) The government cuts taxes and government purchases by equal amounts.
(c) The government cuts taxes and, at the same time, the central bank changes its monetary policy rules so that it sets a lower real interest rate at a given inflation level than before.
