2 Intertemporal budget constraint of the government In this problem, we set up the intertemporal budget constraint of th

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2 Intertemporal Budget Constraint Of The Government In This Problem We Set Up The Intertemporal Budget Constraint Of Th 1 (68.88 KiB) Viewed 27 times

2 Intertemporal budget constraint of the government In this problem, we set up the intertemporal budget constraint of the government, and link it to the Fisher equation and ability to inflate away part of existing debt through a surprise issuance of new money. Because we will explicitly differentiate between nominal and real variables, we will denote nominal variables with superscript N. Consider a government in periods t = 1,2. The government starts period 1 with existing stock of money M (that has already been issued previously). In period 1, the government must pay for government expenditures G (in nominal dollars). These expenditures are financed through taxes TN and borrowing (new government debt) BX The government promises to pay a nominal interest rate is on this debt (iz denotes the interest rate on debt issues in period 1 that must be repayed in period 2). In period 2, the government must finance government expenditures GẠ and repay the debt plus interest. It does so by collecting taxes TV and an increase in the money supply from Mto M.

Question 2.3 Consider the quantity theory of money under classical dichotomy. Imagine that the velocity and output are constant. What is the relationship between the the inflation rate T2 and the growth rate of the money supply, 9m? Question 2.4 Recall the Fisher equation in expectational form 1+ 12 = (1 + r) (1 + R2) or, after a logarithmic approximation in = 75 + R2. Here, R, is the real interest rate that investors (who lend to the government) require for their lending, and is the rate of inflation that the investors expect in period 1 to occur between period 1 and period 2. Assume that the government promises the investors to keep the money supply constant, and investors trust this promise. What is the nominal interest rate investors require on their lending? Question 2.5 Assume that investors in period 1 lend to the government at the interest rate in that you determined in the previous question. At the beginning of period 2, the government can choose a different growth rate of money supply 9 than gm = 0 it promised. How can the government reduce the real value of the outstanding debt? 3 Question 2.6 Now think about what happens in the following period. After the govern- ment inflated away part of the debt by using money growth rate om > O instead of the promised gm = 0, investors will now believe that in the following period, the money growth rate will continue to be gm = 0. How can the government fool investors again? How can this lead to a hyperinflation, and what can the government do to avoid such hyperinflationary periods?