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 M1 (that has already been issued previously). In period 1, the government must pay for government expenditures GN1 (in nominal dollars). These expenditures are financed through taxes T1N and borrowing (new government debt) B1N. The government promises to pay a nominal interest rate i2 on this debt (i2 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 GN2 and repay the debt plus interest. It does so by collecting taxes T2N and an increase in the money supply from M1 to M2.

a)Set up the government budget constraints (in nominal terms) for periods 1 and 2.