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Suppose that dysfunctional politics in this country implies that Congress refuses to collect enough taxes to pay for the amount of spending it decides to do. (Alternatively, one could say that it decides to spend more than the amount of taxes it decides to collect.) Specifically, suppose G_t= 0.2, while T_t= 0.15. Given that the central bank is determined not to allow any inflation, use the government budget constraint to calculate how government debt evolves over the next 30 years. It is convenient to do this in excel.
Info for the problem:
Assume that prices are “perfectly flexible” – i.e., respond immediately oneforone to any change in the money supply. In other words, we assume that M_t =P_t, where M_t is the nominal value of money in the economy in year t – i.e., the quantity of dollar bills outstanding – and Pt is the price level in year t. This is a simplified version of M_tV=P_tY_t, where V=1, and Y_t =1.
G_t: Real value of government spending on goods and services in year t
T_t: Real value of tax revenue in year t
Suppose the government can issue oneyear debt. Let’s denote by B_t the real value of such debt issued by the government in year t to be paid off with interest in year t+1. Finally, let’s denote the net real interest rate that the government has to pay on its debt between year t?1 and year t by R_t1.
The consolidated government budget constraint is then given by
G_t+(1+R_(t1) ) B_(t1)=T_t+B_t+(M_tM_(t1))/P_t
Suppose that in year t=0 the government starts off with no debt to pay off – i.e., B_1=0. Suppose also that the real interest rate that the government must pay on its debt is constant at 5%, i.e., R_t =0.05 for all t. Furthermore, suppose the amount of money in the economy in year 1 is M_1.
