Consider a closed economy with public sector. Let time be discrete. Because we shall concentrate on

income taxation rather than lump-sum taxes, we consider net income and let Y_t denote real Net National Product (GNP minus capital depreciation ) in period t = 0; 1;2............ we ignore business cycle fluctuations. suppose Y_t grows at a given constant rate g_y >- 0; and assume the real interest rate in the economy is a constant r>g_{y :}

_{further notation is :}

G_t = real government spending on goods and services in period t,

GBD_t = real government budget deficit in period t,

B_t = real public debt (all short-term) at the start of period t.

There are no indirect taxes and no government transfers (apart from the interest on the government

debt). Suppose that all private income (whether factor income or interest income from holding

government bonds) is taxed by a given constant rate r E (0,1) : so tax revenue is T_t = t(Y_t+rB_t): t=0;1;2.............

Assume that any government budget decit is exclusively nanced by issuing debt (and any budget surplus

by redeeming debt).

a) Write down an equation indicating how B_t+1 is related to GBD_t