A government debt b evolves over time according to the following law of motion b_{t+1} = Rb_t - z_t, with R>1 being the real interest rate. The variable z_t denotes the government primary surplus and is assumed to be bounded from below and above: z lower bar < z_t < z upper bar. The government initial debt at t = 0 is equal to b_0 > 0. Suppose that the government face a restriction such that \lim_{T \to \infty} \frac{b_{T+1}}{R^T} = 0. There is no Ponzi condition on the government. Derive the lifetime budget constraint of the government for T \to \infty