Consider a model of harmful habit formation. At any time t, the individual derives utility from the consumption, Xt, of a harmful good (e.g., cigarettes, unhealthy meals, alcohol), and disutility from the level of consumption at time t - 1, Xt-1, which captures the role of habit formation. The unit price at time t of the harmful good is pt = 1, for all t. The utility function at time t is given by Ut = 20 ln(1 + xt) - X+ - (20 + 10 ln(1 + X+-1) + Zt The intertemporal preferences take the (B, 1) form. For selft, Ue = ue +B ] T=t+1 The time-invariant fiscal policy of the government is given by (, a), where 0 E [0,1] is the per-unit consumption tax on the sin good, and a is a lump-sum transfer given by the government to the taxpayer. Savings or borrowings are disallowed; therefore, the budget constraint of the individual requires that in each period, expenditure is bounded above by income, i.e., (1 + )x+ Zt