This thesis is of the three article format. All three articles contribute to the literature on optimal fiscal policy with exogeneous government expenditures and distortionary taxation following Lucas and Stokey (1983) and Aiyagari et al. (2002) (AMSS). The first article extends the framework of AMSS by modelling agents ex ante heterogeneous in deterministic labour productivity trends in an infinite-horizon production economy with incomplete markets. The government does not use transfers. When the productivities of different agents grow at different rates, there is a conflict over the timing of tax collection. This is explored in a two-period model. The infinite-horizon model with two agents (‘lowskilled’ and ‘high-skilled’) is used to quantitatively analyse the impact of productivity trends observed in recent decades on the optimal policy. The impact is significant. The model can contribute to explaining the increase in government debt in many advanced economies in recent decades. The optimal policy strongly depends on Pareto weights but welfare of the agents does not. Political economics implications are discussed. The second article analyses the impact of heterogeneous productivity trends on the optimal policy when the social planner can use transfers. There is now conflict over the timing and the level of taxation, and it is explored in a two-period model. The optimal policy is studied in the same environment as in the first article. For most Pareto weights, the change in the tax rate is less pronounced than in the model without transfers, but still greater than the expected change due to shocks. The optimal policy and the welfare of the agents strongly depend on Pareto weights. Policy implications are discussed. The optimal policy in the horizon of decades is significantly affected by even a modest heterogeneity in the growth rates of the agents. Solution methods common to all three articles are discussed. In the third article the closed economy model of AMSS is extended into an open economy setting with two countries. The government of each country finances its exogeneous stochastic expenditures by distortionary labour taxation, and issues one-period bonds. The Ramsey planner chooses policy for both countries, and a no-arbitrage condition on the return of bonds of the two countries restricts her choices. The optimal policy is quantitatively studied in a calibrated model with ex-ante identical countries and equal Pareto weights, and three settings are compared in terms of policy and welfare: autarky (closed economy), partial union (international borrowing allowed), and full union (transfers between governments allowed).