This paper explores prospects for the world economy to the year 2020 through a series of scenarios based on different assumptions about future changes in the structure of individual economies. It differs from most other medium term studies because we do not assume that each economy’s variables (such as output, energy use, resource depletion or pollution) all grow in proportion to GDP. In fact, we argue that simple extrapolations derived by projecting GDP and assuming all variables grow in proportion would do a particularly poor job of explaining the historical record (and there is no reason to expect this approach to do better in the future). In our work we instead start with projections of future population growth and industry-level technical change based on a wide range of empirical studies. We use these projections in an empirically-based multi-sector general equilibrium model of the world economy to calculate GDP and other variables endogenously. We then explore the sensitivity of the aggregate outcomes across economies to the assumptions about sectoral productivity growth. In particular, we use as a metric the emissions of carbon dioxide from fossil fuel use in the global economy. Under each set of assumptions we calculate the size of a carbon tax sufficient to stabilize emissions in 2010 at 1990 levels. We show that this tax varies significantly depending on the assumptions made about productivity growth at the sectoral level.