Scientists are increasingly dissatisfied with funding systems that rely on peer assessment and, accordingly, have suggested several proposals for reform. One of these proposals is to distribute available funds equally among all qualified researchers, with no interference from peer review. Despite its numerous benefits, such egalitarian sharing faces the objection, among others, that it would lead to an unacceptable dilution of resources. The aim of the present paper is to assess this particular objection. We estimate (for the Netherlands, the U.S. and the U.K.) how much researchers would receive were they to get an equal share of the government budgets that are currently allocated through competitive peer assessment. For the Netherlands, we furthermore estimate what researchers would receive were we to differentiate between researchers working in low-cost, intermediate-cost and high-cost disciplines. Given these estimates, we then determine what researchers could afford in terms of PhD students, Postdocs, travel and equipment. According to our results, researchers could, on average, maintain current PhD student and Postdoc employment levels, and still have at their disposal a moderate (the U.K.) to considerable (the Netherlands, U.S.) budget for travel and equipment. This suggests that the worry that egalitarian sharing leads to unacceptable dilution of resources is unjustified. Indeed, our results strongly suggest that there is room for far more egalitarian distribution of funds than happens in the highly competitive funding schemes so prevalent today.