The massive growth of jobs in the platform economy has reignited a long-standing debate on the wage elasticity of labour supply for the self-employed. Overwhelming empirical evidence seems to suggest that workers in the platform economy will work more hours than they wish to, for a lower wage, suggesting a backward-bending labour supply curve. Is this puzzling outcome explained by target earning behaviour or rather by the uncertainty arising from task search? In this paper, we test these hypotheses making use of new data on on-location and online platform workers earning on a piece-rate basis in the EU, exploiting search shocks in a difference-in-differences strategy to reassess the wage elasticity of labour supply. We find that uncertainty in search plays a central role in inflating hours of work, revealing a positive and inelastic wage elasticity for all platform workers. On average, a percentage increase in job search leads to a net loss in income, suggesting that piecework might be an endemic source of demand surplus for monopsonistic markets.