Abstract The problem of market clearing in an economy is that of fifinding prices such that supply meets demand. In this work, we propose a kernel method to compute nonlinear clearing prices for instances where linear prices do not suffifice. We fifirst present a procedure that, given a sample of values and costs for a set of bundles, implicitly computes nonlinear clearing prices by solving an appropriately formulated quadratic program. We then use this as a subroutine in an elicitation procedure that queries demand and supply incrementally over rounds, only as much as needed to reach clearing prices. An empirical evaluation demonstrates that, with a proper choice of kernel function, the method is able to fifind sparse nonlinear clearing prices with much less than full revelation of values and costs. When the kernel function is not suitable to clear the market, the method can be tuned to achieve approximate clearing