Governments traditionally use quotas to limit immigration, but the US government has recently proposed taxes on immigration, focused on high-skill foreign workers. The effects of a high-skill immigration tax hinge on price elasticities of demand and supply that the literature has rarely measured. I estimate key response elasticities to evaluate the effects of a $100,000 tax on Optional Practical Training (OPT) work permits, the largest single channel through which high-skill immigrants enter the US economy. Depending on the incidence of the tax, evaluation requires estimating the price elasticity of demand for US university degrees with the OPT option, the price elasticity of the supply of OPT placements by universities, or the price elasticity of US employers' demand for OPT workers. In all incidence scenarios OPT starts for a given level of international enrollment fall by roughly a fifth or more, and by as much as four fifths under university incidence. The resulting decline in OPT opportunities would reduce international student enrollment at universities, costing them hundreds of millions to over four billion dollars a year in net margin. I illustrate the need for further research on the relevant response elasticities by showing that plausible parameters yield a zero or even negative net fiscal impact of an expanded $100,000 tax on H-1B workers. The need for better models and estimates will grow with the prevalence of immigration taxes.