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We study the equity and efficiency consequences of the allocation of teachers to schools. Within a district, wages are uniform across potential assignments. Because teachers tend to prefer schools with more advantaged students, this uniformity may lead to inequity among students. Because there might be match effects in teaching, this uniformity may lead to inefficient allocations. While we do observe inefficient allocations (there are meaningful gains from reallocation), surprisingly, we do not observe inequity: advantaged and disadvantaged students have teachers with similar value-added. To understand why uniform wages lead to inefficiency but not inequity, we use rich data from the teacher transfer system linked to test score data to estimate an equilibrium model of the teacher labor market. We find that the allocation is equitable because principals hire noisily, tending not to select their most effective applicants. Achieving most efficiency gains, however, requires differentiated wages that compensate teachers for match output.