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Higher education is a form of a merit good. This is why governments usually support the delivery of this good. However, one could doubt the efficiency of such solution. How well do public higher education institutions (HEIs) do their job? How to measure their performance? This paper discusses these issues. First, we discuss the problem of defining and measuring efficiency in the case of publicly held HEIs with particular emphasis put on the Data Envelopment Analysis (DEA) method. Secondly, we present the results of our empirical investigation of efficiency assessed using the DEA method conducted on the sample of 33 Poland faculties specialized in social sciences. We use Charnes-Cooper-Rhodes (CCR) output oriented model with two inputs and three outputs. Next, we present some important differences in efficiency of those faculties. We also define benchmarks for inefficient HEIs and quantify the gaps to be fulfilled by them in order to become efficient. Finally, we pinpoint the directions of further research.