The need for the higher education process to be economically efficient, together with the need for equity and equality in access to higher education services for everyone represents the starting point of this paper. The analysis was conducted using data from a survey on a random sample of young people who recently finished their education using three criterion variables: completion of the study, study success, and the speed of study completion. These variables were chosen because all three individually and in total indicate the efficiency of the process of higher education, but taken together with the data about students and their form of study, other costs of study, family socio-economic background, and eligibility for indirect state financial assistance, also indicate the problems of equality in access to public higher education in Croatia. The obtained results show that the chances for completion of the study are primarily related to the socio-economic status of students. Completion is especially low for students from lower socio-economic strata who do not pay tuition fee, which suggests that the existing instruments of financial aid for non-academic costs are not sufficient for this group. The speed of study completion is primarily influenced by the costs students have to pay for tuition, lower socio-economic status of the students, and eligibility for financial aid conditioned by the dynamics of the study (scholarships).