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Return migration of foreign students and non-resident tuition fees


This paper challenges the notion that optimal non-resident tuition fees should necessarily be raised if the return rate of foreign students after graduation increases. The analysis of a host country’s optimal pricing behavior therefore incorporates a specific student migration model. Students usually are aware of the fact that they might return to their home countries after being educated abroad, even if they initially intended to stay on in the host country. With rational expectations, a change in students’ perceptions of the return probability after graduation can affect their first-round decisions whether to study abroad. The optimal adjustment of non-resident tuition fees in the host country has to take this behavioral response into account. Under certain conditions, the behavioral effect is dominant, and a decline in stay rates of students actually requires tuition fee cuts.

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Fig. 1


  1. The international mobility of students has increased considerably over the last few decades (OECD 2009) and “[students], especially from developing countries, often stay on in OECD countries for further research or employment and contribute to innovation in these countries” (OECD 2008, pp. 83–84). Estimated stay rates of foreign students within the USA are between one fifth (Rosenzweig 2006) and one third (Lowell et al. 2007); for foreign citizens who have received a science or engineering doctorate in the USA, rates approach two thirds (Finn 2003). For Germany, Hein and Plesch (2008) report a stay rate of 35 % for foreign students who participated in a special scholarship program.

  2. The term “tuition fees” is used in a very abstract way in this paper. While it seems justifiable to assume that the government is in charge of setting tuition fees in public higher educational systems (as in some European countries), a more complex view is needed for countries in which private institutions also play an important role in the higher educational sector (for instance, in the USA, tuition fees are determined in a highly decentralized way in a mixed public/private setting). It can be argued, however, that the government at the state/provincial level still exerts an influence on the price charged to students by providing scholarships or certain subsidies in cash or kind. In the model, the host country determines a net price for education, i.e., tuition fees net of subsidies and grants.

  3. The stay rate of students is ultimately px. The assumption p ≥ 1/2 is therefore not too restrictive because overall stay rates could still fall short of 1/2. Therefore, the migration model is consistent with stay rates reported by Rosenzweig (2006) and Lowell et al. (2007) for the USA and Hein and Plesch (2008) for Germany.

  4. The model excludes migration costs, as the focus is on a migration decision primarily dependent on expectations about living standards in the DC. Adding, for example, uniform migration costs would not change the results qualitatively.

  5. An implicit assumption in the migration model is that foreign students can always afford non-resident tuition fees in the DC. That means either that their initial endowment is already sufficiently high or that there are no credit constraints and the return on education always exceeds the cost of tuition. Students also cannot avoid tuition fees by returning to the home country after graduation; an obvious case is non-resident tuition fees which have to be paid up-front (e.g., like in Australia and most other important host countries). From the perspective of a graduate, tuition fees then are sunk costs, which do not affect the return-migration decision. Furthermore, differences in the consumption value of education and the value of “college life” between the two countries are ignored.

  6. The assumed range of parameter p, p ∈ (1/2, 1], ensures that the second-order condition for a maximum holds. As argued in Section 3.1, p ≤ 1/2 was excluded from the analysis to make sure that students’ ex ante expected payoff of having the opportunity to stay on in the host country after graduation is strictly positive.

  7. Lange (2009b) points to some effects which become relevant in a comparative statics analysis in which the composition of the international student body changes.


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I am grateful to Robin Boadway for his hospitality during my research stay at Queen’s University in Kingston and for his comments on an early version of the paper. I also appreciate the valuable comments of Alessandro Cigno, two anonymous referees, Zahra Siddique, Wolfram Richter, and Lindsay Lowell. Financial support by the DFG Research Group “Heterogenous Labor,” Fritz Thyssen Stiftung, and the German Academic Exchange Service DAAD is gratefully acknowledged.

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Correspondence to Thomas Lange.

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Responsible editor: Alessandro Cigno



Non-resident tuition fees and market power

The optimal tuition fee can be expressed as a function of the price elasticity of demand for the educational system (\(\varepsilon:=\frac{\partial S}{\partial f}\frac{f}{S}<0\)):

$$ f = - \frac{\left(\pi^E + \delta_G p\pi^W\right)}{1+1/\varepsilon}. $$

Ignoring expected benefits to the host country from retaining foreign students after graduation, the optimal tuition fee policy resembles standard monopoly pricing (in which π E < 0): the host country charges a price in excess of the marginal cost of providing education, and the higher the country’s monopoly power (as represented by the absolute value of 1/ε, which at \(f=\arg\max \Pi(f)\) equals the “Lerner index” of monopoly power), the higher the tuition fees. Taking into account expected future benefits W per foreign student educated in the host country, a higher price elasticity of demand for the educational system also provides an incentive to reduce tuition fees in order to attract foreign students and realize those benefits. The overall effect depends on the relative sizes of the costs and discounted benefits per student:

$$ \frac{\partial f}{\partial |\varepsilon|} = \frac{\pi^E+ \delta_G p\pi^W}{(1+\varepsilon)^2}, \quad |\varepsilon| = - \varepsilon . $$

Proof Proposition 1

The proof uses the constraint that the optimal tuition fee f results in an interior solution with respect to the foreign demand for the educational system in the DC. The constraint that the exogenous parameters in the model must ensure that \(S(f=\arg \max \Pi(f))\) is strictly smaller than one (i.e., not the entire pool of potential international students ends up in the DC) can be written as follows:

$$ \delta_I \overline{\theta} x(2p-1)\Delta v - \delta_G px\pi^W > \delta_I \left(v^H-\underline{v}\right) + \pi^E, $$

where the optimal tuition fee from Eq. 8 is used in the demand function S(f,·) as given by Eq. 5. This constraint directly demonstrates that if the right-hand side of the inequality is positive, the left-hand side has to be positive as well, i.e., \(\delta_I (v^H-\underline{v}) + \pi^E > 0\) implies \(\delta_I \overline{\theta} x(2p-1)\Delta v - \delta_G px\pi^W > 0\), which finally results in df/dx > 0, as can be seen from Eq. 10. This proves the first part of the proposition. The second part, namely df/dp > 0, can be proved as follows: the inequality \(\delta_I \overline{\theta} x(2p-1)\Delta v - \delta_G px\pi^W > 0\) can be written as

$$ \frac{\delta_I}{\delta_G} > \frac{p\pi^W}{\overline{\theta}(2p-1)\Delta v}. $$

From Eq. 9, df/dp is positive if

$$ \frac{\delta_I}{\delta_G} > \frac{\pi^W}{2\overline{\theta}\Delta v}. $$

The fact that \(\frac{p\pi^W}{\overline{\theta}(2p-1)\Delta v} \!>\! \frac{\pi^W}{2\overline{\theta}\Delta v}\) from the assumed range of p (namely, p > 1/2), ensures that Eq. 18 also holds if Eq. 17 is fulfilled, thereby proving df/dp > 0.

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Lange, T. Return migration of foreign students and non-resident tuition fees. J Popul Econ 26, 703–718 (2013).

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  • Tuition fees
  • Overseas students
  • Return migration
  • Brain drain
  • Rational expectations

JEL Classification

  • F22
  • I29
  • D84