APPENDIX 117

run, the number of learners does not change immediately in response to an increase in school fees (that is, inelastic enrollment), but also that the fees are determined such that most parents can afford to pay them.5 Suppose now that budget constraints are not binding. Then the optimal

solution is

xi* ≡ —— = y* &#62; φ(q —

Li Hi* In this case Hi = β*Li, where β* = —

constraint is binding: y* &#60; φ(q —

— y—. Next consider the case in which the budget 1 *

Hi = —————————— Li φq

i(f), gi; w) = β*Li + —————————— – β* Li [

= β*Li + ———————— – β* Li, i(f) + gi

[

i(f) + gi). The second term is an efficiency loss in terms of the number of educators. The government will allocate the subsidies to those

where w &#60; β*(q —

ieili subject to its budget constraint but does not allocate any subsidy to those schools that are able to attain optimal ratios:

Σ

max Σ [ s.t.

{gi}i i|y*&#60;φ(q —i,0;w)

i|y*&#60;φ(q —i,0;w)

1 – (y* – ——————— )2 qi(f) + gi

w Σ giLi ≤ G. ] Li

with binding budget constraints. Next consider the government’s allocation of school subsidies. Assume that the government maximizes the total educa- tional output

i(f), gi; w) w

q —

] 1

φ(q —

] (A.2)

i(f), gi; w). In this case: 1

i(f), gi; w).

5 Yamauchi and Nishiyama (2005) show that the proportion of learners who cannot pay school fees, including both those who postpone payment and those who receive official exemptions, is positively correlated with the level of the school fees. The result, however, does not directly show the school drop-out rate. My interviews with school principals indicate that those parents

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