Abstract
In this chapter we aim to analyse: (a) the relationship between taxation, income distribution and individual choices with respect to higher education; (b) the resulting collective welfare conditions and personal-intergenerational distribution; and (c) the possibility of public intervention with alternative programmes of education subsidies.
We propose different programmes for financing education through the public administration and we attempt to verify the conditions of optimality with respect to collective welfare.
We determined that, with respect to equity, the best structure is provided by a progressive tax with an increasing marginal rate. In fact, with such a structure we obtain the highest education period and the elimination of its variability. Moreover, given the characteristics of the model used, this allows us to minimize the variance in personal income distribution.
Then, several public policies using education subsidy programmes are proposed again. This type of intervention is more socially efficient if it tends to raise the minimum and average level of education, minimizing at the same time the disparities among individuals. There appears to be a tendency to sustain lower levels of education rather than providing subsidies for higher education. The latter would, in fact, benefit people who have already been selected on the basis of their initial skill endowments which, one can easily understand, do not derive from “uncontaminated” situations but are the result of the system’s social, economic and historical conditions and which are, therefore, in themselves, subject to the intervention of the public administration.
Antony Atkinson and Edgar Cary Brown gave me important critical contributions to improve a first draft of this chapter. Further suggestions came from the participants at the Workshop on Economics of Education at the University of Catania, Italy. I wish to express my gratitude for these criticisms and contributions.
This is a new English version of a paper published in Italian:
Mario Baldassarri, Tassazione, distribuzione ed ottimalità nei programmi di sussidi all’educazione, Rivista Internazionale di Scienze Sociali, Milan 1976.
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Notes
- 1.
See: A. Atkinson, Optimal Income Taxation, in M. Parkin (ed.), Essays on Economics, London 1972. J. A. Mirrlees, An exploration in the theory of Optimal Income Taxation, in Review of Economic Studies, 1971.
- 2.
It should be noted that the opportunity cost resulting from the loss of profit during the period of instruction is implicitly considered in the model which, in fact, refers to a productive life that begins at the time S, that is, at the end of the education programmes. Furthermore, the analysis could focus on the initial moment of education which does not necessarily need to coincide with the year zero.
- 3.
See footnote 1. Regarding programmes aimed at financing education see K. HAMADA, Income Taxation and Educational Subsidy in Journal of Public Economics, May 1974.
- 4.
See P. A. Samuelson, Foundations of Economic Analysis, Harvard University Press, Cambridge (Mass.) 1963, p. 219.
- 5.
A further change relative to the minimum sacrifice theory can be represented by U = G (U), where G' > 0 and G'' < 0 and the first-order condition to obtain the maximum value of W is given by: G' [U' (Z (n)) − T (n)] equal for each individual.
- 6.
Similar to what was presented previously, we have:
$$ {W}_c={l}_nA+\frac{\mathit{\mathrm{di}}}{\overline{n}\left(1-\frac{n_0}{\underset{-}{n}}\right)}+\frac{1}{\overline{n}\left(1-\frac{n_0}{\underset{-}{n}}\right)}-{l}_ni-{l}_nA\overline{n}\underset{-}{n}+{\int}_{\underset{-}{n}}^{\infty }{l}_n\left({Y}_n-H\right)f(n)\mathit{\mathrm{dn}} $$where
\( Y=A\overline{n}\underset{-}{n}-A{n}_0\overline{n}+\mathit{\mathrm{cn}} \) and \( H=A\overline{n}\underset{-}{n}c \)
thus, the condition is:
$$ {l}_n\left[\left(1-c\right)A\overline{n}\underset{-}{n}\right]-1+\mathit{\mathrm{Ai}}\left[1-\frac{A}{A\left(\underset{-}{n}-{n}_0\right)+c}\right]>\frac{1}{\underset{-}{n}\left(1-\frac{n_0}{\underset{-}{n}}\right)}+{l}_n\left(K\underset{-}{n}-H\right)-{\underset{-}{n}}^{\mu }{\left(\frac{K}{H}\right)}^{\mu }{l}_n\left(\frac{\mathit{\mathrm{Kn}}-H}{\underset{-}{n}}\right)-{\underset{-}{n}}^{\mu }{\left(\frac{K}{H}\right)}^{\mu}\sum_{\gamma =i}^{\mu -1}{\left(\frac{K}{H}\right)}^{\gamma } $$ - 7.
One may wish to verify for which period \( \tilde{S} \) the optimal structure of taxation appears identical to the previous case, i.e. β = β'. By simple calculations you get:
$$ \overset{\sim }{S}=\left({l}_n\left(\frac{1}{A}-1-\frac{h}{c}\left(\frac{1}{A}-1+{e}^{-i{S}^{\ast }}\right)\right)\right)\bullet \frac{1}{i} $$ - 8.
This condition is expressed in:
$$ {\int}_{\underset{\_}{n}}^{\infty}\mathit{\ln}\left( A\beta n-c\right)f(n) dn-{\int}_{\underset{\_}{n}}^{\infty}\mathit{\ln}\left(A{\beta}^{\prime }n-h\right)f(n)\mathit{\mathrm{dn}}+\frac{c}{A\beta \overline{n}}-\frac{h}{A{\beta}^{\prime}\overline{n}}>0. $$ - 9.
Such a relation derives from:
$$ {\int}_{\underset{\_}{n}}^{\infty}\mathit{\ln}\left(\frac{\mathit{\mathrm{An}}-c}{\mathit{\mathrm{An}}-h}\right)f(n)\mathit{\mathrm{dn}}+\frac{c-h}{A\overline{n}}\gtrless 0. $$which can be expressed in:
$$ \begin{array}{l}\mathit{\ln}\left(A\underset{-}{n}-c\right)-{\left(\frac{A\underset{-}{n}}{c}\right)}^{\mu}\left[\frac{\mathit{\ln}\left(A\underset{-}{n}-c\right)}{\underset{-}{n}}+\sum_{\gamma =1}^{\mu -1}\frac{1}{\gamma }{\left(\frac{c}{A\beta \underset{-}{n}}\right)}^{\gamma}\right]-\mathit{\ln}\left(A\underset{-}{n}-h\right)\\ {}+{\left(\frac{A\underset{-}{n}}{h}\right)}^{\mu}\left[\frac{\mathit{\ln}\left(A\underset{-}{n}-h\right)}{\underset{-}{n}}+\sum_{\gamma =1}^{\mu -1}\frac{1}{\gamma }{\left(\frac{h}{A\beta \underset{-}{n}}\right)}^{\gamma}\right]+\frac{c-h}{A\overline{n}}\gtrless 0\end{array} $$which is definitely positive excluding the two summations. Obviously, this result depends on the relative size of c and h.
- 10.
As it can be seen, the uncertainty of the relationship in the case of the absence of tax is related to the relative size of h and c disappears completely in the case of TPROGAC taxation.
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Baldassarri, M. (2017). Taxation, Income Distribution and Optimal Programmes to Finance Higher Education. In: The European Roots of the Eurozone Crisis. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-58080-7_7
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DOI: https://doi.org/10.1007/978-3-319-58080-7_7
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