Abstract
This part applies all the previous findings to a fully worked out example. The aim is mainly to explore the tradeoff between efficiency and inequality/poverty, in order to verify when, at least in some instances, a greater degree of inequality can improve the economy’s total productivity, hence also the incomes (and consumptions) of the less favored, i.e. those belonging to the poorest part of the society which, in modern economies, is protected to varying degrees by the P.A., against too low income (and consumption) levels.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
In Sect. 7.5 it will be seen that the value of \(\alpha =\sum\limits_{j}{\alpha }_{j}\) very strongly influences the dynamics of the economy.
- 3.
Here it is possible for \(\bar{Y } = 1\) with no loss of generality. In the dynamic case of Sect. 7.5 we could select Y (0) = 1 but, as total income can vary from period to period, there is no simplification in choosing Y (0) = 1.
- 4.
In the opposite situation, the total productivity parameter, a, is too low for the economy to be capable of growth. As a parallel in standard macroeconomic theory, if capital, K, produces output, Y, according to the production function \(Y = a{K}^{\gamma }\), then there must be a value K verifying \(a{K}^{\gamma } > K\), or \(a > {K}^{1-\gamma }\), for the economy to be capable of growing. For 0 < γ < 1, namely when decreasing returns to scale hold true, given a, the inequality is verified by low K values.
- 5.
In rich economies, a stationary state could be the most interesting state, at least from a social viewpoint, as discussed long ago by Mill (1848, Book IV, Chap. VI).
- 6.
See Theorem C.
- 7.
Remember that \(\gamma =\sum\limits_{j}{\gamma }_{j} =\sum\limits_{j}({\alpha }_{j}{\beta }_{j})\). Considering the case \(0 < {\beta }_{j} < 1\) for every j, it is possible to obtain γ < 1 even with increasing returns to scale in production, i.e. when \(\sum\limits_{j}{\alpha }_{j} > 1\).
- 8.
When γ≠1.
- 9.
In Footnote 6 of Chap. 4 two other possible consumption functions are proposed.
- 10.
Usually, the propensity to consume, κ j , is greater the smaller individual j’s disposable income.
- 11.
Of course, the incentive scheme, \(\hat{v}\), can be translated into an equivalent taxation and subsidies scheme.
- 12.
From here onwards, we shall no longer mention the income vector in I L and in the Lorenz curve L(p).
References
Mill JS (1848) Principles of political economy. Routledge, London
Rostow WW (1960) The stages of economic growth. Cambridge, Cambridge University Press
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Nicola, P. (2013). A Summary Example. In: Efficiency and Equity in Welfare Economics. Lecture Notes in Economics and Mathematical Systems, vol 661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30071-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-30071-4_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30070-7
Online ISBN: 978-3-642-30071-4
eBook Packages: Business and EconomicsEconomics and Finance (R0)