The purpose of this paper is to review theoretical articles on urban unemployment and ruralurban migration in LDC's. The main issues discussed are (a) whether Lewis type economic development can or cannot decrease urban unemployment, (b) what policies lead a LDC economy to the optimal position in which labor is allocated efficiently between the rural agriculture and urban manufacturing without urban unemployment, (c) why the level of wage in the manufacturing sector does not fall to the competitive one irrespective of urban unemployment, (d) why the income differential (per capita rural income/per capita urban wage of employees) becomes greater than the unemployment ratio in the urban area, and (e) under what condition the so-called ‘Todaro paradox’ arises.
In the Harris-Todaro framework, the unemployment ratio in the urban area does not fall as long as the rural wage rises as more employment opportunities are created in the urban area, while the level of urban unemployed workers either increase or decrease depending on how quickly the rural wage rises. The manufacturing wage is fixed substantially higher than the competitive one through the minimum wage legislation (Harris-Todaro), the wage-labor efficiency relationship (Leibenstein), the hiring-training cost for newly employed workers (Stiglitz), limited investment opportunities (Gersovitz), the Trade Union's activity (Calvo), and the unfavorable movement of the relative price under the minimum wage legislation (Takagi).
The Harris-Todaro model explains the existence of urban unemployment at equilibrium, while the discussion of the Todaro paradox presuppose the existence of urban unemployment. An important point is that the probability of getting an urban job is not a known variable but unknown expected one, because the growth rate of urban employment opportunities and number of migrants during the coming period are unknown.

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A simple method is established for approximating the optimal income tax functions in the class T_p of progressive tax functions. The method is, in essence, an approximation by step functions. The income range (fixed and compact) is partitioned into n small income brackets, and T_n is defined to be the set of all tax functions whose marginal income tax rates are constant in each income brackets for each possible partitions. The T_n-optimal income tax function is shown to converge (in the sense of pointwise convergence of functions) to the T_p-optimal income tax function, as n tends to infinity. This fact is used to calculate an approximation to the optimal income tax function, and to analyze various characteristics of the optimal income tax with recourse to 102 cases of numerical examples. Also the optimal income tax function for the case of 1978 Japan is computed.

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This paper is concerned with the issue of the most desirable public pension scheme from the standpoint of the consumer's welfare. The welfare of the representative consumer qualified for public pension depends on the factors, i.e., the choice of public pension program (the full-funded system or the pay-as-you-go system) and the way of financing public pension scheme. However, since Samuelson [10] first made an analysis of this issue, the scholars have not taken into account the second factor in their analysis. We, therefore, build a model by which to analyse the second factor as well as the first one and discuss the first best problem and the second best problem in our paper. By this, conditions securing the improvement of the consumer's welfare are made clear. Our main conclusion is that Samuelson's theorem is not applicable when the second best problem is considered.

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