On the Geometry of Constant Returns

Constant returns to scale, always a simplifying assumption, is often also much more: many important results depend critically on the very special properties of this class of production function. This paper provides a unified set of simple proofs for most of the crucial analytical properties of constant returns production and their implications for firm costs. Only familiar diagrams and high school geometry are used, and the proofs are written to be easily accessible to college sophomores.

Do fringe benefits cause layoffs?

It is commonly believed that firms prefer layoffs to worksharing, in part, because layoffs economize on fringe benefit costs. We find that when labor markets are characterized by optimal implicit contracts, layoffs will never occur in equilibrium, regardless of the level of fringe benefits

An Islamic Perspective on Inequality in Pakistan

This paper examines the distribution of income in Pakistan, and in each of its four provinces, from an explicit and formal Islamic perspective. A cardinally significant Atkinson-Kolm-Sen relative index of inequality reflecting that perspective is proposed and computed from the full HIES data series for the years 1984-85, 1985-86, 1986-87, and 1987-88. There is evidence of a significant decline in overall inequality in Pakistan from 1984-85 to 1987-88, but the level of inequality remains very high. Inter-province and inter-urban/rural differences in inequality profiles within Pakistan and each of its provinces are found to be generally less, significant than intra-province and intraurban/rural differences.

A Note on Some Theorems in the Theory of International Trade

This note provides a unified set of diagrammatic proofs for several fundamental theorems in the modern theory of international trade. A complete diagrammatic context depicting the necessary relations between relative product prices, relative factor prices, factor intensities, and real factor earnings is constructed and then used to provide simple proofs of the Heckscher-Ohlin, factor price equalization, and Stolper-Samuelson theorems, together with Mundell's theorem on factor mobility and a Rybczynski-Johnson theorem on factor growth.

On the geometry of constant returns

Constant returns to scale, always a simplifying assumption, is often also much more: many important results depend critically on the very special properties of this class of production function. This paper provides a unified set of simple proofs for most of the crucial analytical properties of constant returns production and their implications for firm costs. Only familiar diagrams and high school geometry are used, and the proofs are written to be easily accessible to college sophomores

An Islamic perspective on inequality in Pakistan

This paper examines the distribution of income in Pakistan, and in each of its four provinces, from an explicit and formal Islamic perspective. A cardinally significant Atkinson-Kolm-Sen relative index of inequality reflecting that perspective is proposed and computed from the full HIES data series for the years 1984-85, 1985-86, 1986-87, and 1987-88. There is evidence of a significant decline in overall inequality in Pakistan from 1984-85 to 1987-88, but the level of inequality remains very high. Inter-province and inter-urban/rural differences in inequality profiles within Pakistan and each of its provinces are found to be generally less significant than intra-province and intra-urban/rural differences

Inequality in Pakistan, 1984-85 to 1987-88: A social welfare approach

This paper presents new results on income distribution in Pakistan from an analysis of the full HIES data tapes for 1984-85, 1985-86, 1986-87, and 1987-88. An explicit social welfare methodology is adopted to measure changes in inequality at the national level, and within and across provinces, over the period. Estimated Lorenz curves for Pakistan and each of its provinces, in each of the four years, are provided, and cardinally significant Atkinson-Kolm-Sen ethical relative indices of inequality are computed. Strong evidence is found that income distribution in Pakistan improved from 1984-85 to 1987-88, and this conclusion is robust to a wide range of distributional values. Judgements on the trend in inequality over time within and across Pakistan\u27s four provinces are shown to depend more heavily on the investigator\u27s choice of distributional values

Zakat and inequality: Some evidence from Pakistan

This paper presents empirical evidence on the extent to which zakat - a form of religiously-mandated charity under Islam - achieves its intended objective in Pakistan. Detailed income and expenditure data from Pakistan\u27s Household Income and Expenditure Survey for 1987-88 are used to construct two income distributions - one containing the distribution of income which would have obtained if relevant forms of charity were not given, and one containing the distribution of income which obtains under a regime in which such charitable giving takes place. Atkinson-Kolm-Sen (AKS) ethical relative indices of income inequality are computed for Pakistan and each of its four provinces, for each of these two income distributions, and are compared over a range of parameter values. Evidence is found that zakat does redistribute from the better off to the worse-off, and so achieves some reduction in measured income inequality in Pakistan. Both intra-province and inter-province components of over-all inequality decline, though the amount of change is generally small. These conclusions are shown to be robust to a wide range of normative values the investigator may bring elect

Optimal implicit contracts and the choice between layoffs and work sharing

Implicit contract models of labor market equilibrium under work sharing and layoffs are constructed to examine several common explanations for the observed market bias in favor of layoffs. We first establish the optimality of work sharing in the absence of complicating factors. We then show that, contrary to the conventional view, fringe benefits can actually encourage work sharing, and that different hours and employment elasticities of output need not discourage it. Our findings confirm the view that tax distortions in the unemployment insurance system contribute to the bias toward layoffs. However, we show that unemployment benefits for those working reduced hours can help eliminate this bias