On Envelope Theorems in Economics: Inspired by a Revival of a Forgotten Lecture

This paper studies how envelope theorems have been used in Economics, their history and also who first introduced them. The existing literature is full of them and the reason is that all families of optimal value functions can produce them. The paper is driven by curiosity, but hopefully it will give the reader some new insights.Envelope theorems; names and history; value functions

Welfare Theory: History and Modern Results

This paper contains a fairly brief, but self-contained, version of the history of welfare economics, as well as the more modern welfare results. We introduce public goods and asymmetric information, and we hint at some of the modern mechanism design results. The paper also contains a section on welfare measures in a dynamic economy.Welfare Theory;

Sick Pay, Health and Work

The purpose of this paper is to analyze the effects of different sickness insurance regimes on the employee decision reporting sick or not. We can think of the design problem as a representative employer’s decision to determine the optimal relationship between the wage and the sickness pay. The employee bases her decision to work or not on this relative price and her exogenously given health status that varies between individuals. We believe that the incentives present in the model are able to tell as about relevant aspects of the incentives involved in a state managed sickness insurance system. We calculate how the control variables depend on parameters such as the average productivity of the worker, the average productivity of the substitute, the wage of the substitute, and the search cost to find a substitute. Since we assume that the health status of the work force is heterogeneous and represented by a distribution function, we are also able to calculate the change in the work participation rate, as a function of the parameters.Sickness insurance design; wage setting; and labour force participation

Evaluating Projects in a Dynamic Economy: Some New Envelope Results

This paper is concerned with the modern theory of social cost-bene.t analysis in a dynamic economy. The theory emphasizes the role of a comprehensive, forward- looking, dynamic welfare index within the period of the project rather than that of a project.s long-term consequences. However, what constitutes such a welfare index remains controversial in the recent literature. In this paper, we attempt to shed light on the issue by deriving three equivalent cost-bene.t rules for evaluating a small project. In particular, we show that the direct change in net national product (NNP) quali.es as a convenient welfare index without involving any other induced side e¤ects. The project evaluation criterion thus becomes the present discounted value of the direct changes in NNP over the project period. We also illustrate the application of this theory in a few stylized examples.dynamic cost-bene.t analysis; net national product; project evaluation; welfare index

Genuine Saving under Stochastic Growth

The concept of genuine saving appeared for the first time in a proof of a now well known theorem in Weitzman (1976). It was reinvented and used as a local welfare indicator by Pearce and Atkinson (1993). The purpose of this paper is to generalize this welfare measure to a stochastic Brownian motion context. We will use a stochastic version of a growth model introduced by Ramsey (1928). The particular model was developed by Merton (1975). Although the model is simple, it is enough to understand what its welfare results will look like in a general case.Welfare measures under growth and uncertainty; diversified risk versus undiversified risk

The Role of the Hamiltonian in Dynamic Price Index Theory

This paper is an attempt to investigate the cost-of-living index problem in a general equilibrium multi-sector growth model. Instead of using the utility function as a compensation criterion as Konüs’ (1924) did in his original contribution, we take advantage of the current-value Hamiltonian in constructing our dynamic price index. Since the Hamiltonian is a constancy-equivalent of future utilities (Weitzman, 1976), the dynamic price index is defined in terms of the minimum expenditure that, under alternative prices, would support the constancy-equivalent-utility level in the future. We show that, when properly deflated by the dynamic price index, the real comprehensive net national product becomes an ideal measure for dynamic welfare comparisons. For some special cases, we show that the dynamic price index reduces to the simple static index.Dynamic index theory; Hamiltonian; ideal deflator

On the Choice of Metrics in Dynamic Welfare Analysis: Utility versus Money Measures

This paper is concerned with the choice of metrics for social cost-benefit analysis and dynamic welfare comparisons. In a utility-theoretic framework, we show that there is always a money measure that can serve as a substitute for the maximized utility wealth. Thus, under the non-arbitrage course of discount rate, the choice between utility and money measures has no real effect on project evaluations. We also define a generalized comprehensive net national product measure with a consumer surplus term incorporated, which is completely consistent with the Weitzman foundation. It is shown that while a green (comprehensive) NNP growth simply reflects the income effect, the change in consumer surplus captures the welfare effect of relative price changes. We argue that the reason for green NNP to be a weak welfare indicator is not due to its choice of money metric per se but the ignorance of a consumer surplus term.Dynamic cost-benefit analysis; green national accounting; utility versus money metrics; Weitzman´s theorem

Money Metrics Welfare Measures in Imperfect Markets under Growth

This paper shows how utility based welfare measures in dynamic general equilibrium under imperfect markets can be transferred into a money metrics. In order to do this, we need to price forward looking components measured in units of utility. The typical comprehensive quasi-static welfare measure contains a core that looks like a comprehensive (green) NNP component, as well as additional consumer surplus terms for both consumption goods and the externality. In addition, it contains a forward looking component with the discounted value of the marginal externality as the function to be integrated over time is also required. To accomplish this, we need a price index that is independent of the market basket, or to assume that the marginal utility of income is constant over time. With respect to local welfare measures it turn out that growth in traditional NNP will surprisingly work, provided that we condition on a positive average marginal rate of return of investment, and use an augmented genuine saving concept.Welfare measurement under growth; imperfect markets; utility versus money metrics

Stochastic Cost Benefit Rules: A Back-of-a-Lottery-Ticket Calculation Method

In this paper, we introduce cost benefit rules for projects embedded in a stochastic optimal growth framework. We model uncertainty in terms of Brownian motion and Ito integrals. Taking the mathematical expectation of the project means that the Ito integrals vanish, and we end up with a cost benefit rule that closely resembles its deterministic counterpart.Cost benefit analysis; stochastic optimal control theory; Brownian motion

A Note on Environmental Policy Reform, Distortionary Taxation and Imperfect Competition

This paper concerns the welfare effects of public abatement projects, and concentrates on the influence of distortionary taxes and imperfect competition in the labor market. In addition to the direct environmental benefits and costs of resource use, abatement policies give rise to welfare effects via the tax system as well as via changes in the employment. We also show how the cost benefit rule is modified, if the other policy instrument are optimally chosen conditional on the level of abatement.Environmental policy; distortionary taxation; the labor market