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

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

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

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

Waiting time distribution of solar energetic particle events modeled with a non-stationary Poisson process

We present a study of the waiting time distributions (WTDs) of solar energetic particle (SEP) events observed with the spacecraft $WIND$ and $GOES$. Both the WTDs of solar electron events (SEEs) and solar proton events (SPEs) display a power-law tail $\sim \Delta t^{-\gamma}$. The SEEs display a broken power-law WTD. The power-law index is $\gamma_{1} =$ 0.99 for the short waiting times ($$100 hours). The break of the WTD of SEEs is probably due to the modulation of the corotating interaction regions (CIRs). The power-law index $\gamma \sim$ 1.82 is derived for the WTD of SPEs that is consistent with the WTD of type II radio bursts, indicating a close relationship between the shock wave and the production of energetic protons. The WTDs of SEP events can be modeled with a non-stationary Poisson process which was proposed to understand the waiting time statistics of solar flares (Wheatland 2000; Aschwanden $\&$ McTiernan 2010). We generalize the method and find that, if the SEP event rate $\lambda = 1/\Delta t$ varies as the time distribution of event rate $f(\lambda) = A \lambda^{-\alpha}exp(-\beta \lambda)$, the time-dependent Poisson distribution can produce a power-law tail WTD $\sim \Delta t^{\alpha - 3}$, where $0 \leq \alpha < 2$.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter

More on volume dependence of spectral weight function

Spectral weight functions are easily obtained from two-point correlation functions and they might be used to distinguish single-particle from multi-particle states in a finite-volume lattice calculation, a problem crucial for many lattice QCD simulations. In previous studies, it is shown that the spectral weight function for a broad resonance shares the typical volume dependence of a two-particle scattering state i.e. proportional to $1/L^3$ in a large cubic box of size $L$ while the narrow resonance case requires further investigation. In this paper, a generalized formula is found for the spectral weight function which incorporates both narrow and broad resonance cases. Within L\"uscher's formalism, it is shown that the volume dependence of the spectral weight function exhibits a single-particle behavior for a extremely narrow resonance and a two-particle behavior for a broad resonance. The corresponding formulas for both $A^+_1$ and $T^-_1$ channels are derived. The potential application of these formulas in the extraction of resonance parameters are also discussed