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Basic concepts in finance are introduced and modelled via first-order recurrence equations. In particular, we discuss compound interest, present value and the present value of an annuity.
Chapter 6 introduces the concept of present value and of rate of return analysis as the major tools used by economists to measure returns to investment in human capital. To do this, the discussion introduces the costs of an educational investment and what these consist of, and brings these costs into an analysis of estimating the rate of return to education using two different methods – the “calculated rate” and the “Mincer rate,” including critiques of the Mincer rate. The chapter introduces the concept of social costs and social return, the “option value” of schooling, and further analyzes the problem of “selection bias” – how economists try to “identify” the present value or rate of return to the additional skills learned in school, distinguishing the returns to investing in these skills from other factors that influence the higher wages/earnings of those with more schooling. To illustrate this identification problem, a case study is presented of estimating the returns to education for identical twins with different attainment levels.
Mathematical optimization has been used since the early 20th century to improve the profitability of systems and processes. The time-value of money that leads to the concepts of net present value, annual worth, and annual cost of capital investment, is paramount in the optimization of energy systems that typically operate for very long periods. The method of thermoeconomics (which was formulated in the 1960s) and the similar method of exergoeconomics (which emerged in the 1990s) are two cost-analysis methods extensively used for the optimization of energy systems, components, and processes. Calculus optimization and the Lagrange undetermined multipliers are similarly used tools. This chapter begins with an exposition of the basic concepts of economics and optimization theory, and continues with the critical examination of the mathematical tools for the optimization of energy conversion systems using the exergy concept. The uncertainty of the optimum solution, which is an important consideration in all economic analyses, is clarified and an uncertainty analysis for exergy-consuming systems is presented.
Data on the spread of invasive weeds into arid western lands are used to evaluate the environmental and economic importance of controlling invasive weed infestations early. Variable rate and constant rate infestation expansion paths are estimated. The implications of variable vs. constant infestation growth rates for projecting both biophysical and economic effects are illustrated. The projections derived from both constant and variable growth rate expansion paths support the contention that it is expedient to control new infestations early.
Restrictions on the ownership of farmland by nonresidents of Saskatchewan were imposed by the Farmland Security Act (FSA) in 1974. The FSA has been blamed by some observers for depressed provincial land values. An adaptive expectations present value model is developed to estimate the effects of the FSA, with the province of Alberta included as a control. Results of seemingly unrelated regressions and generalized autoregressive conditional heteroscedasticity estimates find no statistically significant effect of the FSA on the value of land in Saskatchewan. This may indicate that the effect of the regulatory change is too small to be measured accurately.
This lesson describes how a government decides whether and how much it should spend on vulnerability reduction. There are techniques and methods by which decision-makers compare development alternatives. The differences between the risk that a potentially catastrophic event will occur and uncertainty are described, with uncertainty providing greater difficulty in economic analyses. There is a range of methods for identifying the complex mix of competing costs and benefits associated with any restructuring of investment priorities to accomplish disaster mitigation. The possibilities are described in terms of the opportunity costs and present value. Impact and consequent losses include: (1) direct monetary effects; (2) indirect monetary effects; (3) direct, non-monetary effects; (4) indirect, non-monetary effects; and (5) loss of non-renewable natural resources. The difficulties in assigning values to these effects are described, as well as the means of judging the costeffectiveness of such interventions. An advantage of screening projects using a framework of analytical methods is that it can assist in focusing on a variety of possible outcomes and make the factors influencing these outcomes quite explicit.
We study the present value Z∞ = ∫0∞ e-Xt-dYt where (X,Y) is an integrable Lévy process. This random variable appears in various applications, and several examples are known where the distribution of Z∞ is calculated explicitly. Here sufficient conditions for Z∞ to exist are given, and the possibility of finding the distribution of Z∞ by Markov chain Monte Carlo simulation is investigated in detail. Then the same ideas are applied to the present value Z-∞ = ∫0∞ exp{-∫0tRsds}dYt where Y is an integrable Lévy process and R is an ergodic strong Markov process. Numerical examples are given in both cases to show the efficiency of the Monte Carlo methods.
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