Abstract
In this chapter we put the different pieces together to perform cost-benefit analyses of the projects under scrutinization. We have deliberately termed the chapter a Blueprint. The reason is that on the one hand we base our evaluations on solid theoretical foundations. On the other hand we lack detailed data or only have access to data from small pilot studies. Still we want to use the incomplete data set to illustrate how to undertake a modern cost-benefit analysis of projects involving environmental and recreational consequences. In the first part of the chapter we provide point estimates of the different costs and benefits items. According to this approach, yielding a single Euro-number (or “krona”-number) for a project’s social profitability, both considered projects are socially unprofitable. The loss of valuable electricity is simply too large to motivate that water is diverted to other uses. Since there is considerable uncertainty with respect to many of the items in the evaluation we undertake an extensive sensitivity analysis. The first part of this analysis is devoted to an attempt to estimate reasonable upper and lower limits, respectively, for the different costs and benefits items. We then turn to a stochastic sensitivity analysis which has some novel features. We introduce and define a cost-benefit acceptability curve and also illustrate how (Monte Carlo) simulation techniques can be used in a sensitivity analysis.
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Notes
- 1.
Assuming that interest is compounded continuously, the present value of a stream of SEK 1 per year for 5 years is equal to SEK 4.64. It should be added that no major change has occurred in the consumer price index since the survey was undertaken.
- 2.
If people are willing to pay for virtually all environmental projects it might be reasonable to look for the most cost-effective way of achieving similar benefits to those provided by the scenarios considered here.
- 3.
. 2(1 ∕ 80)32. 96 ≈ 7. 5, where 18.2 is the WTP of those living today and 32.96 is the present value of a SEK per year for 150 years which is the assumed time horizon; see also Eqs. B.5 and B.6 in Appendix B.
- 4.
For an illustration, see http://www.tushar-mehta.com/excel/software/tornado/decopiled_help/tornado.htm.
- 5.
The reader is referred to [87] for an interesting attempt to compare different methods to estimating confidence intervals for WTP data.
- 6.
Typically health quality runs from zero (death) to unity (perfect health).
- 7.
The base case average WTP is SEK 301 per household for 5 years, while the upper (lower) bound is SEK 399 (SEK 203).
- 8.
We assume that the spot price is SEK 480 per MWh since this is our certainty equivalent price; see the discussion in Sect. 4.2.2.
- 9.
E.ON Stockholm småförbrukarprislista (SEK 239.2 per MWh), Fortum enkeltariff, Stockholm (SEK 194 per MWh), Vattenfall Söder enkeltariff E4 (SEK 174 per MWh). These prices are available on the home pages of E.ON, Fortum, and Vattenfall, respectively (as of fall 2010).
- 10.
A possible refinement would be to truncate (and rescale) the distribution so that all probability mass is in the interval \([-72,-40]\).
- 11.
The associated survivor functions are stated in Eqs. B.12 and B.13 in Appendix B.
- 12.
Loosely speaking, setting the location and scale parameters at lower (higher) values results in a density function that is too narrow (wide) given that the mean is kept unchanged. A further refinement would be to truncate the distribution so that all probability mass is contained in the considered interval.
- 13.
The reader is referred to [44] for a detailed treatment of the properties of the generalized trapezoidal distribution.
- 14.
To implement this in R, libraries Ryacas, triangle and msm are convenient. These libraries are available for automatic download from CRAN.
- 15.
The argument remains unchanged if we assume that both outcomes result in losses.
- 16.
This section draws on [104].
- 17.
For example, taking a Cobb-Douglas cost function with two inputs, the short run MC intersects the long run MC from below at the level of production for which the fixed input is cost minimizing; this holds regardless of whether increasing, constant, or decreasing returns to scale is assumed. Thus if there is slack the short run MC is below its long run counterpart.
- 18.
The Lerner index is: \(({r}^{L} - 5.5)/{r}^{L} = 0.22\), where r L is the lending rate and 5. 5 is the (long run) MC estimated by [161]. Thus r L ≈ 7.
- 19.
Strictly speaking, this holds only if the marginal cost curve is more or less horizontal in a small vicinity of the initial optimum.
- 20.
Under very restrictive assumptions the social opportunity cost of capital and the social rate of time preference coincide, see [27] for details. In such rare cases either concept can be used to define the social discount rate.
- 21.
This amount could be interpreted as a certainty equivalent. That is, the firm is indifferent between receiving this amount with certainty and receiving the extra expected present value profits of continued “full” production at Dönje; see the discussion related to Fig. 6.6.
- 22.
This assumes that Fortum is willing to sell the electricity within their revenue optimization program given that “we” cover their marginal costs.
- 23.
One way to state the problem is as follows. Assume that we have a general equilibrium price vector p ∗ and equilibrium incomes m h ∗ , where a subscript h refers to individual h, with the project. Suppose that individual h is willing to pay WTP h for the project. The vector p ∗ is not an equilibrium price vector for incomes m h ∗ − WTP h , in general. This problem vanishes for the infinitesimally small project which is evaluated at initial or pre-project prices.
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Johansson, PO., Kriström, B. (2012). Blueprint for a CBA. In: The Economics of Evaluating Water Projects. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27670-5_6
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DOI: https://doi.org/10.1007/978-3-642-27670-5_6
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