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import ppf.utility class surface: def init (self, first axis, second axis, values): self. first axis = first axis self. second axis = second axis self. values = values def call (self, x, y): i1, i2 = ppf.utility.bound(x, self. first axis) j1, j2 = ppf.utility.bound(y, self. second axis) f = self. values x1 = self. first axis[i1] x2 = self. first axis[i2] y1 = self. second axis[j1] y2 = self. second axis[j2] r = (x2 - x1)*(y2 - y1) return (f[i1, j1]/r)*(x2 - x)*(y2 - y) + \ (f[i2, j1]/r)*(x - x1)*(y2 - y) + \ (f[i1, j2]/r)*(x2 - x)*(y - y1) + \ (f[i2, j2]/r)*(x - x1)*(y - y1)

We chose the latter approach, and I don t think that anyone among us ever regretted it One huge bene t of the PN was that we now had a body with program managers for each WP, able to assist the WPs in their work as well as keep an overall view of the system work such as identifying the effects in one area of the system when changes were made to another It also had the resources to keep track of the various documents and the changes to them, a monumental task as it turned out to be when the number of Change Requests (CRs)rose to several hundred in each plenary meeting In addition, the PN also took on several other tasks which were of a general nature and thus not necessarily belonging in any particular WP.

Minutes of second IDEG meeting on 6 8 July 1987 in Heck eld, UK, IDEG Doc. 58/87. See 10, Section 1, Fig. 10.1.2. 23 WP4 Doc. 152/87. 24 WP4 Doc. 85/88 rev. 1. 25 See 16, Section 2.

One example of this was the initiative concerning the IPR issue, another one was the work done in the very important eld of operation and maintenance, which after some time led to a regular working party..

The English respondents had similar criticisms to make of evidential interviewers, criticising them for creating suggestion through bias, credulity and insuf cient challenge.

Monopolies produce less than competitive firms because they have different marginal revenue curves. As we show earlier in the chapter, monopolies face downward-sloping marginal revenue curves. By contrast, competitive firms face horizontal marginal revenue curves. You can see the comparison in Figure 12-4, in which we draw both the downward-sloping marginal revenue curve of a monopoly, MRm, and the horizontal marginal revenue curve of a competitive firm, MRc. The graph also has an average total cost curve, ATC, as well as a marginal cost curve, MC. Figure 12-4 assumes that the competitive firm and the monopoly have the same cost structure, which is why we show only one MC curve and one ATC curve. By assuming that both firms have the same cost structure, we can isolate the effect that the difference in marginal revenue curves has on each firm s output decisions.

Just to be absolutely clear on this point, when we write V as in the last equation, this variable is to be interpreted as the value of volatility in price terms (not as a volatility measure expressed as an annualized standard deviation)12 Since there is a number of option pricing formulas in existence today, we need not define a price value of volatility in terms of each and every one of those option valuation calculations Quite simply, for our purposes, it is sufficient to note that the variables required to calculate a price value for volatility include R, T, and , where is the annualized standard deviation of S.