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This situation can occur if tmax is chosen too far in the right tail of the density Because of this feature, there is no danger in setting tmax too large For example, suppose that the desired (unknown) density is concentrated between t-values of 0 and 10 and tmax is chosen to be 106 The program will truncate automatically at the largest numerically sustained value, set c2 , and return the corresponding tmax To nd the lower bound c1 we work on the log scale For time-to-event data, tmin is generally 0 We calculate c1 as follows: 1 Set = 2 and begin with log s = 0 2 If there is an error in evaluating K [ exp(log s)], (a) Set log s log s and evaluate K [ exp(log s)] (b) Stop when K [ exp(log s)] evaluates without error 3.

) Because of the tax, the amount of beef supplied falls from 10 million kilos to 9 million kilos Furthermore, the total surplus is reduced to the triangle whose three corners are G, D and F You can immediately see that this new total surplus is much smaller than the old total surplus But before we start ranting about the evils of government, we need to take account of the fact that taxes are being collected Taxes (theoretically, at least) benefit society, so we need to include this amount when calculating the total surplus of this good sold at this price At the new equilibrium, 9 million in taxes are collected because the 9 million kilos of beef sold are taxed at 1 each The 9 million in tax collections are represented graphically by the parallelogram whose corners are C, G, F and E.

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This area was previously contained in the old total surplus triangle whose corners were C, D and A Consequently, the area that used to be part of the old total surplus hasn t been destroyed, but merely transferred to the government However, part of the old total surplus has been destroyed This part is shown graphically by the shaded deadweight loss triangle (with corners at E, F and A) This area captures the fact that society is made worse off by the reduction in beef output from 10 million kilos to 9 million kilos (Okay, now you can start ranting about the evils of government) Measuring the size of the deadweight loss using the formula for the area of a triangle (1 2 base height) tells us that the tax leads to a deadweight loss of 500,000.

If K [ exp(log s)] < tmin then c1 exp(log s) 4 Set = 1, log s log s + 5 Evaluate K [ exp(log s)] and check (6) If (6) does not occur, go to (7) if K [ exp(log s)] < tmin Otherwise repeat step (5) with log s log s + 6 In the event that there is an error in evaluating K [ exp(log s)], or K [ exp (log s)] K [ exp(log s )], (a) Set log s log s (b) Set /2 and repeat (5) (c) Set log s log s +.

That s a big number representing a huge reduction in total surplus deriving from the fact that for each of the 1 million kilos of beef no longer being produced, benefits exceeded costs All those gains are lost when the tax is imposed..

It should be noted that the GSM MoU Group handles the authentication algorithm (A3/A8) for its members based on a sample algorithm, which can be used at the individual GSM MoU Group operator s discretion. As the A3/A8 algorithm is used exclusively inside the individual operator s network, the operators are free to use propriety algorithms to improve security and it should be noted that the authentication registers are speci ed to handle more than one algorithm. This allows introduction or phasing-in of new algorithms without recalling or reissuing Subscriber Identity Module (SIM) cards. The encryption algorithm (A5) used in the radio part of the network must for technical reasons be identical in all networks and the GSM MoU Group SG is responsible for controlling the restricted distribution of the algorithm speci cation and safeguarding the system. It should be noted that the encryption of the GSM system is designed to protect the privacy over the radio part of the system to a reasonable, non-military level. A5 is a 64 bit algorithm, which met some initial protest by relevant authorities, forcing the GSM MoU Group to activate only 54 bit initially and to accept that some member countries would not at all accept encryption over the radio part of GSM. The security group also plays an important role in spreading knowledge about any attacks on the security. In addition it provides know-how to new members of the GSM MoU Group on all security issues.

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Table 5.4 calculates convexity for a 7.625 percent 5-year Treasury note of 5/31/96. We calculate it to be 20.1036. Estimating price using both modified duration and convexity requires solving for Pe Pd Pd (Dmod Y Convexity Y2/2)

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