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1 40 00
1 20 00
or
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p vol
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0.5 1 1.5 2 2.5 3
q endo t h el i al c el l s
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4
Figure 5.1: Singular curve
p dln = 1 1p q 1 q: (5.58)
q b 3 p bp
This gives us the formula for the singular arc corresponding to singular control usin:
Introducing a new variable x = pq; wet get:
2dp
3 +  1lnx = 1( ) (5.59)
b x
2
dp3 +  = (lnx1)x (5.60)b
1)bx + p2 (lnx= ( )3: (5.61)d
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