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Without specifying <math>R(\cdot)\;</math> above, there is not simple analytical solution to either the first best or the second best. However, as manipulation becomes infinitely costly (i.e. <math>\lambda \to \infty\;</math>) the principal sets:
:<math>\alpha_1 - p_1 \;\mbox{and }\; \alpha_2 = p_2\;</math>
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