An economist believes that the price P t of a seasonal commodity in period t satisfies the

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An economist believes that the price Pt of a seasonal commodity in period t satisfies the recurrence relation

P+2=2(P+1 P) + C (t> 0)

where C is a positive constant. Show that

P = A(1 +j)' + B(1 - i) + C

where A and B are complex-conjugate constants. Noting that

1j = 2(cos+jsin),

explain why the economist is mistaken.

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