Qt^{s} = Quantity supplied at time t

Qt^{d} = Quantity demanded at time t

Pt = Price of good at time t

Qt^{s} = -Pt +2Pt-1

Qt^{d} = 50 Ė 0.5Pt

The market is in equilibrium Qt^{d} = Qt^{s}

I am asked to find the price path for Pt if P0 = 30

Im a little unsure as to whether Iíve plugged the right info into the formula

50-0.5Pt = -Pt + 2Pt-1

Rearranging that I get

Pt=A(\frac {-2}{0.5}) ^{t} + \frac{1+50}{0.5 + 2}

= A(\frac{-2}{0.5})^{t}+ 20.4

A = [30 - (\frac{1+50}{0.5+2})

=[30-20.4] = 9.6

Therefore I get

Pt=9.6(\frac{-2}{0.5})^{t} + 20.4

Iím unsure as to whether Iíve actually done this correctly, as my understanding on this isnít that great, any help would be very much appreciated.