I'm trying to calculate the result of an simple example on page 326-327, in Harrison and Kreps(1978). It's pricing a piece of asset whose dividend stream is a simple Markovian process.
Here's my attempt to replicate investor $1$'s evaluation of this asset.
$p^1(0) = 0 + \frac{3}{4} ( \frac{1}{2} p^{1}(0) + \frac{1}{2} p^{1}(1) )$
$p^1(1) = 1+ \frac{3}{4} ( \frac{2}{3} p^{1}(0) + \frac{1}{3} p^{1}(1) )$
But when I substitute the numerical value given in the bottom of second screenshot, they don't match. Do I miss something?