= Solution
Apply the <transition matrix> once and then again:
$$
x(1)=P\begin{pmatrix}1\\1\\8\end{pmatrix}=\begin{pmatrix}1/2+1/2+4\\1/4+1/2\\1/4+4\end{pmatrix}=\begin{pmatrix}5\\3/4\\17/4\end{pmatrix},
$$
$$
x(2)=P\begin{pmatrix}5\\3/4\\17/4\end{pmatrix}=\begin{pmatrix}5\\5/4+3/8\\5/4+17/8\end{pmatrix}=\begin{pmatrix}5\\13/8\\27/8\end{pmatrix}.
$$
Therefore, in USA, Europe, Rest of World order and in trillions of dollars,
$$
\boxed{x(1)=(5,0.75,4.25)^{\mathsf T},\qquad x(2)=(5,1.625,3.375)^{\mathsf T}.}
$$
Each total remains ten, giving a quick check on the <matrix multiplication>.
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