The Book of Why, Table 8.1, Counterfactuals example I'm reading "The Book of Why" by Judea Pearl and I'm getting an answer for a problem that doesn't match what the book says. This is my first foray into Structural Causal Models and their use, so I want to be absolutely certain that there isn't a gap in my understanding when I try to solve the problem; hence this question.
Here's the problem that I'm stuck on:
The Data
Bert: $EX = 9$, $ED = 1$, $S_1 = 92500$.
Caroline: $EX= 9$, $ED = 2$, $S_2 = 97000$
The equations
According to more data in the table, the following equations hold:
$$S_{ED} = 65000 + 2500 EX + 5000 ED + U_S\\
EX = 10 - 4 ED + U_{EX}$$
where $U_S$ and $U_{EX}$ are background variables that are different for Bert and Caroline.
The Question
The question requires that we calculate the value of $S_1(Bert) - S_1(Caroline)$ (basically subtract from 92500, the value of $S_{ED}$ for Caroline if her $ED = 1$). The problem is posed between pages 273 and 282.
My confusion
The book says that the final value should be 5000. My numbers are either 500, if I assume that the value of EX remains 9 like before (which would be wrong because the value of EX should be updated according to the second equation?), or -9500, if I simply plug in the new value of ED and solve the equations.
Am I missing something here? It's very possible as this whole exercise is couched in the realm of operating with causal model diagrams, and I might have missed an update step to the equations...
 A: You are not missing anything, the correct answer is $-9500$! 
First find the idiosyncratic characteristics of Caroline, by updating her background variables $U$ given the evidence $EX = 9$, $ED = 2$, $S = 97000$. This is the Abduction step,
$$
97000 = 65000 + 2500(9) + 5000(2) +U_{s} \implies U_s = -500\\
9 = 10-4(2) + U_{EX} \implies U_{EX} = 7
$$
Now we perform the action, which is setting Caroline's new education to 1, that is, $do(ED = 1)$, and properly mutilating the graph and structural equations. Finally we perform prediction under the new system (using the new updated information about the exogenous variable and the interventional graph),
$$
EX_1(Caroline) = 10-4*(1) + 7 = 13 \\
$$
And, 
$$
\begin{align}
S_{1}(Caroline) &= 65000 + 2500\times EX_{1}(Caroline) + 5000(1) -500 \\
&=65000 + 2500(13) + 5000 - 500\\
&= 102000
\end{align}
$$
Thus, $S_1(Bert) - S_1(Caroline) = 92500 - 102000 = -9500$.
PS: Pearl is aware of the typo and this will probably be in the errata and corrected soon. 
