Starting the system with $a_0^k =0$ forall $i$ has a striking implication that we can call **state variable degeneracy**.

Starting the system with $a_0^k =0$ for all $i$ has a striking implication that we can call **state variable degeneracy**.

Here is what we mean by **state variable degeneracy**:

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### Matrix $Q$ to Represent Pricing Kernel

### $Q$ is the Pricing Kernel

For any agent $k \in \left[1, \ldots, K\right]$, at the equilibrium allocation,