clarify that Y is a state in phd-journey
"U(C)=\\frac{C^{1-\\rho}}{1-\\rho}\n",
"$$\n",
"\n",
- "Now assume that every consumer faces some uncertainty on her income (e.g. it follows AR (1) process), which is idiosyncratic - the realizations of each shock is (potentially) different for each agent. In this setting the Bellman equation looks like:\n",
+ "Now assume that every consumer faces some uncertainty on her income (e.g. it follows AR (1) process, so that the current value of $Y$ is a state variable that predicts future values of $Y$), which is subject to idiosyncratic shocks - the realizations of each shock is (potentially) different for each agent. In this setting the Bellman equation looks like:\n",
"\n",
"\\begin{eqnarray*}\n",
"V(M_t, Y_t) &=& \\max_{C_t} U(C_t) + E[\\beta V(M_{t+1}, Y_{t+1})], \\\\\n",
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