diff --git a/examples/Gentle-Intro/Gentle-Intro-To-HARK.ipynb b/examples/Gentle-Intro/Gentle-Intro-To-HARK.ipynb index df21b9e31..57c311e47 100644 --- a/examples/Gentle-Intro/Gentle-Intro-To-HARK.ipynb +++ b/examples/Gentle-Intro/Gentle-Intro-To-HARK.ipynb @@ -387,10 +387,10 @@ "Specifically, our new type of consumer receives two income shocks at the beginning of each period: a completely transitory shock $\\theta_t$ and a completely permanent shock $\\psi_t$. Moreover, lenders will not let the agent borrow money such that his ratio of end-of-period assets $A_t$ to permanent income $P_t$ is less than $\\underline{a}$. As with the perfect foresight problem, this model can be framed in terms of __normalized__ variables, e.g. $m_t \\equiv M_t/P_t$. (See [here](https://www.econ2.jhu.edu/people/ccarroll/papers/BufferStockTheory/) for all the theory). Accordingly the normalized utility and continuation value are $u$ and $v_t$.\n", "\n", "\\begin{align*}\n", - "v_t(m_t) &= \\max_{c_t} u(c_t) + \\aleph\\beta \\mathbb{E} [(\\Gamma_{t+1}\\psi_{t+1})^{1-\\rho} v_{t+1}(m_{t+1}) ] \\\\\n", + "v_t(m_t) &= \\max_{c_t} u(c_t) + \\aleph\\beta \\mathbb{E} [(\\Gamma\\psi_{t+1})^{1-\\rho} v_{t+1}(m_{t+1}) ] \\\\\n", "a_t &= m_t - c_t \\\\\n", "a_t &\\geq \\underline{a} \\\\\n", - "m_{t+1} &= R/(\\Gamma_{t+1} \\psi_{t+1}) a_t + \\theta_{t+1} \\\\\n", + "m_{t+1} &= R/(\\Gamma \\psi_{t+1}) a_t + \\theta_{t+1} \\\\\n", "\\mathbb{E}[\\psi_t]&=\\mathbb{E}[\\theta_t] = 1 \\\\\n", "u(c) &= \\frac{c^{1-\\rho}}{1-\\rho}\n", "\\end{align*}\n",