[equalizing_difference] a small issue

Hi @jstac and @thomassargent30 thanks for writing this insightful lecture. I learned a lot.

I find a possible issue in lecture equalizing_difference when I review a PR related:

By definition of $w_t^c$ and assumption on college graduates, should we have $w^c_0 = 0$?

Recall the lecture

• $t=0, 1, \cdots, T$
• $w_t^c$ denote the wage at time $t$ of a college graduate

And in the context, we state that
"""
if someone goes to college for the four years $t=0, 1, 2, 3$ during which she earns $0$, but then goes to work immediately after college and works for the $T-3$ years $t=4, 5, \ldots ,T$,
$$c_0 = \sum_{t=4}^T R^{-t} w_t^c = w_0^c (R^{-1} \gamma_c)^4 \left[ \frac{1 - (R^{-1} \gamma_c)^{T-3} }{1 - R^{-1} \gamma_c } \right] \equiv w_0^c A_c$$
"""
In this sense should we write $c_0$ in terms of $w^c_4$ since $w^c_t = 0, t=0, 1, 2, 3$ by assumption?

Also, define the initial college-high school wage gap $\phi$ defined by $w_4^c = \phi w_0^h$?

Start with the linked equalizing_difference lecture and review the definitions of w_t^c, the college-attendance assumption, and the displayed expression for c_0. Confirm whether the initial wage and wage-gap notation are inconsistent, then update the lecture so the assumptions, formulas, and definitions agree throughout.