Wage Growth Rate in the R&D Model
income is total profit plus wage income, and the two are fixed in proportions


I.e. $y_t = w_t + \pi_t$ and  $w_t = \alpha y_t$ and  $\pi_t = (1-\alpha)y_t$, where $\alpha$ and $(1-\alpha)$ are the fixed proportions.

For $y_{t+1}$ we have $y_{t+1}=(1+g_y)y_t$ and $w_{t+1} = \alpha y_{t+1} = \alpha (1+g_y)y_t = (1+g_y)\alpha y_t = (1+g_y) w_t$ and $\pi_{t+1} = (1-\alpha) y_{t+1} = (1-\alpha)(1+g_y)y_t = (1+g_y)(1-\alpha) y_t = (1+g_y) \pi_t.$

I.e. $g_y = g_w = g_{\pi}$