Wage Growth Rate in the R&D Model I am trying to understand the R&amp;D model and how to calculate the growth rate of wage in this model. 

There is no equation given, but it’s stated that : household income must equal total consumption. as income is total profit plus wage income, and the two are fixed in proportions, wages grow at the same rate as output $g_w=g_y$

I tried to write down the equation of this statement, however, I don‘t really think it’s right: $\pi+w= C_t$.

Can anyone help with the equation and it’s intuition?

Addition: the R&amp;D model introduces final good producers that sell their good in a competitive market and intermediate goods producers that produce either a produced intermediate good or “ideas” that are sold to the final good producers and used to produce the final good. The intermediate good and “ideas” are substitutes.
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. $g_y = g_w = g_{\pi}$