I am studying a paper entitled "The Past and Future of Knowledge-Based Growth" by Strulik et al (2013) where the budget constraint is written as:
$$w_{t}h_{t}(1-\tau n_{t})=c_{t}^{1}+s_{t}+n_{t}e_{t},$$
where $w_{t}$ are wages, $h_{t}$ is the level of human capital, $\tau$ is the amount of time to raise a child, $n_{t}$ is the number of children, $c_{t}^{1}$ is consumption, $s_{t}$ are savings, and $e_{t}$ is educational investment. Wages are a function of human capital since human capital is an input into production and therefore determines marginal product (wages).
My question is as follows. Why are wages multiplied by the human capital term, $h_{t}$, in the equation above when just including $w_{t}$ would presumably imply workers are earning the return to educational investment via human capital. I have seen this sort of setup often and trust there's an explanation, however I do not fully understand the economic intuition here.