Labor intensity shock appears in both household utility function and Cobb-Douglas production function

Dear Johannes,
First thank you for your previous guidance, I am grateful.
In my DSGE model, I plan to capture the effect of utilization rate of labor upon household choice and production sector, e.g. during some period of economic contraction, there are workers who are employed but stay at home and get minimum wages, the labor force officially belonging to a factory is not fully utilized, the production capacity of the factory is not fully used due to unexpected public events or economic downturns.
I model this phenomenon using a labor intensity shock (denoted as V), and I put this labor intensity shock (V) to appear in household utility function and firms’ Cobb-Douglas production simultaneously:
Household utility: U=lnC+rholn(1-VH)
where U is household utility, C is consumption, V is labor intensity shock, H is labor, rho is leisure weight.
Firms’ production: Y=AK^alpha(VH)^(1-alpha)
where A is total factor productivity, K is physical capital, V is labor intensity shock, H is labor, alpha and 1-alpha are elasticities of production Y with respect to K an V
H respectively.
Do you think this specification of labor intensity shock in household utility function and firms’ production function appropriate or not?
Thank you very much and look forward to hearing from you.
Best regards,

That depends on the context. If VH is physical labor services that households supply and firms use, then this is the correct specification. But if V is simply a shock to preferences and H is the physical labor service provided, then why would the shock to preferences affect production possibilities?