May I ask what is the acceptable way to measure welfare in growth models? For example, in OLG models, Docquier, F., Paddison, O., & Pestieau, P. (2007) define the social welfare function of the social planner as follows:

And then solves for a modified golden rule: \frac{\beta f^{\prime}(\bar{k}_t)}{1+n}=(1+g)^{1-b}, where \bar{k}_t = \frac{k_t}{h_t}. So, here, k_t, c^1_t, c^2_{t+1}... grows in steady-state but \frac{k_t}{h_t}, \frac{c^1_t}{h_t}, \frac{c^2_{t+1}}{h_t}... are constants in steady-state, and U(\cdot) is assumed to be homogeneous of degree b. Although a log-utility function is not homogeneous, it seems it can be interpreted as having this property by assuming b=0 and applying some manipulations as discussed in (Del Rey, E., & LOPEZ‐GARCIA, M. A. (2012)).

In my project, however, I am **not** interested in finding optimal \bar{k}_t in the social planner’s problem. I only want to see if some policy is welfare-improving (in steady-state). So, I guess I can use the following welfare function, right?

Del Rey, E., & LOPEZ‐GARCIA, M. A. (2012) suggest using the specification in (2) rather than (1) as an alternative social welfare function of the social planner to find optimal \bar{k}_t. Using either (1) or (2) determines which policy should be introduced in the Laissez-faire/decentralized problem to match the allocations in the social planner’s problem.

But if I only care about whether a policy is welfare-improving, then I guess the welfare function specified in (2) will suffice, right?