# Is there a labor vs leisure model with work experience?

I find the labor-leisure model with utility functions interesting, but I find it lacks the factor of work experience, which is very important in the real life labor market.

This is a reason people why people might start working for a lower wage or even do unpaid internships.

I tried searching for a labor-leisure model including the work experience factor in the internet but had no luck.

I remember doing the following linear regression model in econometrics:

$$\log(Wage_{it}) = \alpha + \beta \cdot \log(Experience_{it}) + \epsilon_{it}$$

So maybe we could solve for the wage here and plug into the usual budget constraint?

By exponentiating, we get

$$w_t = w_0 {E_t}^\beta$$

where $$w_0 := e^\alpha$$ and $$E_t$$ is experience, which we could define as $$E_t = \sum_{k=1}^{t} L_k$$ (the total amount of time worked in the agent’s lifetime)?

With this we would get

$$\max \sum_{t=0}^{\infty} \beta^t [U(c_t, l_t)]$$

subject to

$$w_0 (\sum_{k=1}^{t} L_k)^\beta + (1+r_{t+1}) s_t = c_t + s_{t+1}$$

Here $$l_t := T - L_t$$ is leisure, where $$T$$ is the time endowment on each period.

I would appreciate any insight on an extension of this kind.

• I dont have time for full answers but there are models with experience, one example: jstor.org/stable/…
– 1muflon1
Jul 27 at 18:37
• @1muflon1 Thank you! I'll check the paper when I have time. Jul 27 at 19:02