k here is the question

Question

suppose a government imposed an employment tax. That is upon entering the labour force an, individual had to pay a lump sum tax. (if they don't work, they don't have to pay the tax). How ould this affect the individual's labour supply curve?

Good question!

Start with a classic labor/leisure employment model. Here, people work until the marginal value of leisure equals the wage rate. Under this model, the lump sum tax generally has NO impact on hours worked. (except in the "corner solution" case where the tax causes the person not to work at all) Here, the lumpsum tax is a fixed cost, and does not affect the marginal value of leisure.

However, I would argue the labor/leisure model is incomplete. The tax will have an income affect. Lets change the model to a labor/consumption model. Here, a person will work until the value of the marginal utility from consumption equals the wage rate. Since the first x hours of work go to pay the tax, the value of the marginal utility will be higher at the original pre-tax equilibrium number of hours. Ergo, the person will work more hours (unless the person doesnt work at all.)