That is a regressive tax. It is regressive because it is charged to all families. It would be charged to Bill Gates's family or Alex Rodriguez's family and also to mine. Never mind that they have way more money than I do.
A proportional tax is one where each person pays the same percentage of their income, not one where they all pay the same absolute amount. So a proportional tax would be one where everyone pays 15% of their income.
In that case, Bill and A-Rod would pay way more money than I would, but it would be equal in terms of what we actually have.
A fixed tax of $400 per family is neither regressive or proportional. This types of tax, called fixed tax is one of the four basic types of tax, called fixed tax. the other three type being proportional, progressive, and regressive.
A fixed tax is defined in terms of the amount of tax paid rather than as a proportion of income. A fixed tax means same amount of tax is charged from all irrespective of their income.
A proportional tax is charged as fixed percentage of the total income. There is no change in the in this percentage based on the level of income. A progressive tax is means that the percentage of tax charged increases with the increase in income. Thus people with higher income are charged tax at higher rate than those with lower income. This is the most common method of charging income tax in countries around the world. Regressive tax is opposite of progressive tax. In this system the people with higher income pay tax at lower percentage rate as compared to people with lower income. This was the system prevalent in some countries in olden days, but is not used any more.