What curve would a continuous progressive tax follow?

Question

Another why of answering this would be: What would the equation of the marginal rate?

Answer 1

A linear model would uses the following:

Tax payable (in dollars) = 0.30*(income - threshhold)

The variables are:

1. Tax threshhold

2. Base marginal tax rate ($0.30 per incremental dollar in this example)

Here is a possible non-linear model:

Tax payable (in dollars) = 0.30*(income - threshhold)+0.10*(income - threshhold)^1.05

Variables become:

1. Tax threshhold

2. Base marginal tax rate ($0.30 per incremental dollar in this example)

3. Power tax rate ($0.10 per incremental dollar in this example)

4. Power tax index (1.05 in this case)

Under this scheme and with a threshold of $30,000 the following results arise

Income ($) ............. 30000 ... 80000 ...... 130000 ...... 355000

Linear model ($) .... ........0 ... 15000 ........ 30000 ........ 97500

Nonlinear model .($) ....... - ... 20367.83 .. 43679.07 . 141237.11

Equivalent linear

marginal rate ($) ........ 0.30 ..... 0.41 ........... 0.44 ........... 0.47

These can be readjusted by playing with the variables.

In economics, the marginal rate of substitution is the rate at which a customer is ready to give up one good in exchange for another good while maintaining the same level of satisfaction.

Marginal rate of substitution as the slope of indifference curve