# Piecewise Linear Budget Constraints

This generates a complete two-dimensional budget constraints for some unit (person, benefit-unit, household, etc.) for some tax-benefit system. That is, a list points describing the combinations of net income that the unit would get for different values of gross income (or hours worked, wages, etc.).

See: Duncan, Alan, and Graham Stark. "A Recursive Algorithm to Generate Piecewise Linear Budget Contraints" IFS Working Paper 2000/01 May 2, 2000] https://doi.org/10.1920/wp.ifs.2000.0011.

Here is a live example of this algorithm in action.

## Usage

Define a function that returns the net income for some gross value - this could be (e.g.) hours worked, wage, or gross income, and some set of data (details of a person, tax paramters, etc):

   function getnet( data::Dict, gross :: Real ) :: Real

The call to makebc then generates the budget constraint using getnet. If successful this returns a BudgetConstraint array, which is a collection of x,y points describing all the points where the budget constraint has a change of slope, where x is the gross value and y the net.

The routine is controlled by a BCSettings struct; there is a DEFAULT_SETTINGS constant version of this which I suggest you don't change, apart from perhaps the upper and lower x-bounds of the graph.

## Functions and Data Structures

BudgetConstraints.annotate_bcMethod

This takes a budget constraint and produces a named tuple of METRs and Tax Credits for each one. (really just 1 minus the slope and the intercept at that point). Useful for annotating graphs and tables.

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BudgetConstraints.makebcFunction

Make a budget constraint using function getnet to extract net incomes and settings (see above on this struct). data should hold whatever your getnet function needs (parameters, a househols, etc.) getnet should be a function of the form net=f(data, gross). See the testcase for an example.

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## Problems/TODO

• the tolerance isn't used consistently (see nearlysameline);
• I may be misunderstanding abstract types in the declarations;
• possibly use some definition of point, line, etc. from some standard package.