Welfare Benefits Calculator

Calculator Basics

The Welfare Benefits Calculator helps design and analyze welfare benefit structures by simulating how different parameters affect work incentives and budget utilization.

Key Features

Interactive parameter adjustment
Real-time result visualization
Multiple pre-configured scenarios
Priority-based optimization
Comprehensive population modeling

Available Scenarios

No Scenario

Free-form mode where all parameters can be adjusted manually.

Scenario I

Standard mixed population including all types from hard workers to never-workers.

Scenario II

Work-capable population without non-workers/never-workers.

Scenario III

Reduced budget scenario to explore trade-offs under tighter constraints.

Scenario IV (UBI)

Universal Basic Income variant with lower reduction rates.

Scenario V (Work Req.)

Work requirement scenario with exemptions for certain populations.

Scenario VI (EITC)

Earned Income Tax Credit calculator with phase-in/phase-out benefits.

Parameter Controls

Basic Parameters

Basic Support Level (G): Maximum benefit amount for zero earnings
Breakpoint (BP): Earnings level where higher reduction rate begins
Self-Sufficiency Point (SSP): Earnings level where benefits phase out completely
Benefit Reduction Rates:
- t₁: Rate before breakpoint
- t₂: Rate after breakpoint (typically higher)

Population Types

Type	Description	Work Sensitivity
Type I	Hard Workers	Most responsive to incentives
Type II	Workers	Moderately responsive
Type III	Marginal Workers	Somewhat responsive
Type IV	Non-Workers	High threshold for work
Type V	Never Workers	Unable to work

How the Calculator Works

Optimization Process

The calculator uses a systematic optimization process to find the best parameter combination based on your priorities:

Evaluates different parameter combinations within defined ranges
Calculates benefits and work choices for each population type
Checks budget constraints and program effectiveness
Scores results based on priority weights
Selects the combination with the highest score

Priority Weighting

Priorities are weighted based on their order:

1st priority: 100% weight
2nd priority: 80% weight
3rd priority: 60% weight
4th priority: 40% weight
5th priority: 20% weight

Mathematical Details

Basic Benefit Formula

If E = 0: B = G

If 0 < E ≤ BP: B = G - (E × t₁)

If BP < E ≤ SSP: B = G - (BP × t₁) - ((E - BP) × t₂)

If E > SSP: B = 0

Work Decision Model

Y(No Work) = 0 + Benefits(0)

Y(Part Time) = PT_Earnings + Benefits(PT_Earnings)

Y(Full Time) = FT_Earnings + Benefits(FT_Earnings)

Population Thresholds

Type	FT Threshold	PT Threshold
I	$300	0.55
II	$400	0.60
III	$500	0.75
IV	$1200	0.95
V	∞	∞

Optimization Score

Score = w₁(Work Rate) + w₂(Budget Efficiency) + w₃(FT Rate) + w₄(Basic Support) + w₅(PT Rate)

Special Cases

EITC Addition:

Total Benefit = Basic Benefit + EITC

Work Requirement Penalty:

If non-exempt non-workers > threshold: Total Cost = Regular Cost × 1.10