Question

The Australian NewStart Allowance is an unemployment benefit that provides a basic grant of $400 per fortnight. (The exact amount varies with your family composition.) Recipients can earn up to $62 per fortnight without losing any of the grant. For income between $62 and $250, the benefit reduces at a rate of 50 cents for every dollar earned. For income above $250, the benefit reduces at a rate of 60 cents for every dollar earned.

Calculate the income (per fortnight) at which the grant reduces to zero.

Answer 1

Unemployment Grant = $400

Upto $62 earnings no loss of grant

Between $62 and $250 : 50cents($0.5) for every dollar earned is reduced from the grant

Above $250 : 60 cents($0.6) for every dollar earned is reduced

We know from the first case the grant is not reducing hence it can never be zero

From the second case lets take the highest income of $250 at which highest reduction can be made

At $250 Reduction = 0.5 * $250 = $125

Reduced Grant = $400 - $125 =$275 which is not 0

Hence, Under the third case

Lets take any income $x greater than $250

Reduction in $x = 0.6 * $x = $0.6x

For Grant to be reduced to 0 :

$400 - $0.6x = 0

$400 = $0.6x

x = $400/0.6 = $666.67 ~ $667

So, At Income of $667 per fortnight the grant reduces to zero