Note $8,$ states Harnischfeger$$s allowance for doubtful accounts. Compute the ratio of the allowance to receivables $($receivables after the allowance$)$ in $1983$ and $1984.$ What would the allowance have been $($$$)$ if the company maintained the ratio at the $1983$ level? How much did the pre$-$tax income increase $($$$)$ as a result of the changed ratio in $1984?$