Price: \(y\)
Sales tax rate: \(t\)
The good is then sold for \(y+ty\)
Price: \(y +ty\)
tax rate: \(t\)
Sold for: \((y+ty)+t\cdot (y+ty)\)
And so on for the subsequent sales.
This creates a tax cascading effect. Not desirable. Increases artifically the price of inputs used in production. Thus sales tax was abandoned and moved to a system of value added tax (VAT)
Output, input
Then,
\[ \text{VAT} = t(y-x) \\=ty-tx \]Example. Say you purchase input for \(100\), with a tax \(10\%\). Thus Rs \(100+10\) is paid for the input. When you sell this good, the tax rate is again \(10\%\), applied on Rs \(110\). The buyer pays \(110+110\cdot10\%\) which is Rs \(121\). The tax you will pay to the goverment is \(11-10\). The \(10\) Rs deducted is called ITC (input tax credit). This ensures that there is no tax cascading. The producer does not pay tax on inputs.
\[ A\xrightarrow[10%]{100}B\xrightarrow[10%]{110+20}C:\;{143} \]B adds 20 rupees value.
\[ A\xrightarrow[10\%]{100(v)}B\xrightarrow[10\%]{100(v)+10(t)}C:120 \]Thus,
No tax on inputs
No tax cascading
However, disadvantages,
Requires detailed bookkeeping by both A and B