G’ = (G-S) * (1-CT) / (1 – bnrt) + S  

shoot! so, now the can company received not only an increase in cost but also an increase in taxes.

Previous earning is: (C-G) * ( 1-CT)
now the earnings is:
(C’-G’) * (1-bnrt) = (C’-(G * (1-CT) + S*o)/(1-CT-o)) *(1-CT -o) = (C’*(1-CT-o) – G*(1-CT) – S*o)

solve for C’ 

to arrive at P’ = (P*(1-CT) – S*o)/(1-CT-o) as the price that the final retailer’s price to arrive at the same profit as before.

P’ = P * (1-CT)/(1-CT-o) – S * o / (1-CT-o)

ugh! let’s plug in some numbers.

Example 1
original seed S=1 final original price P=10 Corporate Tax CT = 10% tax increase o= 1%

P’ = 10 * (1-10%) / (1-10%-1%) – 1 *1% /(1-10%-1%) P’ = 10.1012

price increase of 1.01% results from an bnrt over ct by 1%

Example 2
original seed S=1
final original price P=50
Corporate Tax CT = 20%
tax increase o= 5% P’ = 50 * (1-20%) / (1-20%-5%) – 1 *5% /(1-20%-5%) P’ = 53.27

This corresponds to a 6.53% sales tax.

Example 3
original seed S=1
final original price P=100
Corporate Tax CT = 20%
tax increase o= 5%
P’ = 106.6

equivalent of 6.6% tax. The doubling of profit from example 2 to example 3 with all else being equal illustrates how the implicit sales tax increase when the Value Added increases with out changing any explicit tax rates.

Example 4
original seed S=1
final original price P=50
Corporate Tax CT = 20%
tax increase o= 6%
P’ = 53.97

The equivalent sales tax rate is 7.945%. An increase of 1 percent in bnrt tax(as compared to example 2 results an equivalent of 1.416% increase in sales tax in this situation.

Equivalent sales tax is 9.40% which is an increase of 2.87% in equivalent sales tax due to an increase of 2% BNRT as compared to example 2.

So an increasing the BNRT automatically increases in price equivalent to sales tax by a %-age larger than the raw BNRT increase.