# The effect of California’s proposed VAT/BNRT 3

Instead of talking about the stability of the BNRT in the long run, let’s talk about the effect of sudden introduction of BNRT
Same examples as previous post. Recall that farmer buys fruit seed at price S. Plants the seed (adds value to it) and sells the fruit at price G. A canned fruit company buys the fruits, cans them, and sells at price C to distribution, distributor sells to Retailer for price D, and retailer finally sells the product to consumer at price P. We have established last time that the BNRT will be set to be higher than the current corporate tax to cover the elimination of the sales tax. For simplicity sake, let’s call bnrt = CT + o; The farmer’s previous profit was (G-S) * (1-CT) but is now (G-S) * (1-bnrt) the income is now less, so to make up for the difference, he charges for a price G’ such that (G’ – S) * (1-bnrt) = (G-S)*(1-CT) solve for G’

G’ = (G-S) * (1-CT) / (1 – bnrt) + S

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

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’

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

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.

Example 5
original seed S=1
final original price P=50
Corporate Tax CT = 20%
tax increase o= 7%
P’ = 54.70

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.