# 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.

# The effect of California’s proposed VAT/BNRT 2

We’re still not necessarily convinced that things will remain great. Let’s use a more concrete example: 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 should also define some taxes: bnrt is the rate of BNRT, CT is the corporate income tax, ST is sales tax.

current case:
Farmer: pay S, get G, pays tax (G-S)*CT
Canner: pay G, get C, pays tax (C-G)*CT
Distributor: pays C, gets D, pays tax(D-C)*CT
Retailer: pays D, gets P, pays (P-D)*CT
Consumer: pay P, pays tax: (P)*ST

total tax received: (P-S)*CT + P*ST

BNRT case:
Farmer: pay S, get G, pays tax (G-S)*bnrt
Canner: pay G, get C, pays tax (C-G)*bnrt
Distributor: pays C, gets D, pays tax(D-C)*bnrt
Retailer: pays D, gets P, pays (P-D)*bnrt
Consumer: pay P, pays tax: 0
total tax paid: (P-S)*bnrt

if the government wants to keep income the same how much should he set the bnrt?

(P-S)*bnrt = (P-S)*CT + P*ST
bnrt = CT + ST * P / (P-S)
bnrt = CT + ST / ((P-S) / P)

bnrt is to be set as approximately the current corporate tax plus sales tax divided by the gross profit margin of all business processes in the state.

Next time, we should analyse the claimed stability of BNRT resistant to fluctuations in business cycles.

# The effect of California’s proposed VAT/BNRT

What is the effect of eliminating sales tax, lowering income tax and establishing BNRT?

The sales tax is lowered to 1/5 of previous, sales tax of nearly 9% or 10% is completely gone, but a tax is added to transactions. The only deductions are house, charitable, and…

For a business, the Business Net Receipt Tax is a percentage of

OUT=\$ listed on receipts I receive while doing business (after paying \$)
IN=\$ listed on receipts I issue while receiving \$ in the process of doing business.

So BNRT a business has to pay is Tax_Percentage * (IN – OUT)

Cool, eh?

Not having income tax and lower sales tax means the money made in California will tend to stay in California (because tax is lower, so it’s not worth it to take the high income and spend it out of state where tax is higher)

One reaction people will have is this: Wouldn’t businesses tend to become more vertically integrated. If the making of a product requires either two companies or three companies, which one would I prefer?

bnrt = bnrt tax rate
r=original raw cost
p=market price for the final product

2 company case:
p1 is the price the intermediate product sells for
p2=p is the price of the final product.
total tax paid is: (p1-r)*bnrt + (p-p1)*bnrt + 0 sales tax
do the math, and the total tax paid is (p-r)*bnrt

3 company case:
p1 is the price the intermediate product sells for
p2 is the price of the intermediate product between p1 and final result
p3=p is the final sales price
the total tax paid is: (p1-r)*bnrt + (p2-p1)*bnrt + (p-p2)*bnrt + 0 sales tax
do the math, and the total tax paid is (p-r)*bnrt

same!! they’re the same!! (to the government, if the sales price remain the same as a result) Since the original costs are the same, and the the cost of final product are the same, the total money made by private sector is

p-r-(p-r)*bnrt = (p-r) * (1-bnrt) is the same for both case. So the tax doesn’t fundamentally affect the cost of doing business, more or less, the money made is the same.

tomorrow, we will check if the final price will remain the same…