Can Colorado Meet Its Marijuana Revenue Expectations?

Retail sales of recreational marijuana in Colorado for January came in at $14 million.  That seems light.  Colorado tax officials say those numbers are in line with expectations.  But official projections call for increasing sales over time, building from an average rate of $32 million per month from January to June 2014 ($194 million for the six months) to a rate of $51 million per month from July 2014 to June 2015 ($613 million for the fiscal year).  

Those six- or 12-month projections aren’t granular enough to reveal monthly growth -– sales won’t stay flat for six months and then suddenly jump to a new plateau for the next 12.  So I asked my friend Steve Schecter, a mathematician, how to smooth then out.  (I thought there was an excel program to do that).

His answer, with work shown below, is that recently estimated January revenue, based just on regranularizing (which is not a word, I know) the data, would figure out to some $28 million -– twice the actual amount reported, and that monthly growth would be around 5 percent.

Can monthly sales jump up from that January level?  Maybe so.  Sales growth should happen because more stores will open.  “[O]nly 24 cannabis businesses were open on January 1, and 59 by January 31. The number has now [March 11] risen to 167 and will expand further.” – That’s from The Telegraph.  New licenses are being issued.  And sellers who sold in January will gear up and make more supply as pot production builds momentum.

But new stores need customers, and new (post-January) buyers of recreational marijuana could plausibly come from three categories:  (1) switchers from the medical market to the recreational market, (2) switchers from the black market to the legal market, and (3) former non-consumers.  OK, that’s simplistic, because it’s sales dollars -– purchases — that matter, not buyers.  January buyers could spend more dollars in later months than they did in January.  That is, existing (January) customers in any of those three categories could buy more and push up sales numbers.

Medical cardholders have no discernable incentive to switch to the recreational market.  Medical marijuana is tax free, and qualifying as a medical user is inexpensive.

Black market buyers could move to the legal market for two reasons:  convenience, or lower prices.  More stores will indeed offer more convenience, and could add substantially to legal sales.  Lower prices in the legal market could also result in greater quantities of marijuana being sold.  Legal prices can sink while black market stay firm:  the legal market doesn’t have to bear the economic burden of sneaking around, so it doesn’t have to pay the “risk premium” that drives prices for dried plant material into the three-digit dollars per ounce range.  But there’s a problem:  If lower prices lure consumers to the legal market, tax collections suffer:  Colorado taxes at 10 percent of retail price and nominally at 15 percent of the wholesale price.  That percentage-of-price tax base means lower legal prices produce lower tax revenues.  Colorado could simultaneously hit the sales target and miss the tax target.

Whatever revenue comes from sales to former non-consumers is problematic for legalizers:  Getting tax revenue from new pot smokers — turning non-consumers into consumers – would turn up as a selling point in the minds of only the most ardent fans of marijuana.  Few others would see new consumers and the revenue they bring as totally positive.  Even some supporters of legalization would say, “Let the revenue go” in that case.

[UPDATE:  See more recent posts on Colorado revenue on this blog.]


Here’s the math — from a real mathemetician:

Hi, Pat, this is a fun problem!

Let’s assume receipts are ‘a’ the first month and go up by a factor ‘r’ each month.  For example, if receipts go up 5% every month, then r=1.05.
Receipts the first month = a
Recepts the second month = a times 1.05
Receipts the third month = a times (1.05)^2
Total receipts for n months are then
S_n = a + ar + ar^2 + … + ar^{n-1} = a(r^n – 1)/(r-1).  This is the formula for the sum of a finite geometric series, see the wikipedia article on geometric series.
According to your information,
S_6 = 32,327,011.49 times 6.
S_18 = (32,327,011.49 times 6) + (51,065,497.13 times 12).
So you have two equations in the two unknowns ‘a’ and ‘r’.
I don’t know how to solve this system by hand, so I asked a computer algebra program, Maple, to do it.  See the attachment.  Maple found many solutions, most of them involving I = square root of -1.  The only real solution is
a = 28,456,622.65 (first month’s revenue), r=1.050825724 (revenue increases 5.08% per month).
The attached program, Deciphering the first 18 months, finds this answer and checks that it works.  The last line about unassigning the variables is just there so I could rerun the program.   [UPDATE:  Here is a solution from Dr.  Schecter without using that computer algebra program: pat’s_problem 2.]
Of course, there is no guarantee that the Coloradans assumed the same percentage increase in revenue every month, but if they did, it was 5.08%.

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