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A

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Okay welcome to the cannabis data science meetup March 17 2021

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21. Visit Can-Lytics if you want more information and you want to contribute to open source

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research on cannabis analytics. Today, I thought it would be interesting to look at the rates

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of return on capital in the cannabis industry. Last week, we looked at the real wage that

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workers can be expected to be paid. So this week, it would be interesting to look at the

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other input, which is capital. If you look at an article by Poulsen from 2013, it would

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be interesting to look at the current rate of capital. He expects that there are high

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rents from capital because you have a semi-legal market. So the states consider it legal, the

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federal government still considers it illegal, which results in a high rate of capital because

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large banks and investors are often hesitant to lend to cannabis businesses. So when you

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start a business, you may need to take out loans. And then investors also want to get

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rate of return on their loans. So it's interesting to know what the rate of return is in the

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cannabis industry because you may expect it to be high. So we're going to use a similar

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production function as we used last week. However, we're going to use an even simpler

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production function. So first, we're going to take the simplest model and we're just

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going to assume that cannabis sold in a given period, yt, is a function of the number of

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plants, kt. And it's augmented by technology and there's a random element. And so that'll

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be epsilon, or random shop. So of course, the actual production of cannabis is more

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complicated than just cultivating plants and turning that into revenue. However, we're

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going to abstract just to create the simplest model and then you can expand on it to make

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it more realistic. So if you plot these variables against each other, we can start to see some

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positive trends. So if you plot retail revenue against cultivated retail plants, you do see

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the positive trend like we would expect. And there may or may not be diminishing marginal

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returns. What that simply says is you would expect that the more plants you cultivate,

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you're going to get less and less revenue for each additional plant. So as you grow

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more plants, the overall cannabis becomes less valuable. And so the average price per

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output decreases and you're only going to be able to get so much revenue from the additional

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plants cultivated. What's interesting to note is that there seems to be a lot steeper. It

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seems that diminishing marginal returns have taken place in the medical cannabis market.

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So if you just look at the comparison, you can see that there's between 300 and 350,000

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retail plants cultivated. And the timeframe on this is 2014 through 2016. At the same

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period, retail plants went from 50,000 to 450,000. So you see high returns in the beginning

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and as the market matures, like in the medical industry, the medical markets, you get diminishing

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marginal returns. So we're interested in estimating alpha. And we expect that it should be between

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zero and one. So we can take the production function from earlier and we can simply take

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the log of both sides. And then you can estimate it using a linear regression. Once we estimate

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it, the competitive rate of return is equal to the marginal product of capital. So if

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you take the derivative...

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Are you still there Charles?

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Yes. Yeah, you froze up.

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Okay. So I must... Well, that's why we're recording. So anyways, we're back now.

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So where was I when things cut off?

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So let's see, you're taking the log of both sides and you were going to estimate alpha.

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And then it was just right after that.

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Okay. So we take the log of both sides and then we want to calculate the marginal product

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of capital. So capital is KT. Right? So that's our number of plants.

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And so we want to estimate alpha. So if we take the log of both sides, we can run a linear

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regression of the log of sales. Great. So we've got the log of sales and then this is

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going to be a constant.

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So your slides aren't showing now.

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Okay.

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Okay. Yeah.

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Okay. So we're back. Okay. So just to kind of get back into things.

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Okay. So just sort of to do a recap here after sort of that bumpy transition. Okay. So we've

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got the total amount of cannabis sold and that's YT. And that's going to be a function

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of the number of plants, KT. So we've got our production function.

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We take the log of both sides and we get log of cannabis, log of sales equals a constant

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plus alpha log of plants. So we can estimate this with the linear regression. And then

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given alpha, we can find the marginal product of capital.

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So that's the marginal product of capital. And so that's simply the derivative of the

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production function with respect to alpha. And so that would be how productive your capital

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is going to be. And then we're going to subtract off depreciation. And for this simple example,

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we're going to assume zero depreciation. So in reality, there is depreciation. So once

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again, this is the simplest model. And so, and then this is just the simplest way that

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you could estimate the rate of return on capital. And just to go ahead and look at the empirical

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literature so we can go ahead and get our Bayesian prior. We saw in Poulsen's paper

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that the interest rates are typically between 7 and 15%. And so that was from Poulsen's

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research. And so we want to look at data that we have and see if we can estimate a marginal

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product of capital. So let's go ahead and jump into that and do just that. So I'm going

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to share with you the data resources. So here is the Colorado Department of Revenue

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annual updates. And so you also have them quarterly as well. And so for these particular

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updates, they're simply PDF documents with tables of data. So here you have the number

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of stores. You have the occupational license data. You have the number of plants. You have

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retail. This is retail plants. But then you also have flowers sold per month. And then

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you get down here to break down for the different product types. And then you also have total

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sales. So we'll be utilizing that as well. So we're not given the rate of return, but

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we're given just these raw data points. And we're going to figure it out. And for future

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research, it may be worth looking into the testing data here. So it could be worthwhile

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to compare what's going on in the Colorado testing market versus Washington. But these

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are the data sources. So they're a little tricky. You have to sort of essentially copy

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and paste out of these tables. And I've done that here. And I've currently got through

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data through December of 2016. But as you can see, there is data through October of

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2020. So for future exercise, and I'll be adding this to the Cannabis Data Science GitHub

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repository, but we can essentially get the latest data and calculate the rate of return

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up through 2020. However, for this exercise, we'll simply calculate it through 2016, since

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that's the data that I've already compiled. So let's go ahead and just jump right into

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that. I will be using Spyder in Python. Of course, you can use your favorite programming

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language and text editor. However, I find Spyder simple and easy to use. It's not glamorous,

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but easy to use. So to do this, we only need three Python packages. We just need numpy,

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stdc, stdc and stdc. Next, after importing the packages, you can import the data. And

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so I'll just be importing this spreadsheet here, which I'll make available on the GitHub

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repository after the presentation. Once you've read in the data, of course, number one rule,

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look at the data. So you've got some observations or columns. Essentially, we just have date.

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I grabbed the number of licenses for future work. Then we can do number of plants, cultivations

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and revenue. These are variables that will be useful. However, as you saw in the reports,

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there are many more variables that you could grab to do further analysis. So we've read

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in the data. Now, if you go back to our model, we need to calculate the log of sales and

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the log of capital. So we can use numpy, np.log and go ahead and create the log of retail

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revenue and the log of retail plants. And now we can do a simple ordinary least squares

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regression of the log of sales, yt, on a constant, which will be the log of technology, a, in

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addition to the log of capital, which is retail plants. So we can go ahead and fit this model

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in. What's interesting to observe is for such a bare bones model. So we've got 36 observations.

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You do have a decent R squared. So we are explaining a lot of the variation and retail

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plants. It's significant to the 5% level. So like I said, there's this model, it's got

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its flaws, but there does seem to be correlation between the number of plants grown and the

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amount of capital. One should note that obviously, cannabis grown in time t is not sold in time

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t. So it may be more realistic to estimate an autoregressive regression, where you would

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estimate yt sales on kt minus one, kt minus two, perhaps all the way up to kt minus six

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or more. That would simply mean that sales today are dependent on the plants grown six

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months ago, or one month ago, or three months ago. So it would be an interesting analysis

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to add multiple lagged capital variables and see if that has a more significant effect.

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But that's research for the future. So in our regression, if you go back to our presentation,

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you see that we're looking for alpha. So we're looking for the coefficient on log t. And

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so in that case, that's going to be 0.67. So we can go ahead and grab alpha. And now

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that we know alpha, we can now calculate the rate of return on capital, which will be alpha

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times kt to the alpha minus one. And we're assuming depreciation is zero. So we can program

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that in SPDR. So here we have alpha times kt, which is retail plants, to the alpha minus

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one. And I'm multiplying this by 100 because I would like to display r as a percentage.

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And remember, r is the real rate of return of capital. And so let's estimate that, and

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then we'll talk a little about that. Rule number one about data, look at the data. So

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here we have what we have estimated to be the real rate of return of capital in the

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cannabis market in Colorado from 2014 to 2016. So what we're essentially estimating is we're

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saying that an investor would expect a rate of return of 2.6% in 2014 to about 1% in 2016.

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In 2015. And that would be at time t. So that would be their monthly rate of return. So

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they would like to get a 2% to 1% rate of return per month. And then this would be if

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everything was entirely efficient. But as Olson noted, he observed that interest rates

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were typically between 7 and 15%. So this model doesn't take into consideration risk.

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So risk is likely driving these interest rates well above their real rate of return. Like

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last week, we noted that when we added in our uncertainty that we couldn't be quite

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so precise in our estimations. So let's do let's add our confidence intervals. So what

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is our confidence interval? Well, remember earlier, we estimated alpha to be 0.6777.

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Our 95% confidence interval, so we're 95% sure given the data at hand, that alpha given

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the model at hand is between 0.6 about 0.61 and about 0.74. So that's our 95% confidence

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interval. And so we can calculate our upper and lower alpha. But those those are upper

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and lower alpha. So we can calculate our upper and lower interest rates. And we can plot

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them. And so now you see our original estimation with interest rates being roughly 2% and dropping

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to 1%. Then you see our lower estimation with interest rates being close to 1% and then

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dropping quite low to well below 1%. However, our upper bound under confidence interval

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is starting around 6 or 5% and then drops down to a little above 3%. Once again, this

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is a crude estimation, we're using plants to proxy capital, and we're excluding labor.

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So for future work, you can estimate what's called a Cobb-Douglas production function,

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where you augment the production function with labor. So a Cobb-Douglas production function,

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you can estimate the same model and add another regressor. And that's just going to be beta

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log LT. And so that's going to be your labor. And so you can you can estimate a more realistic

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function simply by adding the log of labor to our regression. So I'm going to leave that

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as a future exercise. And I'll go ahead and do the code and post it to the GitHub repository,

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the Candidates Cannabis Data Science repository. So you can check it out there to see the latest

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code after the presentation. So we set out to estimate the rate of return on capital.

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We knew that because the cannabis industry is still gray in terms of legality, that there

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would probably be a high rate of return on capital. However, our model does not factor

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in any sort of legality. Our model is simply a function of cannabis sold and plants. We've

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got cannabis sold and plants. Of course, we also have technology and then a shock to explain

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the random variation. So given this simple model and ignoring the legality, we saw that

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there does appear to be diminishing marginal returns as medical plants increases.

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Next we estimated the production function, which was simply the log of sales on the log

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of capital. For future work, you could add labor. And then we were able to estimate the

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actual rate of return of capital. And so here, based on our research, we can actually estimate

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the mean rate of return between 2014 and 2016 in Colorado. And so we're seeing it's as low

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as 1.2.6%. So just approximation, we'll say 1.25. So the rate of return is, you know,

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the real rate of return could be as low as 1.25% per month. So investors in the long

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term would be satisfied with a rate of return that low for that amount of production. And

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likewise, businesses would be looking at low interest rates for taking out loans for capital

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equipment for their cultivations. What we currently see as far as in 2013 is we saw

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that the, so this is real, right? And then here we have the actual. And so the actual

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rates of return that we observe are between 7 and 15%. So that means risk is explaining

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between, you know, six and, you know, about six and 14% of the rate of return in the cannabis

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industry. Also, I would like to mention that this is a monthly rate of return. And this

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may be an annual rate of return. So it should be, we may want to convert this to APR to

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make a good comparison. However, what you could take away from this is that as cannabis

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becomes more mainstream and as additional states continue to legalize, so that's what

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we've seen since 2016. So from 2016 to the present, 2021, we've seen more states legalize

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cannabis, you know, cannabis production and cannabis markets. So, and it will be interesting

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to do research to see if cannabis laws and regulations have loosened in the states with

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legalized cannabis. Long story short, early on in cannabis markets, we saw high real rates

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of return, I mean, high actual rates of return. However, we estimated the real rate of return

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would be low. So we would predict that over time, cannabis businesses may see their real

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rates of return decrease. So over time, it may become easier and easier for producers,

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cultivators to take out loans, whereas investors are currently making large margins because

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they're taking on a high amount of risk. So you would expect the margins for investors

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will decrease as the risk decreases. And with that, that brings us to the end of the presentation.

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And so I'll go ahead and just cut back to the meeting if you have any questions.

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No, that was a really good presentation.

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Thank you. Yeah. Exactly. So essentially last week, we looked at the labor input. So we

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saw, okay, we estimated the real wage for labor, right? Because essentially, that's

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what economics is, you know, that's a purpose of economics is sort of estimating the prices

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in different markets. So that's actually the labor market. So the wage is the price in

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the labor market. And the rate of return is the price in the capital market. So the wage

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is what you pay for labor. And the rate of return is what you pay for your capital input.

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In this point, in this example, we proxied it with plants. So we're basically assuming,

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okay, for every X amount of plants you grow, you have to invest a certain amount into capital.

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And then when you put together labor and plants, you get output. And so in this case, it's

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going to be cannabis sold. And so we're also abstracting out the retail component. Because,

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of course, the cultivators are producing the raw flour and plant material, some of which

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is then manufactured into manufactured goods and edibles, at which point they're then sold

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to the consumers for the actual revenue. So our model abstracted away a large portion

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of how the industry actually operates. But it's an abstraction. And so there's a lot

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of room for improvement. So I think I'll leave it there. And like I said, I'll make the data

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available. And so we can add data up through 2020. So that way we can see how these estimations

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evolve over time. And we can maybe even compare our predictions to the actuals. So we looked

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at data from 2014 to 2016. And we made some hypotheses. I personally predicted that the

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real rate of return is going to continue to decrease. So now we can look at the data and

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see what happened.

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Okay, yeah, that sounds cool. You know, the other thing I was thinking about was price

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of items sold compared to number of licenses.

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Exactly. So you can gauge sort of how much each company is taking away at the end of

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the day.

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Yeah, it is competition increases, price goes down.

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Exactly. So we may not have the best measure on price. We could proxy it because we have

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essentially we have total revenue in Colorado. Well, we may actually have prices in Washington.

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Actually, this could that could actually be a good analysis for Washington. Because you're

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right, you could I mean, one way to look at it would just be, I guess, like total amount

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of revenue per retailer. And then you could see the market share. In Washington state,

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you can actually calculate the actual market share per retailer. And you can make estimations

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of the market concentration. In fact, have you heard of the Herfindale? It's HHI, the

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Herfindale Hirschman index. And so I may I may present that next week, because it's actually

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one of the simpler measures of market concentration you can do. And it's easy to calculate if

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you have the right data. And in Washington state, we do. So you simply need to know the

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market share per retailer. So market, the retailer, A has shares 0.3, retailer B has

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market shares 0.5. And then you actually do the squared. So it's just the sum of all shares

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squared. So it would be 0.3 squared plus 0.5 squared plus, you know, 99.2 squared. And

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you would see, oh, that's a that's an incredibly concentrated market. Because I forget, I think

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I'll need to do a bit of research and tell you more about it next week, because I forget

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off the top of my head if the lower numbers or higher numbers represent sharper concentration.

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But I want to see higher numbers represent larger, because I feel like the if it's close

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to one. But anyways, I may touch on that next week, because that's something that I've been

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wanting to look at. And you and it seems they that's your idea as well is, it would be interesting

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to look at the concentration in the cannabis markets over time to see if it's becoming

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more competitive or more concentrated. Yeah, and we can do it statistically and we can

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plot it over time. So that way we could even see month by month, the competitiveness and

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it's interesting research, because you could start to find trends and you can maybe find

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if if any actions. So if you notice any point in time where there was a big change in the

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competitiveness, you may be able to pinpoint the piece of legislation or something that

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happened that changed the competitiveness of the market. Yeah, yeah. So I think, of course,

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I don't think we have time today. But I think for next week, let's look let's look at just

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that because that that's the simplest. That's the simplest measure that I can think of to

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look at market concentration. In Washington State, we do have the data. It's in that giant

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sales data dump. So it's possible. And it's going to be a good excuse to look at the data.

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So that's our philosophy here, correct is look at the data. So I think we've got a good

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project for next week. Great. All right, Charles, I think I may just go ahead and wrap up a

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little early today. Unless you have anything you want to talk about. Yeah, okay. Well,

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I think for today, let's just go ahead and wrap up 10 minutes early. I sort of went through

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the presentation quickly. I didn't anticipate moving through it so quickly. So I could have

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added a bit more detail. And so like I said, I'll add a bit more detail to the actual GitHub

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repository. Just a little technical error. Didn't get it committed before the presentation,

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but I'll commit it right after. And then, yeah, and then we'll look at market concentration

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next week. And, you know, let me know if you have any questions about this economics. Okay.

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Cool. Awesome, Charles. And everyone. So thank you for listening in. And I'll see you this

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time next week. See you. Bye. Bye, Charles.

