# A simple analysis of token value — Part 2

The goal of this series is to understand where the value of a token comes from, in order to design effectively a token economy on a blockchain. Following up on the previous post, we are now looking at a utility blockchain and introducing a model for a utility token having all the properties of the tokens described previously. We comment on its properties and advantages, and we generalize further by removing some assumptions. Series written in collaboration with Veltys. Special thanks to Martin Worner, Klara Sok and Pierre Laurent for their numerous comments.

### Reminder from Part 1

In the part 1 of this series, we looked at the different sources of value for a token: the store of value, the settlement and the right for reward. We derived a couple of formal equations connecting the important quantities. If the previous post is still fresh in your mind, you can skip this part. The quantities are:

• The velocity (v) is the number of economic cycles per unit of time for a settlement token. It has a direct influence on the price of the settlement token.
• The turnoverº is the total amount of EUR collected by the gatekeeper per unit of time.
• The token supply () is the total number of tokens used for settlement.
• We call l the fraction of the settlement tokens supply which are “lost” or not circulating. The circulating supplyº of settlement tokens is equal to (1-l)Tº.
• The price (π) of the token is the amount of money in EUR you need to buy a token at the cashier.
• The market capº is the total value in EUR of all the tokens used for settlement. The market capº is equal to πTº and the circulating market capº is the value of the circulating supplyº, which is π(1-l)Tº.
• The token supplyª () is the total number of tokens giving right for reward.
• The risk-free interest rate ( r ) is the interest rate per unit of time available to lend and borrow without risk. It has a direct influence on the price of the security token.
• The turnoverª is the total value in EUR to be distributed as reward per unit of time.
• The market capª is the value in EUR of all the tokens giving right for reward. The market capª is equal to πTª.

We now recall the two main equations from part 1:

• For the settlement token, we have the Settlement Token Equation

circulating market capº = πTº(1-l) = turnoverº/v

• For the token giving right for reward, we have the Security Token Equation

market capª = πTª = (turnoverª-nc)/r

### The Utility Blockchain and a few practical considerations on market caps

We are now looking at a utility blockchain. A utility blockchain provides a service. The total value of the service per unit of time is the turnover of the blockchain and it is settled in settlement tokens. The cashier of the previous example is the crypto-exchange, and the gatekeepers are the validators operating the chain. At the same time, this turnover is distributed in settlement tokens to the the agents owning the rights to this reward thanks to the security tokens.

In a utility blockchain, the turnoverº of the service is integrally distributed as reward, and the turnover of the blockchain is

turnover = turnoverº = turnoverª

The blockchain can operate with both token types, however, there are a few practical considerations about the absolute values of the market caps:

• For a blockchain, v can potentially have a very high value. If for example people clear their rewards weekly, v is in the order of 52 per year. This creates a settlement token market capº much smaller than the annual turnoverº. If v is 52 per year, then the market capº is equal to turnoverº/52. It means that the turnoverº needs to increase by 52 EUR for the market capº to increase by 1 EUR. In practice, for a well functioning blockchain, v can be expected to be much higher than 52.
• A low circulating market capº for circulating token might be a problem if the circulation is controlled by malicious traders: a low market capº means that a malicious actor could easily buy a large part of it and manipulate the price as described in the previous part of this series. In the crypto world, we can observe the “pump and dump” situations which are as likely as the market capº is small.
• A low circulating market capº in the context of a utility blockchain is also a problem as it potentially impacts the ease of access to the tokens, interfering with the access to the service of the chain and deteriorating the perceived value of the service.

When considering tokens that are pre-sold to fund the development of the service, typically through an ICO or a Token Sale, a low expected market capº is an issue. We call initial market capº the market cap at issuance. If the operating market capº is higher than the initial market capº using reasonable turnoverº expectation, then the pre-sale offer is attractive.

Indeed, for contributors to be willing to participate, considering a fixed token supply, they need to expect that the operating market capº of the settlement tokens will be higher than the initial market capº into which they bought. In this case, they will make a profit. For a settlement token, we define the implicit breakeven turnoverº for contributors as

breakeven turnoverº = initial market capº * v

We see that for v with a high value like 52, the contributors needs to expect a turnoverº several times higher than the initial market capº to break even.

The situation is opposite with the security token market capª. The breakeven turnoverª is much smaller than the initial market capª due to the small value of the rate of return r:

breakeven turnoverª = initial market capª * r + nc

Given a running cost nc, we see that for r with a low value like 5%, the contributors needs only to expect a turnoverª several times smaller than the initial market capª to break even.

This lower breakeven turnoverª may be easier to expect than the breakeven turnoverº. For a given initial market cap, it makes the tokens pre-sale more attractive.

### The Token of a Utility Blockchain: the Utility Token

A utility blockchain has a distinct purpose, namely to provide a service and distribute rewards. It may function with just a settlement token, or with two separate settlement and security tokens, or with one token covering both functions. In the case of just a settlement token, the distribution of the reward (if any) is done following a predefined rule. In the case of two separate tokens, the analysis from the first part of this series has covered the tokens’ values. We focus here on a token covering both functions.

The total supply of this token is T = Tª = Tº and the market cap is πT.

We introduce s as the proportion of the total token supply T held so that it has a right to receive rewards (s for security). These tokens are not circulating and are giving right to reward. The supply of tokens giving right to reward is sT.

We define l more precisely as the proportion of the total supply which is not circulating and not giving right to reward. The total proportion of not circulating token is s+l and the circulating supply is (1-s-l)T tokens.

Adapting the settlement and security token equations from the previous parts, we then have the Utility Token Equations:

πT(1-s-l) = turnover/v = circulating market capº

and

πsT = (turnover-nc)/r = market capª

By adding these 2 equations, we get:

πT(1-l) = turnover (1/v + 1/r) -nc/r

which is

market cap = πT = (circulating market capº + market capª)/(1-l)

and this gives

π = [ turnover (1/v + 1/r) -nc/r ] /T(1-l)

or

π = (circulating market capº + market capª)/T(1-l)

and it follows

s = (1-l) market capª /(circulating market capº + market capª)

It is interesting to see that the lost and held tokens exacerbate the market cap due to the higher demand for the reward side of the utility token since a fraction l of tokens is not used to receive reward in addition to not be used to pay for the service. Since 0≤l≤1 and 1/(1-l) ≥1, the market cap of the utility token is greater than the sum of the market caps of the settlement token and the security token.

market cap ≥ market capº + market capª

We see that this utility token used for settlement and reward gives sufficient availability of circulating tokens for settlement while supporting at the same time a stronger market cap from the demand on the reward side.

The demand for the utility token comes from demand for settlement and demand for right for reward. The difference in demand between the settlement and reward sides comes from the difference in order of magnitude in the practical values of the velocity v and the interest rate r. While v might be in the order of 100 per year, r is in the order of 1% per year. For a given annual turnover, the demand for the settlement token is about turnover / 100 while the demand for the reward token is about turnover x100, which is a difference in the order of 10,000: we can expect the market cap of the utility token to be mostly coming from the market capª of the corresponding security token:

market cap ~ market capª / (1-l)

Until now, we have considered the case where the utility tokens are only used for the service provided within the utility blockchain. This is why the turnover is the same for the settlement and security token equations.

However, the utility token may very well be used as a means of payment outside of the utility blockchain. In this case, the market cap equality still holds and the market capº from settlement value keeps increasing. The price and s ratio equations are adjusted to reference the total settlement turnoverº and the turnoverª to be distributed as reward:

π = (turnoverº/v + (turnoverª-nc)/r)/T(1-l)

and

s = (1-l) / (1 + r*turnoverº/v(turnoverª-nc))

When this utility token is eventually widely accepted as a means of payment (without giving right for more reward), its market cap will derive mostly from its demand for settlement, and we will get

market cap ~ market capº

### The turnover, the governance and the design of the blockchain’s service

As we have seen, the turnover of the utility blockchain is the key driver of value for the utility token in this model. This leads to a classical question of turnover maximization and cost minimization. The turnover of the utility blockchain comes from all the fees paid for the services provided by the utility blockchain.

turnover = sum over all services of ( quantity of service offered x unit price for the service )

In this case, the objective translates into defining services and their prices and quantities of the utility blockchain that maximize the long term turnover and designing the system attract participant through incentives and low barriers and costs to entry.

It introduces the question about who can design these services’ definitions, prices and incentives. The persons, entities and algorithms who can decide about these topics forms the Governance of the blockchain.

Let us go back to the carousel exemples from the previous post. The questions about the pricing of the service and the role of governance can be illustrated as follows:

The Very Convenient Supermarket has a promotion and has a campaign to offer tokens for a free ride on the carousel to encourage people into the shop leading up to carnival time. People are very excited by the thought of a ride on the carousel and they flock to the Very Convenient Supermarket to claim their free tokens.

The day the carousels arrive and open up for business and the people are queuing around the market place.

To meet the demand the cashiers have to put up a sign “No cash rides today, only pre-sold tokens” to keep their customers who have been patiently waiting happy. The carousels work at 100% capacity for three days. There are still people without tokens who want a ride on the carousel and the operators decide to stay for two more days to meet demand. What do they do about the price? Do they offer a premium ride where you can book a slot at a higher price? Do they put up the price to manage demand?

Conversely the carousel operators arrive in town to the worst weather experienced in April for 100 years, it is cold, raining hard and people stay at home. They are struggling to fill the rides, what do they do? Offer 2 rides for the price of 1?

These are examples of dynamic price management for the carousel in order to maximize the turnover over a specific period of time. By asking for more tokens for each ride during high demand, the carousel might still run a maximum capacity while collecting more tokens and therefore increasing turnover. By reducing the ride price during low demand, there might be more people joining in, and if the increase in number of customers is greater than the lowering in price, then the turnover will increase and it is a wise decision from the governance.

Both these scenarios do have an impact on the price of the token, because the price management of the service has an impact on the turnover, which in turn has an impact on the token price.

For a constructive analysis, it is important to have the concepts of token price (in EUR) and service price (in EUR) clearly identified. They can easily be confused because the service price is expressed in token, but this is only to facilitate settlement. The “real” price of the service in seen ultimately by the customer as a price in EUR and “ideally” a settlement token price is stable between the time the token is purchased and the time it is used for the service.

Side note on the EUR: We have been talking here about prices in EUR. Implicitly, we are saying that we are in the Eurozone, that the carousel’s customers make their living in EUR and look at their costs in EUR. For them, Euro is the numeraire. The numeraire is the asset against which one evaluates the value of all other assets. Without loss of generality, in all the arguments in these posts we can replace EUR by any other numeraire (other fiat currency, crypto currency or asset). For practical reason, one should pick their “natural” numeraire of their daily life.

### Beyond a single utility for the token

So far we have been looking at the turnover of the blockchain. As seen in the market cap analysis, the utility token market cap (and price) benefits from wider adoption beyond its original “hosting” blockchain. It can be illustrated as follows:

The Very Convenient Supermarket realises that the carousel is very popular and there is a large crowd waiting in line with their tokens. The supermarket decides to accept these tokens as a settlement for any shopping in the supermarket.

Suddenly, the settlement turnoverº of the token is not limited by the carousel turnover and will also include a part/all of the turnoverº of the Supermarket. Each additional acceptance of the token for settlement can have a significant impact on the settlement turnoverº and eventually on the token price.

It is worth noting that the treasurer of the Supermarket might not go back to the token cashier every day to get their EUR as the gatekeepers do. The Supermarket treasurer might only go once a month. This will have an impact on the average velocity of the settlement token and therefore an impact on the token price from that effect. The settlement token equation can be extended to account for multiple services turnovers and velocities.

As a side note: a blockchain charging a transaction fee for sending tokens can be seen as a utility blockchain whose service is the transfer of tokens, and an increase in settlement turnoverº leads to an increase in reward (fees) turnoverª.

### Reality check: the assumptions of this simple analysis

We have assumed in this simple model that the blockchain is in equilibrium: all parameters are known and constant from one unit of time to the next. This allowed us to look at the relationships between the various quantities and understand the effect that one may have on the other. It was helpful for this simple analysis and we could derive interesting results on velocity and market cap.

However, in reality we are actually making two important simplifying assumptions which we need to be aware when looking at real cases:

• parameters are constant from one unit of time to the next: in reality, all the variables can vary over time. If we want to develop the analysis in this direction, we will need to use time dependent quantities and discounted values of future economic quantities. We need to introduce the subscript _t to refer to the value of the parameters at the period t and we are reaching the limits of the readability on this blog post. We leave the calculation to the curious reader.
• parameters are known: In reality the parameters are stochastic and deterministic variables of these models are in fact random variables. The price and market cap become the results of expectations under an appropriate measure in the previous formulas. This will lead to different valuations of market cap, token price and optimal s ratio by different persons and the observable quantities will be the result of the market equilibrium between the different token holders. This is beyond the scope of this post.

### Conclusion

Through this simple model, we see that in a utility blockchain economy at equilibrium there are structural relationships between the turnover generated by the service, the costs (nc) to operate the service, the amount of tokens held for reward (sT), the velocity (v)of the circulating tokens (T(1-s-l)), the available interest rate (r)and the token price (π).

This simple analysis helps to understand where the value of a token comes from. We understand now that the turnover is the key driver to a token value, either from the demand for settlement of this turnover or from the demand for right to receive this turnover. We see that the target of the governance of a utility blockchain is to develop the blockchain turnover through adoption and service design, which will reflect in its token price. We also see that the token value benefits from a wider adoption beyond its own utility blockchain, to be used for settlement of other services and giving right to other rewards.

However, we have left untouched the topic of how to distribute the reward between token holders. It can be implicitly understood that each token gives right to an equal share of the reward. It needs not be, and this opens another field of study to create a good incentive model for the utility blockchain participants through reward design. This will be the topic of the following post.

Disclaimer: This simple model is for theoretical thought experiment only, it does not pretend to be an accurate method to estimate utility blockchain quantities and should not be used as such. Please do your own analysis before estimating quantities of a utility blockchain, such as expected turnover and token prices.