$25B total

$21B in 2018

for comparison: total size of

• Toronto Stock Exchange: $2,200B

• Toronto Venture Exchange: $41B

Is there economic merit to tokens?

Do tokens solve an economic problem?

\(x_i\)

\(x_j\)

\(x_k\)

\(c\)

\(MR=x-2q\)

\(q^m=(x-c)/2\)

\(q^m=q^e\)

general idea: sell future output

two approaches for token sales

• sell a fraction of future revenue
• we call it revenue sharing
• formally: sell \(\alpha_t\) of \(T\) tokens
• produce \(q\) units a require \(T/q\) tokens per unit

• sell units of future output
• we call this output presale
• formally: sell \(t\) tokens
• produce \(q\) units and keep revenue from \(q-t\) tokens

\(q^{rs}<q^m\)

• Solution \[q^{rs}=\frac{x-c/(1-\alpha_t)}{2}<q^m.\]
• Under-production!

\(\alpha_t MR\)

\(q^{ps}>q^m\)

• Solution \[q^{rs}=\frac{x-c+t}{2}>q^m.\]
• The problem: over-production!
• Intuition: entrepreneur does not internalize that extra output unit affects revenue for tokenholders!

\(MR+t\)

• revenue sharing: underproduction
• output presale: overproduction

\(q^t=q^m\)

• "does not internalize" = externality
• address externality: TAX!
• here: tax future token income
• incremental token income gets shared

\(\alpha_tMR+t\)

• obvious answer: combine the two!

• issue \(t\) tokens ex ante
• share \(\alpha_t\) of new tokens
• Entrepreneuer solves \[\max_q (1-\alpha_t) (q-t)(x-q) - cq\] solution \[q^t=(x+t-c/(1-\alpha_t))/2\]
• token share \[\alpha_t=\frac{t}{c+t}\]

Token financing is NOT inferior!

Presell \(t\) tokens.

If quantity produced \(q>t\), then share \(\alpha_t\) of revenue from incremental \(q-t\) tokens with tokenholders

As with equity, the entrepreneur receives the full NPV.

The entrepreneuer produces optimally at \(q^t=q^m\)

If \(q<t\)  \(\Rightarrow\) redeem at rate \(t/q\) and tokenholders receive refund of \(c(t-q)\).

• costs her \(0\)
• \(\theta\sim U(0,\theta_l)\)
• \(\theta_l<\theta_h\)

• costs her \(C_e\)
• \(\theta\sim U(0,\theta_h)\)

• common topic in corporate finance
• very relevant in "decentralized" world where developers are scattered around the globe
• also applicable to, e.g. established firms that do something new

assume \[\textit{NPV}(\theta_h)>0>\textit{NPV}(\theta_l)\]

possibly break even

cannot break even

entrepreneur

earns \((1-\alpha_e)\ \frac{(\theta_h-c)^3}{12\theta_h} -C_e \)

earns \((1-\alpha_e) \frac{(\theta_l-c)^3}{12\theta_l}\)

\(>\) ?

exert effort iff

\[\textit{NPV}_h-C_e\ge \textit{NPV}_h\times\frac{\theta_h}{\theta_l}\left(\frac{\theta_l-c}{\theta_h-c}\right)^3\]

token holders

possibly break even

cannot break even

entrepreneur

earns \(\frac{c}{c+t} \frac{2}{3\theta_h}\left(\frac{\theta_h-c}{2}-t \right)^3 -C_e \)

earns \(\frac{c}{c+t} \frac{2}{3\theta_l}\left(\frac{\theta_l-c}{2}-t \right)^3\)

\(>\) ?

exert effort iff

\[\textit{NPV}_h-C_e\ge \textit{NPV}_h\times\frac{\theta_h}{\theta_l}\left(\frac{\theta_l-c-2t}{\theta_h-c-2t}\right)^3\]

• With moral hazard,
  • all projects that can be financed by equity can be financed by the optimal token contract but
  • some projects that can be financed by optimal tokens contracts cannot be financed by equity.

key math insight

\[\textit{NPV}_h\times\frac{\theta_h}{\theta_l}\left(\frac{\theta_l-c}{\theta_h-c}\right)^3 >\textit{NPV}_h\times\frac{\theta_h}{\theta_l}\left(\frac{\theta_l-c-2t}{\theta_h-c-2t}\right)^3\]

• Simple model of ICO vs equity financing from the standard corporate finance toolbox

• Theorem 1: Without frictions,
  • an optimal token contract finances the same projects as equity
  • the entrepreneur earns the same rents under the optimal token contract

• Theorem 2: With entrepreneurial moral hazard,
  • any equity-financeable project can be financed by an optimal token
  • some token-financeable projects cannot be financed by equity

• ​\(\Rightarrow\) There is economic and conceptual merit to token financing

Key: you cannot collect money from just anybody!