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# System prepended metadata

title: Untitled

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Again, the system works from t0 to t1:

Reward paid out to juicers in total: R
- R_1:Reward if sale does not happen
- R_2:Reward if sale happens

Returns made by juicers: r
- r_a:return by juicer A
- r_b:return by juicer B

% of JUICE owned: S
- S_A1: Share of JUICE owned by Juicer A if sale does not happen (100%)
- S_A2: Share of JUICE owned by Juicer A if sale happens
- S_B2: Share of JUICE owned by Juicer B if sale happens
- S_A2+S_B2 = 100%

Price: p

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Juicer A increases value (rewards & returns on token investments) at t1 IF:

$S_{A_1}*R_{1} < S_{A_2} * R_{2} + p * (1+r_A)$ || $S_{A_1}=1$

$p >{R_{1} - S_{A_2} * R_{2}  \over 1+r_A}$

Juicer B increases value (rewards & returns on token investments) at t1 IF: 

$p * (1+r_B) < S_{B_2} * R_{2}$

$p < {S_{B_2} * R_{2} \over 1+r_B}$

Market exchange can happen if we find a price that satisfies: 

${R_{1} - S_{A_2} * R_{2}  \over 1+r_A} < p < {S_{B_2} * R_{2} \over 1+r_B}$

${R_{1} - S_{A_2} * R_{2}  \over 1+r_A} < {S_{B_2} * R_{2} \over 1+r_B}$

$R_{1} - S_{A_2} * R_{2} < S_{B_2} * R_{2} * {1+r_A \over 1+r_B}$ || $/R_{2}$

${R_{1} \over R_2} - S_{A_2} < S_{B_2}* {1+r_A \over 1+r_B}$ || ${1 \over 1+g} = {R_{1} \over R_2}$, $S_{A_2} = 1-S_{B_2}$

$g > {1 \over 1-S_{B_2}*(1-{1+r_A \over 1+r_B})}-1$



