14 Interactive: money creation

Pick the required reserve ratio and the OMO size. Watch the geometric series of new deposits.

viewof rrr = Inputs.range([0.05, 0.50], {value: 0.20, step: 0.01, label: "Required reserve ratio"})
viewof omo = Inputs.range([10, 1000], {value: 100, step: 10, label: "OMO purchase ($)"})

Ks = 1 / rrr
deltaMs = Ks * omo
newMoney = deltaMs - omo

md`### Live results

  - **Money multiplier:** \`K_S = 1 / ${rrr.toFixed(2)} = ${Ks.toFixed(2)}\`
  - **Total change in money supply:** \`ΔM^S = ${Ks.toFixed(2)} × \$${omo} = \$${deltaMs.toFixed(2)}\`
  - **New money created** (above the original injection): \`\$${newMoney.toFixed(2)}\`
`

rounds = {
  let rs = []
  let dep = omo
  let total = 0
  for (let i = 0; i < 12; i++) {
    let rr_amount = dep * rrr
    let er_amount = dep - rr_amount
    total += dep
    rs.push({
      round: i + 1,
      deposit_received: dep,
      kept_as_RR: rr_amount,
      lent_out: er_amount,
      cumulative_deposits: total
    })
    dep = er_amount
  }
  return rs
}

Inputs.table(rounds, {
  format: {
    deposit_received: x => "$" + x.toFixed(2),
    kept_as_RR: x => "$" + x.toFixed(2),
    lent_out: x => "$" + x.toFixed(2),
    cumulative_deposits: x => "$" + x.toFixed(2)
  },
  width: {round: 60, deposit_received: 130, kept_as_RR: 130, lent_out: 130, cumulative_deposits: 160}
})

Plot.plot({
  width: 600,
  height: 320,
  marginLeft: 70,
  marginBottom: 50,
  x: {label: "Round", type: "linear", domain: [0.5, 12.5]},
  y: {label: "Cumulative deposits ($)", domain: [0, deltaMs * 1.05]},
  marks: [
    Plot.ruleY([deltaMs], {stroke: "#b7410e", strokeDasharray: "4 3"}),
    Plot.text([{x: 6, y: deltaMs * 1.02, l: `Geometric sum → $${deltaMs.toFixed(0)}`}], {x: "x", y: "y", text: "l", fill: "#b7410e", fontSize: 11}),
    Plot.barY(rounds, {x: "round", y: "cumulative_deposits", fill: "#0e7c7b", fillOpacity: 0.25}),
    Plot.line(rounds, {x: "round", y: "cumulative_deposits", stroke: "#0e7c7b", strokeWidth: 2.2}),
    Plot.dot(rounds, {x: "round", y: "cumulative_deposits", fill: "#0e7c7b", r: 4})
  ]
})

14.1 What to play with

Set rrr = 0.10, OMO = $100. K_S = 10, \Delta M^S = \$1{,}000. New money = $900. The lower the reserve requirement, the more banks can lend, the bigger the multiplier.
Set rrr = 0.50. K_S = 2, \Delta M^S = 2 \times \$100 = \$200. New money = $100. High reserve requirements throttle money creation.
Watch how fast convergence happens. By round 6 you’re typically within 95% of the geometric sum. After round 12 you’re at >99%. The series converges quickly when rrr is high (each round shrinks fast); slowly when rrr is low.

14.2 What this tool hides

It assumes (1) banks lend until ER = 0, and (2) all loaned money returns as deposits (no cash leakage). Real-world money multipliers are smaller. With cash-leakage ratio cr:

K_S^{\text{real}} = \frac{1 + cr}{rrr + cr}

For rrr = 0.20 and cr = 0.10: K_S^{\text{real}} = 1.10 / 0.30 \approx 3.67, well below the textbook 5.