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Week 4 · Lecture outline

Week 4 — Lecture Outline · Economic Growth & Productivity

Principles of Macroeconomics · ECON 2 Fall 2026 · Prof. Ashford Fictional sample

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 4 — growth rates, the rule of 70, per-capita growth, sources of growth · SLO A & B
Meeting pattern: two 75-min sessions (≈150 min). Segment minutes below total ~150 — scale to your room.

The deck (E), the tutorial (C), and the workshop (P) all teach from this outline. Every number here is pre-computed and independently verified (see the verified box in §4).

Week at a glance
Big question Why do tiny differences in a growth rate compound into enormous differences in living standards — and where does growth actually come from?
By week's end students can (1) compute a growth rate from two GDP figures using percentage change; (2) apply the rule of 70 (divide, don't multiply) to estimate doubling time; (3) compute a rough per-capita growth rate (GDP growth − population growth) and explain why it matters; (4) name the three sources of long-run growth and the Solow model as the field's organizing framework (named, not derived).
Key vocabulary economic growth, growth rate, percentage change, the rule of 70, doubling time, compounding, per-capita GDP, physical capital, human capital, technology, productivity, the Solow growth model
Materials whiteboard; calculator; the Week-4 readings/links; a spreadsheet or Desmos for the compounding table; an approved chatbot
Timing note 8 segments ≈ 150 min across two sessions. Trim Segment 7 (interaction) if short on time.

Segment 1 — HOOK: "Would you rather grow at 2% or 7%?" (10 min)

Open with the question cold: "Two countries start at the exact same GDP. One grows 2% a year, the other 7% a year. After 10 years, is Country B just 'a little' ahead, or a LOT ahead?" Take guesses — most students underestimate badly. Promise: by the end of today you'll be able to answer that question with one division problem, and the answer will surprise you.

Frame the week: the last two weeks measured the economy's snapshot — its size (GDP) and its vital signs (inflation, unemployment) right now. This week we switch to the time-lapse camera: how fast is the economy's productive capacity growing, and why does that number, more than almost anything else in this course, determine whether a country is rich or poor a generation from now?

Segment 2 — PLAIN-LANGUAGE IDEA: growth rates are just percentage change, again (15 min)

Reassure the room first: you already know this formula. It's the same percentage-change tool from Weeks 2–3 (inflation, unemployment), now aimed at GDP over time.

Economic growth rate = (GDP this period − GDP last period) ÷ GDP last period × 100.

Name what's new this week, not the math: growth is a flow measured over time — it tells you how fast the economy's engine is running, not how big the economy is right now (that's the level, Week 2's job). A $20-trillion economy growing 1% and a $2-trillion economy growing 5% are very different stories, and neither the level nor the rate alone tells you everything.

Memory hook: "Level answers 'how big?' Growth rate answers 'how fast is it getting bigger?' Never confuse the two."

Segment 3 — WORKED EXAMPLE #1: computing a growth rate, digit by digit (12 min)

Do every step on the board.

Meadowbrook's real GDP was 800 (billions) last year and 840 (billions) this year. What's the growth rate?

  • Step 1 — the change: 840 − 800 = 40.
  • Step 2 — divide by the STARTING (last-period) value: 40 ÷ 800 = 0.05.
  • Step 3 — convert to a percent: 0.05 × 100 = 5%.

Say it in words: Meadowbrook's economy grew 5% this year — its real output is 5% bigger than it was last year. Named trap: always divide by the OLD (starting) value, never the new one — dividing 40 by 840 instead of 800 gives a different (wrong) answer (≈4.76%), the same "wrong base" mistake as a misapplied inflation-rate calculation from Week 3.

Segment 4 — THE MODEL: the rule of 70 — why small rate differences compound huge (30 min)

Now the week's centerpiece idea. The rule of 70 is a shortcut for estimating doubling time — how many years it takes something growing at a steady percentage rate to double in size:

Years to double ≈ 70 ÷ (growth rate, as a whole number).

Work all four canon values on the board, one at a time, DIVIDING every time:

  • 2% growth → 70 ÷ 2 = 35 years to double.
  • 5% growth → 70 ÷ 5 = 14 years to double.
  • 7% growth → 70 ÷ 7 = 10 years to double.
  • 10% growth → 70 ÷ 10 = 7 years to double.

✅ VERIFIED NUMBERS (pre-computed; do not recompute live)

  • 2% → 35 yrs; 5% → 14 yrs; 7% → 10 yrs; 10% → 7 yrs (all = 70 ÷ rate).
  • Proof the shortcut works: growing at 2% for 35 years compounds to 1.02³⁵ ≈ 2.0 — almost exactly double. (Verified: 1.02³⁵ = 1.9999.)
  • The named trap: the rule is divide 70 BY the rate, never multiply. A chatbot or a rushed student will sometimes compute "70 × 2 = 140" instead of "70 ÷ 2 = 35" — flag this explicitly.

Now make the "small differences, huge gap" point land with real numbers (this is the workshop's engine, previewed here): take a $100 billion economy. At 2% growth, after 10 years it's worth about $121.90 billion. At 7% growth, after those SAME 10 years it's worth about $196.72 billion — nearly double the 2% path, and (cross-check!) almost exactly the $200 billion the rule of 70 predicts for a 7%-growing economy doubling in 10 years. Same starting point, same 10 years, radically different outcomes — that's the whole lesson of the week in one comparison.

Read the comparison out loud: after year 1, the two paths ($102.00 vs. $107.00) look almost identical. By year 10, they've pulled miles apart. Compounding is invisible in the short run and enormous in the long run — which is exactly why growth-rate differences that sound tiny in a news headline ("2.1% vs. 2.4%") matter enormously for a 30-year retirement or a 50-year national development story.

Segment 5 — PER-CAPITA GROWTH & THE SOURCES OF GROWTH (20 min)

Per-capita growth — the "growth for whom?" question. Total GDP growth alone can mislead: an economy can grow simply because it has more people, without any single person getting richer. The fix is a rough approximation:

Per-capita growth rate ≈ total GDP growth rate − population growth rate.

Worked example: an economy grows GDP by 3% while its population grows 1% → per-capita growth ≈ 3% − 1% = 2%. Say it in words: the average person's slice of output grew about 2%, not 3% — some of that extra output just had to be spread across more people. Misconception to name: a country can have impressive total growth and disappointing per-capita growth at the same time if population is rising fast — total output and living standards per person are NOT the same question.

The sources of long-run growth — where does it actually come from? Three broad ingredients, in plain language:

  1. Physical capital — more/better factories, machines, roads, ports: workers produce more per hour when they have better tools.
  2. Human capital — education, training, skills, health: a more capable workforce produces more with the same tools.
  3. Technology — new ideas, better processes, innovation: doing more (or something entirely new) with the same labor and capital.

Name the field's organizing framework, factually: economists organize these three ingredients using the Solow growth model — the standard workhorse framework for thinking about long-run growth (named here as the field's own term for this framework; we are not deriving its equations at the principles level, just naming what it organizes). (Growth theory has more nuance below the surface — economists debate exactly how much each ingredient contributes and why some countries convert these ingredients into growth better than others — but the three-ingredient list itself is not a contested claim.)

Segment 6 — TECHNOLOGY WORKFLOW + AI-CRITIQUE (18 min)

Live demo (spreadsheet or Desmos): build a two-column compounding table — Year 0 through Year 10, one column growing at 2%/year, one at 7%/year, both starting at 100. Watch them visibly separate after year 3 or 4.

AI-critique moment (do this with the class): ask an approved chatbot: "If a country's real GDP grows steadily at 5% a year, about how many years will it take to double? And if instead it grows at 10 million dollars total this year on top of $200 million, what is its growth rate?" Audit it together. The right answers: 70 ÷ 5 = 14 years to double; and $10 million ÷ $200 million × 100 = 5% growth rate for the second part. Chatbots frequently multiply instead of divide on the rule of 70 (giving "350 years" instead of 14), or divide by the wrong base (using the new total instead of the starting value) on a growth-rate calculation. Make the class catch the error and restate the correct method out loud. The habit all term: the tool drafts, you judge.

Segment 7 — INTERACTION: mini-debate / think-pair-share (15 min)

Pose: "Two fictional economies, Northfield and Southbrook, both have GDP of 500 this year. Northfield grew at 2% last year; Southbrook grew at 6%. A classmate says, 'They're basically tied — 2% and 6% are both just small numbers.' Is that classmate right?" Pairs discuss for 3 minutes, then share. Target answer: no — over any meaningful stretch of years, a 6% economy compounds toward doubling in about 70 ÷ 6 ≈ 11.7 years, while a 2% economy takes 35 years — a difference that becomes enormous within a single working lifetime. This previews Discussion 4 directly: if growth compounds this powerfully, should policy chase the fastest possible growth rate above all else — or does "maximize growth" leave out something that matters?

Segment 8 — CALLBACKS, TEASE & THE WEEK'S WORK (10 min)

  • Callback: every example today shared one engine — a steady growth rate compounds, and the rule of 70 turns that compounding into a number you can feel: years to double.
  • Tease next week: "So far we've measured the economy's size, its vital signs, and now its long-run growth engine. Next week we build the model that explains short-run ups and downs — the aggregate demand–aggregate supply model, where we'll finally answer why an economy sometimes sits below its potential."
  • The week's work: Lecture Tutorial (growth rates → the rule of 70 → per-capita growth → sources of growth), Practice (6 reps), Quiz 4, Discussion 4, Assignment 4, and Workshop 4 (compound a small economy in a spreadsheet or Desmos and watch a rate gap become an output gap).

Instructor FAQ — common stumbles

  • "Is the rule of 70 an exact formula?" No — it's a close approximation built on the math of compounding (it comes from the natural-log relationship ln(2) ≈ 0.693, and 70 is a round number close to 69.3 chosen because it divides cleanly by common growth rates like 2, 5, 7, and 10). It's excellent for building intuition and is not far off for realistic growth rates; don't present it as a law of nature.
  • "Divide or multiply?" Always divide: 70 ÷ rate. Multiplying (a genuinely common slip, including in AI output) gives a wildly wrong, much larger number.
  • "If GDP grows 3%, does everyone get 3% richer?" Not necessarily — check population growth. If population also grew, per-capita growth (the number that tracks the average person's slice) is smaller: per-capita ≈ total growth − population growth.
  • "Which source of growth matters most?" This is genuinely, actively debated among economists and is not settled — some emphasize capital accumulation, others human capital or institutions, others technology/innovation. Present it as an open research question, not a solved one; the three-ingredient list itself, however, is standard and uncontested.
  • "Is faster growth always better policy?" That's a normative question this week deliberately leaves open (see Discussion 4) — compounding is a powerful positive/factual result, but whether to prioritize it above other goals (distribution, environment, stability) is a values question, not one growth theory alone answers.
  • "What's the Solow model, exactly?" At the principles level, just its name and role: the standard framework economists use to organize capital, labor, and technology into a growth story. We are not deriving its equations here — that's intermediate macro.

~ Prof. Ashford's edition · Fall 2026 · built with thecoursemaker.com