ECON1002 · Introductory Macroeconomics
Long-Run Growth & Growth Accounting
Long-run growth shifts the focus from fluctuations to the level and trend of output per person. Small differences in growth compound hugely (the rule of 70), and institutions matter (the two Koreas). Production follows the Cobb-Douglas function Y = AKᵃL¹⁻ᵃ, exhibiting constant returns to scale and diminishing marginal product, with a per-capita form y = Akᵃ. Growth accounting then decomposes output growth into capital, labour and the residual — total factor productivity (the Solow residual).
It is examined as a growth-accounting calculation (e.g. per-capita output growth = a × growth of k when A is constant) and concept MCQ on returns to scale and the role of institutions.
What this chapter covers
- 011. Stylised facts of growth; institutions matter (North vs South Korea); the rule of 70 (doubling time ≈ 70/growth%)
- 022. Cobb-Douglas production Y = AKᵃL¹⁻ᵃ; A = total factor productivity
- 033. Constant returns to scale (in K, L together) AND diminishing marginal product (one input fixed)
- 044. Per-capita production y = Akᵃ (k = K/L), 0 < a < 1, diminishing in k
- 055. Growth-accounting equation: ΔY/Y = ΔA/A + a·(ΔK/K) + (1−a)·(ΔL/L)
- 066. The Solow residual ΔA/A = TFP growth = the rate of technical progress
- 077. Factor shares: a = capital's share, (1−a) = labour's share (factors paid marginal product)
- 088. Per-capita output growth = a × (growth of k) when A is constant
Growth accounting — per-capita output growth
- 1 markWith A constant, growth of per-capita output is the elasticity a times the growth of capital per worker: %Δy = a × %Δk = (1/3) × 6% = 2%.
- 1 markAdd the TFP contribution from the growth-accounting equation: %Δy = %ΔA + a × %Δk.
- 1 markSubstitute: %Δy = 1.5% + (1/3) × 6% = 1.5% + 2% = 3.5%.
Key terms
- Rule of 70
- A quick approximation for doubling time: a variable growing at g% per year roughly doubles in 70/g years. It shows how small differences in growth rates compound into large differences in living standards over decades.
- Cobb-Douglas production function
- Y = AKᵃL¹⁻ᵃ, with A total factor productivity, K capital, L labour and a capital's output elasticity. It exhibits constant returns to scale (doubling both K and L doubles Y) and diminishing marginal product (adding one input with the other fixed yields ever-smaller gains).
- Total factor productivity (A)
- The efficiency with which inputs are converted into output — technology, organisation, institutions. It is the part of output not explained by measured capital and labour, and its growth is the Solow residual.
- Per-capita production function
- y = Akᵃ, output per worker as a function of capital per worker k = K/L. Because 0 < a < 1 it is concave: extra capital per worker raises output per worker but at a diminishing rate.
- Growth-accounting equation
- ΔY/Y = ΔA/A + a·(ΔK/K) + (1−a)·(ΔL/L): output growth decomposes into TFP growth plus the share-weighted growth of capital and labour. It lets economists attribute growth to its sources.
- Solow residual
- The TFP-growth term ΔA/A in the growth-accounting equation — output growth left over after accounting for measured capital and labour growth. It is interpreted as the contribution of technical progress to growth.
Long-Run Growth & Growth Accounting FAQ
How is long-run growth examined in ECON1002?
Mainly as a growth-accounting calculation — given factor shares and input growth rates, find output growth, or given output and input growth, back out the Solow residual (TFP growth). The recurring MCQ version is per-capita output growth = a × growth of k when A is constant. It is supported by concept questions on constant returns vs diminishing marginal product and on why institutions drive cross-country differences.
What is the difference between constant returns to scale and diminishing marginal product?
They describe different experiments on the same Cobb-Douglas function. Constant returns to scale means scaling ALL inputs together (K and L) scales output proportionally. Diminishing marginal product means adding ONE input while holding the other fixed yields progressively smaller output gains. Cobb-Douglas has both: it is CRS in K and L jointly, but has diminishing returns to each input separately.
What is the Solow residual and why does it matter?
The Solow residual is the part of output growth left unexplained after accounting for the contributions of measured capital and labour — the ΔA/A term in growth accounting. It is interpreted as total-factor-productivity growth, the contribution of technology and efficiency. It matters because, in the long run, sustained growth in output per worker comes mainly from TFP growth, not endless capital accumulation, which runs into diminishing returns.
Why do small differences in growth rates matter so much?
Because growth compounds. The rule of 70 shows a country growing at 2% doubles its income in about 35 years, while one growing at 1% takes about 70 years — so a single percentage point compounds into a vast gap over a lifetime. This is why economists care intensely about the determinants of long-run growth, especially institutions and TFP, even when annual differences look tiny.
Exam move
Anchor everything on the growth-accounting equation ΔY/Y = ΔA/A + a·(ΔK/K) + (1−a)·(ΔL/L) and its per-capita shortcut %Δy = %ΔA + a·%Δk. Drill both directions: forward (inputs and shares → output growth) and backward (output and input growth → the Solow residual). The key discipline is weighting capital growth by its share a, which captures diminishing returns. Keep crisp one-line distinctions for the concept MCQ — constant returns to scale (scale all inputs) vs diminishing marginal product (one input fixed), and TFP/institutions as the ultimate driver of long-run living standards — and remember the rule of 70 for any doubling-time question. This per-capita function y = Akᵃ is also the foundation of the Solow-Swan model, so over-learn it here.
