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Lesson M08.L02: Sources of Growth: Capital, Labour, and Technology (TFP)

Module: The Economy in the Long Run: Introduction to Economic Growth Level: intro Duration: 30 minutes Learning Objective: Decompose GDP growth using growth accounting to identify separate contributions of inputs. Data as of: 2023 Provenance: pc.gov.au (Productivity Commission) | ABS | OpenStax Macro 3e

Explanation

What actually drives an economy to grow? Economists use growth accounting to break down GDP growth into three sources:

  1. Capital (K): Physical assets used in production — machinery, buildings, infrastructure, computers. More capital means workers can produce more output per hour.

  2. Labour (L): The number of hours worked in the economy, which depends on population, workforce participation, and hours per worker.

  3. Total Factor Productivity (TFP), or technology (A): The efficiency with which capital and labour are combined. TFP captures everything that raises output without simply adding more inputs — technological innovation, better management practices, improvements in education, and institutional quality.

The growth accounting equation is:

ΔY/Y = ΔA/A + α(ΔK/K) + (1−α)(ΔL/L)

Where: - ΔY/Y = GDP growth rate - ΔA/A = TFP growth rate - α = capital's share of income ≈ 0.3 (estimated from national accounts) - (1−α) = labour's share of income ≈ 0.7

This equation says: total output growth equals TFP growth plus a weighted contribution from capital growth plus a weighted contribution from labour growth.

Key insight: Because of diminishing returns to capital, you cannot sustain long-run growth by just adding more machinery. In the long run, TFP growth is the primary driver of rising living standards. This is why investing in research, education, and technology is central to Australia's Productivity Commission recommendations.

Worked Example

Suppose in a given year Australia's economy experiences the following:

Variable Value
GDP growth (ΔY/Y) 3.5%
Capital stock growth (ΔK/K) 4.0%
Labour hours growth (ΔL/L) 1.5%
Capital share (α) 0.30
Labour share (1−α) 0.70

Step 1: Calculate capital's contribution.
α × (ΔK/K) = 0.30 × 4.0% = 1.2%

Step 2: Calculate labour's contribution.
(1−α) × (ΔL/L) = 0.70 × 1.5% = 1.05%

Step 3: Sum contributions from capital and labour.
1.2% + 1.05% = 2.25%

Step 4: Solve for TFP growth (the residual).
ΔA/A = ΔY/Y − [α(ΔK/K) + (1−α)(ΔL/L)]
ΔA/A = 3.5% − 2.25% = 1.25%

Interpretation:
Of Australia's 3.5% GDP growth that year: - 1.2 percentage points came from capital accumulation - 1.05 percentage points came from labour growth - 1.25 percentage points came from TFP (technology/efficiency improvement)

TFP contributed the largest single share (~36% of total growth), illustrating its importance as the engine of long-run prosperity.

Common Misconception

Misconception: TFP growth is simply technological progress in the sense of new inventions or gadgets.

Correction: TFP (Total Factor Productivity) is broader than just technological invention. It is the "residual" in growth accounting — everything that makes inputs more productive. This includes better management practices, improved worker skills and education, stronger institutions, reduced regulatory barriers, better resource allocation across firms, and yes, technological innovation. The Productivity Commission identifies all of these as drivers of Australia's productivity performance, not just R&D spending.

Practice Prompts

  1. If capital grows at 5%, labour grows at 1%, α = 0.3, and TFP grows at 0.5%, what is GDP growth? → Answer: ΔY/Y = 0.5% + (0.3 × 5%) + (0.7 × 1%) = 0.5% + 1.5% + 0.7% = 2.7%

  2. Australia's TFP growth slowed significantly after the mining boom (post-2013). Why would this reduce long-run GDP growth even if capital investment remained high? → Answer: Capital investment alone faces diminishing returns — each new unit of capital adds progressively less output. Without TFP growth (efficiency improvements), just adding more machinery cannot sustain GDP growth in the long run. Slowing TFP means the economy is not becoming more efficient, dragging down potential output growth.

  3. What does it mean if a country has high GDP growth but zero TFP growth? → Answer: All growth is coming from adding more inputs (capital and/or labour), not from using them more efficiently. This is unsustainable in the long run because diminishing returns will eventually limit the contribution of additional inputs. Economists call this "extensive growth" as opposed to "intensive growth" driven by TFP.

Further Resources