EF5472 Chap.5 Solow Growth and Convergence
Solow Growth and Convergence
Separate transition from balanced growth
Solow capital per worker changes according to the gap between saving and break-even investment. Diminishing returns make saving concave, while depreciation and population dilution create a linear requirement, so their positive crossing is stable.
A higher saving rate shifts the steady-state level and produces temporarily faster growth during transition; exogenous technology sets lasting growth in living standards. The golden rule selects capital that maximises steady consumption.
Growth accounting attributes output growth to factor-share-weighted inputs and a residual, while conditional convergence compares economies relative to their own steady-state determinants.
Audit the unit of every growth claim
Start from aggregate accumulation and divide by the relevant workforce before using a per-worker diagram.
The saving curve and break-even line are flows evaluated at the current capital stock; their vertical gap determines the direction of the stock's next movement. At a steady state, solve their equality, compute output, investment and consumption, and verify that actual saving exactly covers depreciation and dilution.
A higher saving rate shifts the destination and creates temporary growth during adjustment, but diminishing returns restore a zero long-run growth rate per worker when technology is fixed. With labour-augmenting progress, transform variables per effective worker and add technology growth to break-even investment.
Translate the stationary transformed result back carefully: output per effective worker is constant, output per worker grows with efficiency and aggregate output also incorporates population growth. For evidence questions, distinguish absolute convergence among economies with shared determinants from conditional convergence toward different destinations.
In growth accounting, calculate the productivity residual after weighting input growth by factor shares, then describe it as an unexplained residual rather than pure innovation. Measurement error, utilisation and omitted input quality can all enter the same number.
What this chapter covers
- 01
Per-worker accumulation
- 02
Break-even investment
- 03
Stable steady state
- 04
Golden-rule capital
- 05
Balanced growth
- 06
Growth accounting
- 07
Conditional convergence
Worked example · free
Compute a stable Solow destination
- 4Equate saving with break-even investment.
- 3Compute all steady flows.
- 3Use the saving gap to establish stability.
Key terms
- Break-even Investment
- Investment needed to replace depreciated capital and equip additional workers while keeping capital per worker unchanged.
- Balanced Growth
- A path on which key aggregate variables grow at constant rates while stationary ratios remain fixed.
- Golden Rule
- The steady-state capital stock maximising consumption after replacement and dilution.
- Solow Residual
- Measured output growth unexplained by factor-share-weighted capital and labour growth.
- Absolute Convergence
- Faster growth by poorer economies when they share the same steady-state destination.
- Conditional Convergence
- Faster movement toward each economy's own steady state after its determinants are considered.
Solow Growth and Convergence FAQ
Why does higher saving not permanently raise Solow growth?
Capital deepening raises output, but diminishing marginal products make each additional unit contribute less. The economy eventually reaches a higher steady state where saving again only covers depreciation and population dilution. During the transition growth is faster, while the long-run per-worker growth rate returns to the exogenous technology rate.
What is the difference between golden-rule and Ramsey capital?
Golden-rule capital maximises sustainable steady consumption and sets the marginal product equal to break-even dilution. Ramsey capital maximises discounted lifetime utility and includes impatience in its modified condition. With positive impatience, the Ramsey destination generally contains less capital than the consumption-maximising golden-rule stock.
Does the Solow residual measure pure technology?
It is calculated as the part of output growth not attributed to weighted capital and labour growth. Technology is an important interpretation, but utilisation, omitted human capital, changing markups, data error and other unmeasured influences can enter the same residual. Report the accounting result without overstating causation.
Exam move
Derive the per-worker law from aggregate capital and labour laws until the population-growth denominator feels automatic. Redraw the saving and break-even curves and annotate both the sign and size of capital change. Work one closed-form Cobb-Douglas or square-root steady state, then shift saving, population growth and depreciation one at a time and explain levels versus rates.
Add technology by converting to effective-worker units and list the growth rates of effective-worker, per-worker and aggregate quantities. For empirical practice, compute one growth-accounting residual and write two reasons it may not equal pure technology. Compare absolute with conditional convergence using two economies whose destinations either match or differ.
End each result by labelling it as a level effect, transitional growth effect or balanced-growth rate.
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