ECOS2025 Chap.2 Growth Models and Productivity
Growth Models and Productivity
This chapter builds the Solow-Swan model from the production function, saving and required investment, then uses it to analyse saving and population shifts. It adds endogenous growth and growth accounting so students can distinguish higher output levels from permanently faster growth and interpret the Solow residual with appropriate caution.
What this chapter covers
- 01
Production per worker
- 02
Saving and investment
- 03
Required investment
- 04
Steady-state shifts
- 05
Endogenous growth
- 06
Solow residual
Worked example · free
Decomposing output growth
- +1Capital contributes 0.35 times 10.0, equal to 3.5 percentage points.
- +1Labour share is 0.65, so labour contributes 1.3 percentage points.
- +1The residual is 7.0 minus 3.5 minus 1.3, equal to 2.2 percentage points.
- +1Verify that the contributions sum to 7.0 and label the residual cautiously.
Key terms
- Steady state
- The point where saving per worker equals required investment and capital per worker is constant.
- Capital deepening
- An increase in capital per worker that raises output per worker subject to diminishing returns.
- Required investment
- Investment needed to replace depreciation and equip a growing workforce, written as (d+n)k.
- Solow residual
- Output growth remaining after the weighted contributions of capital and labour have been removed.
Growth Models and Productivity FAQ
Does a higher saving rate permanently raise the growth rate?
In the basic Solow model it raises the steady-state level of capital and output per worker. Growth accelerates during transition, but diminishing returns prevent a permanently higher rate without technological progress.
Why is the Solow residual not a pure technology measure?
It absorbs whatever measured capital and labour do not explain, including utilisation, human capital, omitted inputs and measurement error. It is informative but should not be interpreted as directly observed innovation.
What should be labelled on a Solow diagram?
Label output per worker, capital per worker, the production function, saving, required investment, the initial and new steady states, and the direction and cause of any curve shift.
How does higher population growth change the steady state?
It steepens the required-investment line because more new capital is needed to equip additional workers. With saving unchanged, steady-state capital and output per worker fall under the model assumptions.
What does endogenous growth add to the toolkit?
It allows knowledge, research and human capital to influence technological progress inside the explanation. This creates a role for policy in long-run growth rather than treating productivity growth as wholly external.
How should institutions be added to a model answer?
Use the model to organise capital, labour and productivity, then explain the institution that changed those variables. Keep the formal result and the deeper historical mechanism distinct but connected.
What does a complete Solow comparison require beyond drawing the curves?
State whether the shock changes saving, depreciation, population growth or productivity, then move the break-even or investment schedule in the correct direction. Distinguish the transition path from the new steady state and report output per worker rather than aggregate output when that is the model's object.
For East Asian evidence, classify observed investment and labour changes inside the model, but do not label the residual pure technology. Add education, allocation, institutions and measurement as competing explanations, then use historical evidence to decide which mechanism fits the period.
Exam move
Rebuild the model from equations rather than tracing a memorised picture. Start with y = Af(k), identify diminishing marginal productivity and derive saving per worker as sAf(k). Write required investment as (d+n)k and explain separately why depreciation and population growth require new capital. Only then draw the two curves and mark the steady state where saving equals required investment.
Explain why every curve slopes as it does, then practise saving, population and productivity shifts. For a higher saving rate, show the upward saving shift, excess investment at the old steady state and transition to higher capital and output per worker. State explicitly that the level rises but the permanent growth rate does not. For higher population growth, rotate required investment upward and explain capital dilution.
For higher productivity, lift the production and saving curves and distinguish that change from movement along a fixed production function. Build a direction table with four columns: shock, curve, transition and long-run result. Redraw each case without notes and use a different colour only after every label is correct. Recompute the residual under a second capital share to see how assumptions change the interpretation.
Use at least two fresh numerical decompositions and make capital, labour and residual contributions add back exactly to output growth. Label every result in percentage points. Then list what can enter the residual besides technology: utilisation, human capital, hours, input quality and measurement error.
For a country essay, use Solow first to organise proximate growth sources, then add institutions that explain why saving, investment or productivity changed. Do not claim that the basic model contains leadership, trade policy or financial coordination when those mechanisms sit outside it. Practise a conclusion that says the model is useful but incomplete and names the missing mechanism precisely.
End the session with a blank-page test: reproduce the equations, steady-state condition, three shifts, one growth-accounting calculation and one limitation in ten minutes. Any unlabelled axis or unexplained residual returns to the next day's retrieval set.
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