Explain the concept of golden rule in the neoclassical growth model. What are its implications ?

The Golden Rule in the neoclassical (Solow) growth model identifies the optimal level of capital accumulation that maximizes steady-state per capita consumption. Introduced by Edmund Phelps, it provides a benchmark for evaluating whether an economy’s saving rate is too high or too low for intergenerational welfare maximization234.

Concept and Derivation

In the Solow model, the steady-state capital per worker ($k^*$) is determined by the balance of investment ($s \cdot f(k)$) and capital depreciation ($\delta k$) plus population growth ($nk$):

$$s \cdot f(k) = (n + \delta)k$$

Per capita consumption ($c$) in steady state is:

$$c^* = f(k^*) - (n + \delta)k^*$$

To maximize $c^*$, the Golden Rule condition requires the marginal product of capital (MPK) to equal the sum of population growth and depreciation rates:

$$MPK = n + \delta$$

This ensures that the marginal benefit of additional capital equals its marginal cost (depreciation and dilution due to population growth)245.

Implications

Optimal Saving Rate:
The Golden Rule defines the saving rate ($s_{gold}$) that achieves $k_{gold}$. If the actual saving rate ($s$) exceeds $s_{gold}$, the economy over-accumulates capital, reducing long-run consumption (dynamic inefficiency). Conversely, if $s<s_{gold}$, increasing saving enhances future consumption35.

Policy Guidance:
Governments can use taxes, subsidies, or pension reforms to adjust saving rates toward $s_{gold}$. For example, reducing excessive saving in capital-rich economies redirects resources to consumption35.

Intergenerational Equity:
The Golden Rule embodies the ethical principle that each generation should save at a rate it would have preferred previous generations to adopt, balancing current and future welfare35.

Efficiency vs. Growth:
While higher saving boosts output, the Golden Rule emphasizes that maximizing consumption-not output-is the welfare goal. Growth beyond $k_{gold}$ is counterproductive for living standards45.

Key Conditions and Variations

• Simplified Models: Some sources assume zero population growth ($n = 0$) or depreciation ($\delta = 0$), leading to $MPK = \delta$ or $MPK = n$24. However, the standard Solow model includes both factors.

• Real Interest Rate Link: Under the Golden Rule, the real interest rate ($r = MPK$) equals the economy’s growth rate ($n$), ensuring saving equals profit in steady state5.

Criticisms

The Golden Rule assumes:

• No technological progress.
• Perfect substitutability between capital and labor.
• A single representative household, ignoring inequality.

Despite these limitations, it remains a foundational tool for analyzing long-run growth policies34.

References:

1. https://www.egyankosh.ac.in/bitstream/123456789/76553/1/Unit-2.pdf
2. https://content.patnawomenscollege.in/Economics/GOLDEN%20RULE%20OF%20ACCUMULATION.pdf
3. https://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/golden-rule-growth-models
4. https://mgcub.ac.in/pdf/material/202005060446103aa42a2e15.pdf
5. https://www.albany.edu/~bd445/Economics_301_Intermediate_Macroeconomics_Slides_Spring_2014/Golden_Rule.pdf
6. https://www.ignouassignmentwala.in/explain-the-concept-of-steady-state-growth-in-the-solow-model-with-appropriate-diagram-show-that-the-golden-rule-of-phelps-is-not-a-steady-state/
7. https://www.scribd.com/document/688864478/GOLDEN-RULE-OF-ACCUMULATION
8. https://www.investopedia.com/terms/n/neoclassical-growth-theory.asp
9. https://www.studyzone.co/ignou-solved-assignment-mec-002-macroeconomic-analysis
10. https://www.youtube.com/watch?v=DuSjRjKcGvs
11. https://bpchalihacollege.org.in/online/attendence/classnotes/files/1627617200.pdf
12. https://es.scribd.com/document/200345633/Neoclassical-Growth-Model
13. https://www.coursehero.com/file/56813711/Golden-Rule-of-Capital-Accumulation-Economic-Growthpdf/
14. https://jncollegeonline.co.in/attendence/classnotes/files/1621226697.pdf
15. https://www.youtube.com/watch?v=kAaw0kU-EXs
16. https://webservices.ignou.ac.in/Pre-Question/Question%20Paper%20December%202022/SOSS/MA%20ECONOMICS/MEC-002.pdf
17. https://www.egyankosh.ac.in/bitstream/123456789/23016/1/Unit-7.pdf
18. https://www.youtube.com/watch?v=qJnrB2kWtbM
19. https://www.sfu.ca/~bkrauth/econ808/808_lec1.pdf