1 / 32

[slides for Part (b) of this topic here]

[slides for Part (b) of this topic here]. The golden rule. The golden rule level of capital accumulation k* gold That level of steady-state capital which implies maximum steady-state consumption c* gold In this version, given by MPK = 

roxy
Download Presentation

[slides for Part (b) of this topic here]

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. [slides for Part (b) of this topic here]

  2. The golden rule • The golden rule level of capital accumulation k*gold • That level of steady-state capital which implies maximum steady-state consumption c*gold • In this version, given by MPK =  • All golden rule equilibria are steady-states, but... • not all steady-states are golden rules...

  3. Solow Growth Model:The golden rule y = c + i y, k, i 0 k

  4. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) 0 k

  5. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k 0 k

  6. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k MPK =  0 k k*gold

  7. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k MPK =  c*gold i*gold 0 k k*gold

  8. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k y*gold MPK =  c*gold i*gold 0 k k*gold

  9. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k y*gold MPK =  c*gold i = sgoldf(k) i*gold 0 k k*gold

  10. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k y*gold MPK =  c*gold i = sgoldf(k) i*gold 0 k k*1 k*gold

  11. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k y*gold MPK =  c*gold i = sgoldf(k) i*gold 0 k k*1 k*gold

  12. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k y*gold MPK =  c*gold i = sgoldf(k) c*1 i*gold 0 k k*1 k*gold

  13. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k y*gold MPK =  c*gold i = sgoldf(k) c*1 i*gold 0 k k*1 k*gold k*2

  14. Solow Growth Model:The golden rule y = c + i y, k, i y=f(k) k c*2 y*gold MPK =  c*gold i = sgoldf(k) c*1 i*gold 0 k k*1 k*gold k*2

  15. The Golden Rule: policy to get there • k*gold is that steady state k which maximises steady state c • Found where MPK =  • Consider when economy not at k*gold • Economy is dynamically inefficient • Two cases: • k* < k*gold • k* > k*gold • What sort of policy problem does the government face?

  16. Getting to the golden rule:either from k*1 or from k*2 y = c + i y, k, i y=f(k) k c*2 y*gold MPK =  c*gold i = sgoldf(k) c*1 i*gold 0 k k*1 k*gold k*2

  17. Solow Growth Model: Full Versionpopulation growth + technological change • Y = F(K, AL) • Y output • K capital • L labour • A the efficiency of labour • so AL = the effective labour force • Assume L/L = n • Assume A/A = g • both n and g are exogenous (rather than endogenous)

  18. Solow Growth Model: Full Versionpopulation growth + technological change • Define y = Y/(AL) output per unit of effective labour • and k = K/(AL) …ditto for i and for c • Given constant returns to scale • y = f(k) • i = sf(k) • Fundamental equation of capital accumulation: k = i - (+ n + g)k or k = sf(k) - (+ n + g)k

  19. Faculty of Arts Public Lecture Series • “In the Shadow of the Market” • Aidan Kane • 8.00pm Wednesday 23rd February • Lecture Hall ML150Millennium Arts Building • Free drink • (sortof)

  20. a digression on growth rates • If P and Q grow at rates p and q: • (PQ) grows (approx.) at a rate (p + q) [product] • (P/Q) grows (approx.) at a rate (p - q) [quotient]

  21. Solow Growth Model:Steady-state in the full version y, k, i 0 k

  22. Solow Growth Model:Steady-state in the full version y, k, i y=f(k) 0 k

  23. Solow Growth Model:Steady-state in the full version y, k, i y=f(k) i = sf(k) 0 k

  24. Solow Growth Model:Steady-state in the full version y, k, i y=f(k) n + gk i = sf(k) 0 k

  25. Solow Growth Model:Steady-state in the full version y, k, i y=f(k) n + gk i = sf(k) 0 k

  26. Solow Growth Model:Steady-state in the full version y, k, i y=f(k) n + gk i = sf(k) 0 k k*

  27. Solow Growth Model:Steady-state in the full version y, k, i y=f(k) n + gk i = sf(k) 0 k k*

  28. Solow Growth Model:Steady-state in the full version y, k, i y=f(k) n + gk y* i = sf(k) 0 k k*

  29. Solow growth modelSteady-state in the full version • y = Y/(AL) growing at rate 0 [from graph] • Given that A is growing at rate g.. • and L is growing at rate n [by assumption] • then, AL growing at rate n+g • and Y growing at rate n+g • [i.e. growth in total GDP] • so Y/L growing at rate (n+g)-n = g • i.e. technological progress only source of long-run growth in income per capita

  30. The Solow Decomposition • Given constant returns to scale • and  = share of capital in income • Then, growth rate of GDP = • contribution of capital + contribution of labour + technological progress • Y/Y = K/K + (1-)L/L + A/A • Y, K, L,  observable • A/A Solow residual, total factor productivity

  31. The Solow Decomposition United States 1960-90 GNP Capital Labour TFP 3.1% 0.9% 1.2% 1.1%

  32. Newer models of growth • Failure of convergence hypothesis • Solow model over-simplifies technological progress • This key factor is exogenous to the model • Human capital • Endogenous growth • e.g. externalities • Institutional explanations

More Related