- This model has a steady state when: Kt+1/Kt - ’t+1/Nt’ =0 and will be unchanging) (k’ y’ So: -  - n -  = 0 s∙Yt/Kt or - ( + n + )kt’= 0 (multiply above by s∙yt’ Kt/Nt’) - In this steady state are not changing (Y, K and all grow at the rate n+). y’, k’ N’ - But y=Y/N and k=K/N are growing at the rate . - Do economies settle into a steady-state of this last sort? - Living standards grow at the rate of technological progress. - Barro and Sala-i-Martin (2004) : argue that long-term US growth is well approximated by something like this. - Can the model explain differences across countries or across time? - For reasonable production function estimates: differences in do ‘k’ not appear to be the critical factor. - Is it technology (or its growth rate)? or something the model misses? (see Romer Ch. 1 discussion; growth accounting Solow’s exercise) Appendix: the AK Model - Drops the diminishing returns to capital assumption from Solow. - Production: Yt =AKt A = a constant (reflects state of technology)
- This model has a steady state when: Kt+1/Kt - ’t+1/Nt’ =0 (k’ and y’ will be unchanging) So: s∙Yt/Kt -  - n -  = 0 or s∙yt’ - ( + n + )kt’= 0 (multiply above by Kt/Nt’) - In this steady state y’, k’ are not changing (Y, K and N’ all grow at the rate n+). - But y=Y/N and k=K/N are growing at the rate . - Do economies settle into a steady-state of this last sort? - Living standards grow at the rate of technological progress. - Barro and Sala-i-Martin (2004) : argue that long-term US growth is well approximated by something like this. - Can the model explain differences across countries or across time? - For reasonable production function estimates: differences in ‘k’ do not appear to be the critical factor. - Is it technology (or its growth rate)? or something the model misses? (see Romer Ch. 1 discussion; Solow’s growth accounting exercise) Appendix: the AK Model - Drops the diminishing returns to capital assumption from Solow. - Production: Yt =AKt A = a constant (reflects state of technology)