1. Explaining Catch-up Growth BASIC SOLOW MODEL SCOTT BAIER

2.  Saving gets channeled into investment  Investment adds to the capital stock  Each period some capital wears out with use. KEY ASPECTS OF THE SOLOW MODEL

3.  Assume that we save a constant amount (S= 50)  Assume an initial level of capital (K=300)  Assume 10% of the capital stock depreciates each period (Depreciation = d*K)  Observe how the capital stock changes each period SIMPLEST SOLOW MODEL

4. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 130050 TABULATION

5. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300) TABULATION

6. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300)20 (=50-30) TABULATION

7. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300)20 (=50-30) 232050 TABULATION

8. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300)20 (=50-30) 23205032 (=.1*320)18 (=50-32) TABULATION

9. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300)20 (=50-30) 23205032 (=.1*320)18 (=50-32) 333850 TABULATION

10. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300)20 (=50-30) 23205032 (=.1*320)18 (=50-32) 33385033.816.2 TABULATION

11. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300)20 (=50-30) 23205032 (=.1*320)18 (=50-32) 33385033.816.2 4354.250 TABULATION

12. TimeCapital (K)Saving (S)Depreciation (d*K) Net Investment =S-d*K 13005030 (=.1*300)20 (=50-30) 23205032 (=.1*320)18 (=50-32) 33385033.816.2 4354.250…… … … 10250050 0 TABULATION

13.  At some point, it will be the case that savings is exactly equal to investment and the capital stock reach a steady state.  When you are far away from the steady state, the capital stock grows faster.  More rapid growth in the capital stock implies more rapid growth in output. KEY OBSERVATIONS

14.  When saving equals investment, the economy reaches a steady state and the capital stock stops growing.  Mathematically, the capital stock stops growing when: S = d*K ss Since we know S and d  K ss = s/d In our example, K ss = 50/.10 =500 STEADY STATE

15. SIMPLE SOLOW MODEL: GRAPHICALLY

19.  Important Point: The steady state occurs where savings is equal to depreciation.  In the simple Solow Growth Model, S=d*K  Given values for S and d, we can find the steady-state value of K SOLOW GROWTH MODEL

20.  It is unrealistic to assume that people save a constant amount.  It is more likely to be the case that saving is related to the level of income.  We assume that people save a constant fraction of income. SOLOW GROWTH MODEL

21.  Saving gets channeled into investment  Investment adds to the capital stock  Each period some capital wears out with use. KEY ASPECTS OF THE SOLOW MODEL

22. PRODUCTION FUNCTION

23. PRODUCTION FUNCTION AND SAVING FUNCTION

24. SAVING FUNCTION AND DEPRECIATION SCHEDULE