Understanding Solow's Model of Economic Growth

1. Instructor Sandeep Basnyat Sandeep_basnyat@yahoo.com 9841 892281 Macroeconomics & The Global EconomyAce Institute of ManagementChapter 7 and 8: Economic Growth I

2. The Solow or Neo Classical Model • A major paradigm by Robert Solow: • widely used in policy making • benchmark against which most recent growth theories are compared • The rate at which the output of the economy grows basically depends on the rate at which the followings grow over time: • Capital Stock • Labour Force • Technological Progress Factors of Production - Production Function

3. The Solow Model- Accumulation of Capital Stock in an Economy • How much capital an economy can accumulate depends on: • supply of goods (Output) : depends on Production function • demand of goods (Input): depends on Consumption function

4. The production function • In aggregate terms: Y = F (K, L ) • Define: y = Output k = Capital Stock L = No. of Labour • Assumption: Constant return to scale. So,zY= F (zK, zL) for any z > 0 • Suppose, z = 1/L. Then, Y/L = F (K/L , 1) Amount of Output per worker (Y/L) is the function of amount of capital per worker (K/L) .

5. The production function • Assume, Y/L = y and K/L = k. Then, y = f(k). Ignore ‘1’ as a constant. …(i) • Eqn, (i) shows how much extra output a worker produces given an extra capital (Marginal Product of Capital-MPK).

6. Output per worker, y f(k) MPK 1 Capital per worker, k The production function Note: When capital per worker is high, extra unit of capital produces lower output Vice Versa. Note: this production function exhibits diminishing MPK.

7. The Demand for Goods and Services • y= c + i (remember, no G : Two Sector) • In “per worker” terms: Output per worker is divided into consumption per worker and investment per worker • Since people save and consume their income, If savings rate = s, then, c = (1-s) • So, fraction of the income that people consume is c = (1-s)y ….. Consumption Fn.

8. The Demand for Goods and Services • Substituting the value of ‘c’ in y; y= (1-s)y + i or i = sy Shows that investment equals saving where ‘s’ is the fraction of the output/ income devoted to investment.

9. Basis of Neo-Classical Growth Model • The main building block of the model: production function (Y depends on K, L and the technological progress) • Investment : K • Depreciation : K So, When I > D; K When I < D; K When I = D; K- Unchanged (Steady State) • Big Question: When does investment exceed depreciation, and when does it fall short of it?

10. Basis of Neo-Classical Growth Model • Depreciation: we may safely assume it as a constant(usually shown by 45 degree). • Investment: Can be shown in terms of savings. • Saving is a fixed share of to total income. Therefore, savings and/or investment at different capital stocks can be presented as a part of the total output (Income).

11. Graphical representation without Technology Output Per Worker Steady State Capital Per Worker

12. The model and increase in the saving rate Output Per Worker Capital Per Worker

13. The model and increase in population

14. y y’ = f(k) y*’ y = f(k) ir = dk y* i = s' f(k) i = s f(k) k k1* k* Effect of Technological Advancement • Productivity per worker increases • Shifts the Production functions upward • Saving rate shifts upward • Capital stock per worker increases • New Steady State is formed • Output per worker is increased but greater than “k”

15. k*gold y ir = dk y = f(k) C*gold i = s f(k) I*gold k Golden Rule Level of Capital • Bench mark for highest level of movement of steady state • The Golden Rule level of capital accumulation is the steady state with the highest level of consumption.

16. Policy issues: How to increase the saving rate? • Reduce the government budget deficit(or increase the budget surplus). • Increase incentives for private saving. Example: Reduce tax

17. Policy issues: Allocating the economy’s investment • In the Solow model, there’s one type of capital. • In the real world, there are many types,which we can divide into three categories: • private capital stock • public infrastructure • human capital: the knowledge and skills that workers acquire through education. • How should we allocate investment among these types?

18. Policy issues: Allocating the economy’s investment Two viewpoints: 1. Let the market allocate investment to the type with the highest marginal product. 2. Industrial policy by government: Govt should actively encourage investment in capital of certain types or in certain industries, because they may have positive externalities that private investors don’t consider.

19. Policy issues: Establishing the right institutions • Creating the right institutions is important for ensuring that resources are allocated to their best use. Examples: • Legal institutions, to protect property rights. • Capital markets, to help financial capital flow to the best investment projects. • A corruption-free government, to promote competition, enforce contracts, etc.

20. Policy issues: Encouraging tech. progress • Patent laws:encourage innovation by granting temporary monopolies to inventors of new products. • Tax incentives for R&D • Grants to fund basic research at universities • Industrial policy: encourages specific industries that are key for rapid tech. progress

21. Thank You