Chapter 4

1. Chapter 4 Theories of Economic Growth

3. Five Equations • Aggregate production function • Saving function • Saving = Investment • Relation between new investment and change in capital stock • Growth rate of labor

4. Aggregate production function • What is exactly the shape of the function F ? • Where do K and L come from?

5. Saving function

6. Saving and Investment • Assume no trade and no government • Or assume thatwith “foreign saving” = capital inflows

7. New investment and change in capital stock • d = rate of depreciation

8. New investment and change in capital stock

9. Labor Force Growth • n = rate of population growth

10. The Harrod-Domar Model • R. F. Harrod, The Economic Journal, Vol. 49, No. 193. (Mar., 1939), pp. 14-33. • Econometrica, Vol. 14, No. 2. (Apr., 1946), pp. 137-147

11. Fixed Coefficient Production Function • Isoquants • Combination of inputs that produce equal amounts of output • Fixed coefficient production function • Assume capital and labor have to be used in constant proportions (i.e., 10 people for every $1m of capital). • What happens if you raise K, keeping L constant?

12. Y=200,000*$50=$10,000,000 K/Y=$20,000,000/$10,000,000 =2

13. Fixed Coefficient Production Function • Fixed coefficient production function • K/L is constant if production is efficient • Constant returns to scale • K/Y and L/Y are constant

14. The Harrod-Domar Model • Assume labor is unemployed • Capital is the binding constraint

15. The Harrod-Domar Model • Capital-output ratio • Capital intensity of production process and of product • Efficiency with which capital is used • Capital-output ratio versus Incremental Capital-Output Ratio • Assume average K/Y = ICOR

16. The Harrod-Domar Model

17. The Harrod-Domar Model

18. The Harrod-Domar Model

19. The Harrod-Domar Model • Capital created by investment is the main determinant of growth. • Saving makes investment possible

20. The Harrod-Domar Model

21. The Harrod-Domar Model • Consequences • Saving as crucial for growth • Knife-edge dynamics • If n>g (g=s/v-d), then chronic unemployment • If n<g , then chronic labor shortages, capital becomes idle • No endogenous process to bring the economy to equilibrium

22. The Harrod-Domar Model • Strengths • Simplicity • Few data requirements • Short-term accuracy • Saving as necessary

23. The Harrod-Domar Model • Weaknesses • Saving as sufficient • Investment is uncertain, subject to inefficiency, etc. • Rigid assumption of fixed proportions • No diminishing returns; no factor substitution • No technological change • Un-realistic lack of response of v to policy, changes in income levels, etc. • Development should raise ICOR endogenously

24. The Harrod-Domar Model • Still widely used to calculate financing gaps • How much foreign assistance to achieve a particular rate of output growth?

25. “Technical Change and the Aggregate Production Function,” Review of Economics and Statistics 39 (August 1957), 312-20.

27. Solow Growth Model • Drop fixed coefficients • Neoclassical production function • Factor substitution, depending on factor availability, marginal product, and prices

28. Y=200,000*$50=$10,000,000 K/Y=$24,000,000/$10,000,000 =2.4 Y=200,000*$50=$10,000,000 K/Y=$20,000,000/$10,000,000 =2 Y=200,000*$50=$10,000,000 K/Y=$17,000,000/$10,000,000 =1.7 $24 $20$17

29. Solow Growth Model • Because factors can be substituted for each other, policy (and the market) can encourage the use of abundant inputs by making scarce resources more expensive.

30. Solow Growth Model • Constant returns to scale • Diminishing returns to capital

32. Solow Growth Model • The capital stock grows as more is saved out of output… • and declines as more capital depreciates.

33. Solow Growth Model

34. Solow Growth Model • The amount of capital per worker • grows as more is saved out of output… • declines as more capital depreciates… • and declines as population grows faster

35. Solow Growth Model Capital deepening Saving - Required for capital widening

36. Solow Growth Model

37. Steady state change in k =

38. Solow Growth Model • In the steady state, Dk=0

39. Getting a Senseof the Magnitudes • Assume the production function is: • Output per worker is: • That is, the first relation of the model(capital/worker determines output) is

40. Getting a Senseof the Magnitudes • And the second relation of the model (output determines capital accumulation) is • Then,

41. Getting a Senseof the Magnitudes • In steady state,the left side equals zero: • Squaring both sides, • Dividing by k and rearranging,

42. Getting a Senseof the Magnitudes • The steady state capital per worker is equal to the square of the ratio of the saving rate to the depreciation rate + population growth rate. • Steady-State Output per worker is given by:

43. Getting a Senseof the Magnitudes • Steady-state output per worker is equal to the ratio of the saving rate to the depreciation rate+population growth rate. • A higher saving rate, a lower depreciation rate, and a lower population growth rate lead to higher steady-state capital per worker and higher steady-state output per worker.

44. Solow Growth Model • At the steady state • y stays constant • k stays constant • Y grows at the rate n • K grows at the rate n

45. Solow Growth Model • Ceteris paribus, poor countries have much larger growth potential. • Ceteris paribus, growth will slow as a country gets richer • Ceteris paribus, poor and rich countries will converge.

46. Solow Growth Model Depreciation / worker, dk* Output / worker, f(k*) output / worker, y Saving / worker, sf(k*) krich Steady State capital / worker, k* kpoor

47. Effects of Changes in the Saving Rate • Higher saving rate leads to more investment… • Capital accumulates faster… • But eventually diminishing returns lead to an end to growth.(at a higher steady state level of output)

49. Effects of Changes in the Population Growth Rate • Higher population growth rate requires more capital for widening… for a given sy, • So k and y decline to a lower steady state • But because L is growing faster, Y* must grow faster to keep y* constant.