Economic Growth Models

Transcription

1 Economic Growth Models Prof. Goldstein Economic Demography Econ/Demog c175 Week 3: Lecture A Spring 2018 UC Berkeley econ c175 1

2 Malthus (review) Technology Mini-Olympics Today s agenda Neo-classical growth (with savings) ( Solow model) Production functions Steady state Role of population growth Role of technological change econ c175 2

3 Effect of exogenous Crude birth and death rates technological improvement w* b(w) d(w) Wage (w) Exogenous technology increasing wages Do wages stay higher, or revert to old level? N* w (N) w(n) Wage (w)

4 Effect of exogenous Crude birth and death rates N N* technological improvement w* b(w) d(w) Wage (w) w (N) w(n) Exogenous technology increasing wages But -- increased wages increase population growth Which reduces wages End result: bigger pop, same living conditions Wage (w) Can check with App

5 Virtual i-clicker "mini-olympics" Your answer is determined by your first name "Adam" "Ester" à A "Felicia" "Morris" à B "Nina" "Samuel" à C "Tali" "Zoey" à D Your "team" gets a point if majority is correct about your answer being true or false. 5

6 iclicker Quiz In our Malthusian model, improving technology A. Shifts the w(n) curve and permanently raises income B. Shifts the w(n) curve and temporarily raises income C. Changes the b(w) and d(w) curves D. Changes w* econ c175 6

7 iclicker quiz In our Malthus model, A. Land is a variable factor, and labor a fixed factor B. Labor is variable, and land fixed C. They are both fixed D. They are both variable econ c175 7

8 Under Malthus, we had no capital accumulation, just land and people. What happens if we add savings and productive capital? Population Income (per capita) A Steady growth Steady growth B Constant Steady growth C Steady growth Constant D Constant Constant Return to this, when you review econ c175 8

9 Economic Growth Models Question usually framed very generally: What determines long-run economic growth rate? Our specific interest: What effect does population change have on economic growth and on individual welfare? econ c175 9

10 Do high population growth rates hurt the economy? GDP Per capita GDP per capita Ukraine Japan Causality could go in either way United States Mexico Philippines Pakistan Population growth rate Nigeria But today we ll see a theory of how population growth could hurt econ c Source: World Bank

11 In coming lectures, Boserup pop growth will induce tech change and thus increase per capita income Ehrlich (environmentalists) pop growth will deplete natural resources and will reduce per cap income, perhaps catastrophically econ c175 11

12 Malthus vs. Solow With Malthus, 1 fixed factor (land) and 1 variable factor (labor) With Solow, no fixed factor, but 2 variable factors (capital K & labor L) Technology still exogenous With Solow, population is exogenous econ c175 12

13 Solow s Neo-Classical Growth Model Our assumptions Full employment of labor and capital All savings gets invested Labor = constant proportion of population Output depends only on capital / labor ratio (i.e., no natural resources, absolute amount of capital or pop doesn t matter) econ c175 13

14 Other assumptions that could be made Savings rate increases with pop growth rate because fewer old dissavers (Modigliani) Technological progress is constant (easy) Technological progress depends on pop size (harder) (Boserup) Natural resource constraints (harder) (environmentalists, Samuelson) Demography depends on economy (harder) econ c175 14

15 Notation Capital per person = k = K/L Output per person = y = Y/L = f(k) s = savings rate; Savings per person = s y d = depreciation rate n = population growth rate (a.k.a. R ) (Note: we use this notation because it is in reading.) econ c175 15

16 Our production function 1. Total output is a function of capital and labor Y = f(k, L) 2. Diminishing returns in K or L if other is held constant 3. Constant returns to scale (e.g., if we double K & L, we double Y). Size doesn t matter since we don t have any fixed resources econ c175 16

17 For example Cobb-Douglas production function is often taken Y = f(k, L) = K a L 1-a, 0 < a < 1 Per capita, divide both sides by L More generally, Y/L = y = (K/L) a = k a y = f(k/l) = f(k, 1) = f(k) econ c175 17

18 Our picture Notation K = capital, k = per worker n = pop growth rate (our R ) Y = output; per worker: y = f(k) s = proportion of output saved Assumptions: 1. decreasing returns to capital 2. savings is proportional to output Output per worker per year (y) Per capita consumption Per capita savings y = f(k) s y capital per worker, k econ c175 18

19 What happens to capital per person over time? Without new capital investment, Population growth dilutes the capital per person at a rate of n per year Depreciation will reduce capital stock by a rate d per year In order to keep K/L ratio constant, we need to invest (n + d) K total, or (n + d) k per person econ c175 19

20 Investment required just to stay even K = $1 million of capital L = 1,000 workers k = $1,000 of capital per worker If population growth is 3% and depreciate rate is 7%, what will k be next year? $1 million * exp(-.07) $900 per worker 1,000 workers * exp(.03) à Must buy $100 of capital per worker to maintain k = $1,000 per worker econ c175 20

21 What savings rate? What aggregate savings rate allows investments of $100 per worker? If a worker with $1,000 of capital produces $400 of output, then s = 0.25 will keep k = K/L constant. econ c175 21

22 The steady-state: equilibrium k* is the steady-state amount of capital per worker y* is the steady-state output per worker (n+d) k = loss of capital per person per unit of time s y(k) = new investment per person Is this equilibrium stable? (next slide) y* Output per worker per year (y) y = f(k) (n+d) k s y(k) k* capital per worker, k econ c175 22

23 Malthus-like dynamics, except we can do everything on one picture y* Output per worker per year (y) y = f(k) (n+d)k s y(k) death rate of capital birth rate of capital k* capital per worker, k econ c175 23

24 Standard implications In the steady state, there is no change in output per worker, so what happens to size of economy? What happens if we increase savings rate? to level of output? to level of consumption? to long run growth rate? econ c175 24

25 Consequences of faster population growth? Let s find new steady state k* and new output y*. Is there anything we could do to keep old level of per capital output? econ c175 25

26 Consequences of faster pop growth To keep per capita income y constant, could save more and consume less Faster pop growth y = f(k) y* (n +d)k y* Output per worker s y(k) per year (y) With higher savings (n +d)k s y(k) k* k* capital per worker, k k* k* capital per worker, k econ c175 26

27 Price of population growth Reduced consumption If we compensate for higher growth by saving more, then consumption falls. If we don't save more, new steady state k*' < k*, y*' < y* and consumption still hurt econ c175 27

28 Can technology save us? A new technology allows us to increase output at all capital-labor ratios In short run, we're clearly better off How about long-run? (Let's check with app) econ c175 28

29 Conclusions: (Im) Possibility of Progress? Malthus Explains why pop stayed constant No growth in standard of living Technology gains disappear Demographic determinism [b(w) & d(w)] Solow Can support steady pop growth Still, no growth in standard of living BUT technology ratchets (gains are preserved) Production function determinism econ c175 29

30 Additional conclusions More capital (e.g., foreign aid ) won t change steady state output Faster population growth implies lower income (unless forego consumption and keep savings up) Key to growth is technology, not savings. Next time : Using Solow model to study inequality Piketty reading econ c175 30