Three Lectures on Economic Growth. and International Trade. Robert E. Lucas, Jr. Wuhan University. June 16-17, 2004

Transcription

1 Three Lectures on Economic Growth and International Trade Robert E. Lucas, Jr. Wuhan University June 16-17, 2004

2 Plan of Lectures: Ricardian Theory of a Pre-Industrial Economy Fertility and Sustained Growth General Equilibrium Analysis of the Eaton-Kortum Model of International Trade (joint research with Fernando Alvarez)

3 Aim of Lectures: Believe that economic growth and development are closely related to the economics of the family, and the economics of international trade.

4 Theory has made progress toward understanding these connections, but we have not yet succeeded in finding a unified theory. Will not offer a solution in these lectures. Will bring you as close to the current research frontier as I can.

5 Procedures: Speak for one hour, fifteen minutes; ten minute break; complete lecture. Questions welcomed at any time.

6 Ricardian Theory of a Pre-industrial Economy Robert E. Lucas, Jr. Wuhan University June, 2004

7 Outline 1. Malthusian fertility theory: Dynastic preferences 2. Equilibrium in three societies (a) A hunter-gatherer society (b) An egalitarian, landowning economy (c) A two-class economy of workers and landowners 3. Assessment of Ricardian theory: influence, strengths, weaknesses

8 Recommended readings: David Ricardo (1817). Principles of Political Economy and Taxation. Piero Sraffa edition, Cambridge University Press, Robert E. Lucas, Jr. Lectures on Economic Growth, chapter 5, sections 3,4. Harvard University Press, 2002.

9 World Population and Production Population (M), Production (B $1985) Population Production

10 World Growth, Annual growth rate of (Percent) Population Real GDP GDP per capita

11 18000 GDP per capita, five regions Dollars Population in millions UK, USA, Canada, Australia, New Zealand 354 Japan 124 France, Germany, Netherlands, Scandinavia 184 Rest of Western Europe, Eastern Europe, Latin America 986 Asia (except Japan), Africa 3590

12 Dynastic Preferences Utility u t of member of generation t depends on c t his own lifetime consumption, n t u t+1 the number of children he has, and the utility each of his children will have: u t = W (c t,n t,u t+1 )

13 Solving forward, he cares about all of his descendants and the consumption they will enjoy: u t = W (c t,n t,w(c t+1,n t+1,w(c t+2,n t+2,...))) Log example: W (c t,n t,u t )=ln(c t )+η ln(n t )+βu t+1. Solving forward: u t = X s=0 β s [ln(c t+s )+η ln(n t+s )]

14 Examine the implications of these preferences in three societies: A hunter-gatherer economy. An egalitarian, landowning economy A two-class economy of workers and landowners

15 A Hunter-Gatherer Economy Population of N t families; identical preferences W. Fixed amount L of land, territory, resources: not privately owned Total production: Y = F (L, N), F CRS. Production per capita: y = Y/N = F (L/N, 1) = f(x),x= L/N

16 Family s decision problem: max n W (y t kn,n,u t+1 ) First-order condition: kw c (y t kn, n, u t+1 )=W n (y t kn, n, u t+1 ).

17 The equilibrium conditions are u t = W (c t,n t,u t+1 ), kw c (c t,n t,u t+1 )=W n (c t,n t,u t+1 ), x t+1 = x t /n t, c t + kn t = f(x t ). Four equations in the state-like variables x t and u t and the flow-like variables c t and n t.

18 Steady state must satisfy: n t =1;u t = u t+1 = u; then(c, u) satisfy u = W (c, 1,u), (*) kw c (c, 1,u)=W n (c, 1,u). Solve (*) for u = g(c), say. Define the steady state MRS function m(c) m(c) = W n(c, 1,g(c)) W c (c, 1,g(c)). Steady state consumption c m solves m(c) =k.

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20 Logarithmic example: m(c) = ηc = c m = k η Full dynamics: x t+1 = k( 1+η η )[x t/f(x t )]. If f(x) =Ax α, x t+1 = k A (1+η η )x1 α t

21 Note properties of equilibrium behavior: Since α (0, 1), the steady state is a stable equilibrium. Long-run consumption c m does not depend on resources L or the technology parameter A In the short-run, increases in L or A result in increased consumption per person In the long run, increases in L or A result only in increases in population (decreases in x)

22 HUNTER-GATHERER SOCIETY

23 Discussion of theory Ricardo or Malthus? Arithmetic versus geometric growth? Modelofanimalpopulations? Model of property-less workers? Model of catastrophic population growth?

24 An Egalitarian, Landowning Economy Family s decision problem: subject to: µ v(x) =max c,n W c, n, v( x n ), c + kn f(x). Here the utility of an individual dynasty head is expressed as a function v(x) of his landholdings x. By passing on x/n to each of his n children, he determines their utility levels v(x/n).

25 First-order and envelope conditions: W n (c, n, v( x n )) W u(c, n, v( x n ))v0 ( x n )( x n 2) = kw c (c, n, v( x n )), v 0 (x) =W c (c, n, v( x n ))f 0 (x)+w u (c, n, v( x n ))v0 ( x n )(1 n ).

26 Full dynamics: Let u t = v(x t )andq t = v 0 (x t ). u t = W (c t,n t,u t+1 ), kw c (c t,n t,u t+1 )=W n (c t,n t,u t+1 ) W u (c t,n t,u t+1 )q t+1 x t+1 ( 1 n 2 t ), q t = W c (c t,n t,u t+1 )f 0 (x t )+W u (c t,n t,u t+1 )q t+1 ( 1 n t ), x t+1 = x t /n t, c t + kn t = f(x t ). Five equations in the state-like variables x t,q t, and u t and the flow-like variables c t and n t.

27 Steady state: n =1,u= v(x), q= v 0 (x). u = W (c, 1,u), kw c (c, 1,u)=W n (c, 1,u) W u (c, 1,u)qx, q = W c (c, 1,u)f 0 (x)+w u (c, 1,u)q. c + k = f(x). Define g(c), m(c) asabove. Letρ(c) =(1 W u )/W u, adiscountrate. Then m(c) =k + f 0 (x)x ρ(c).

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29 In log/cobb-douglas case, m(c) = ηc and ρ(c) =(1 β)/β, so c + k = Ax α, ηc = k + β 1 β αaxα. If (1 β)η >αβ,wecansolvethesetwoequationsfor: c e = 1 β + αβ k, (*) (1 β)η αβ Ax α (1 β)(1 + η) = (1 β)η αβ k. If α = 0, this reduces to the last model.

30 To derive the full dynamics for the log/cobb-douglas case, solve µ v(x) =max n W f(x) kn, n, v( x n ) for the value function v(x). (FE) Method? Guess and verify. Conjecture a solution of the form v(x) =C + D ln(x) Insert conjectured solution into (FE) Find values of C and D (if any) such that (FE) holds.

31 The application of this method yields: v(x) =C + α 1 β + η 1 β + αβ ln(x), n(x) = Ã η αβ 1 β + η! Ax α k. The implied dynamics are: x t+1 = k A Ã 1 β + η η αβ! x 1 α t.

32 Note properties of equilibrium behavior in this case Since α (0, 1), the steady state is a stable equilibrium. αβ > 0, so the SS consumption level c e givenin(*)exceedsthelevel c m for the case where resources are owned in common. The difference, which can be large, measures the benefits of a private property system over a system of common property But in both cases, long-run consumption does not depend on total resources L or on the technology parameter A In the long run, increases in L or A result only in increases in population (decreases in x)

33 HUNTER-GATHERER SOCIETY

34 A Two-Class Economy of Workers and Landowners Same technology, resources as last example. Different ownership arrangements. Total population N divided into workers and landowners N = N w + N Workers own no land Landowners do no work.

35 State variable of system is x = L/N w =landl per worker N w Each worker receives wage income w - marginal product of labor, f(x) xf 0 (x) A landowner with z units of land receives land rents f 0 (x)z

36 In this economy, a worker s situation is exactly the same as a huntergatherer s, except that his income in the marginal product f(x) xf 0 (x) of labor instead of the total product f(x). Again, the equilibrium conditions are u t = W (c t,n t,u t+1 ), kw c (c t,n t,u t+1 )=W n (c t,n t,u t+1 ), x t+1 = x t /n t, c t + kn t = f(x t ) x t f 0 (x t ). Four equations in the state-like variables x t and u t and the flow-like variables c t and n t.

37 Steady state must satisfy: n t =1;u t = u t+1 = u; then(c, u) satisfy u = W (c, 1,u), (*) kw c (c, 1,u) = W n (c, 1,u). Solve (*) for u = g(c), say. Define the steady state MRS function m(c) m(c) = W n(c, 1,g(c)) W c (c, 1,g(c)). Steady state consumption c m solves m(c) =k.

38 Then steady state land per worker, x = L/N w, is given by the budget constraint c m + k = w = f(x) xf 0 (x). Given c m, this equation fixes x. Given L, the this fixes the number of workers N w.

39 Logarithmic example: m(c) = ηc = c m = k η All of this exactly as in the hunter-gatherer case: Landless worker has nothing to leave to his children; faces no quantityquality tradeoff.

40 If f(x) =Ax α, then the marginal product of labor is f(x) xf 0 (x) =(1 α)ax α Thefulldynamicsare x t+1 = k (1 α)a (1+η η )x1 α t. All of these dynamics worked out independently of behavior of landowners.

41 Landowners income consists of land rents only. They solve v(z) =max c,n W (c, n, v(z/n)) subject to c + kn f 0 (x)z.

42 Landowner s SS consumption, c, solves m(c) = k + f 0 (x)z ρ(c). Budget constraint implies f 0 (x)z = c + k. Combine to get m(c) = k + c + k ρ(c). Solve for c > c m. Note that both c and c m are independent of the technology.

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44 In log/cobb-douglas case c m = k η and, provided η(1 β) >β, c = k η(1 β) β. Population of workers is given by x = L/N w and c m + k =(1 α)ax α..

45 Population of landowners is given by equality of total land rentals and total landowner consumption: which implies N w xf 0 (x) =N (c + k), N /N w = α η(1 β) β. 1 α η(1 β)

46 Note properties of equilibrium behavior in this two-class case In two-class economy, it continues to be the case that no one s longrun consumption depends on total resources L or on the technology parameter A :Seeformulasforc m and c. But c is necessarily larger than c m (becauses only landowners face a quantity-quality tradeoff) and possibly much larger (if η(1 β) β is near zero). Consistent with high civilization. Upward mobility (workers that buy land and become landowners) does not occur in this equilibrium, but this is an assumption of the theory, not a conclusion from the theory.

47 Evaluation of Ricardian theory Ricardo wrote in 1800, on the eve of the industrial revolution Tried to understand world of vast within-society inequality and very little across-society inequality First systematic theory of the determination of population, production, and distribution Accurate, operational theory of workings of pre-industrial societies

48 18000 GDP per capita, five regions Dollars Population in millions UK, USA, Canada, Australia, New Zealand 354 Japan 124 France, Germany, Netherlands, Scandinavia 184 Rest of Western Europe, Eastern Europe, Latin America 986 Asia (except Japan), Africa 3590

49 Influence of Ricardian theory amplified by Marx All history is... class struggle economics or politics? Landowners and capitalists Capitalism up to 1950 Predictions for the future Legacy of Ricardo/Marx

50 Homework Exercise 1: One-Child Policy Consider a Ricardian economy of farm families of equal-size. Suppose this economy is in a steady state, for given technology, so that n =1. Suppose that the government now imposes the constraint on the birth rate. n θ<1 (a) What is the immediate (first generation) effect of the policy on consumption, land inheritances, and family welfare W? (b) What are the dynamic consequences if this policy is maintained forever? (c) What are the dynamic consequences if this policy is maintained for T generations and then discontinued?