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Trade and Growth

Trade and Growth. A Brief Tour. Suggested Reading. Aghion, Phillipe and Howitt, Peter (1998), Endogenous Growth Theory, MIT Press, Chapter 11 Note in particular that this chapter discusses Ventura (1997) which I have neglected. The Solow-Swan Model.

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Trade and Growth

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  1. Trade and Growth A Brief Tour

  2. Suggested Reading Aghion, Phillipe and Howitt, Peter (1998), Endogenous Growth Theory, MIT Press, Chapter 11 Note in particular that this chapter discusses Ventura (1997) which I have neglected

  3. The Solow-Swan Model • We have already seen (in Chapter 4) that the rate of growth of per capita income is given by the formula: (dy/dt)/y = ζ[sA{f[k,1]/k} -n ] (15) Trade (openness) could plausibly increase: • S • A

  4. Growth is not Efficiency The chief reason why trade does not necessarily increase growth is that growth is not a simple measure of good economic performance. In the original von-Neumann growth model maximal steady-state growth is the objective

  5. The von-Neumann Growth Model Theorem 2: If two or more von-Neumann growth models are allowed to trade with each other, either at predetermined relative prices (when there may be quantity rationing), or with voluntarily-negotiated quantitative trade agreements, the maximal balanced growth rate of no country can fall, and often maximal balanced growth rates will increase. Proof: The possibility of international trade is equivalent to adding extra activities to the input and output matrices of the model. As these additional activities need not be used, the maximal growth rate cannot fall. As the additional activities will be useful in many cases of interest, maximal growth rates may well rise.□

  6. The Ramsey von-Neumann Model Max Σ∞t=1U[ct]δt-1 0 < δ < 1(6) Subject to: Bxt-1 ≥ Axt + ct (7) Assume that consumption is proportional to c0 ≥ 0 although c0 will have many zeros. The level of consumption is measured by ct and utility can be written U[ct]

  7. Ramsey von-Neumann Model II The Lagrangean is Σ∞t=1U[ct]δt-1 + pt.[Bxt-1 - Axt – ctc0] (1) Maximization requires: U1[ct]δt-1- pt.c0 = 0 (2) pt.B– pt-1.A ≤ 0 (3) Where the inequalities (3) are complementary to xt-1 ≥ 0 Such a solution is called a Price Equilibrium

  8. CES Utility Function [1/(1-η)]ct1-η(8) Max: Σ∞t=1 [1/(1-η)]ct1-ηδt-1 (9) Bxt-1--Axt - ct c0 ≥ 0 (10) Lagrangean: Σ∞t=1 [1/(1-η)]ct1-ηδt-1 + pt{Bxt-1--Axt - ct c0} (11)

  9. The Steady-State Growth Menu ct-ηδt-1 - ptc0 = 0 (12) Pt+1B – pA ≤ 0 (13) In a Steady State: xt = (1+γ)t-1x0 (14) ct = (1+γ)t-1c0 (15) The Steady-State Growth Menu is the set of values c0 and γ that satisfy (14) and (15)

  10. Theorem 3 If a von-Neumann model with Ramsey optimization is allowed to trade with another economy growing at the same balanced growth rate, this will expand (strictly cannot contract) the said economy's steady-state growth menu. The consequence of this menu expansion for the choice of γ is ambiguous. Informal Argument: Note again that the possibility of international trade is equivalent to adding extra activities to the input and output matrices of the model. The benefit of having these additional activities need not be taken out as higher growth, because the growth rate is not being maximized. All that is certain is that the value of the objective function (6) can only increase as additional activities are made available.□

  11. A Simple Model of Endogenous Growth The Production Functions Oi = ni[liβi - αi] (16) Maxnl n[lβ-α] + λ[L - nl] (17) O is: α{(β-1)/β}βL(1/(1-β))-((1+β)/β) (24) Output is linear in L Oi = μiLi (25)

  12. Production equations Log consumption is: lnC = T + Oc (26) Total labour is 1. Lc is labour producing consumption The dynamic equation for T is: dT/dt = aμr(1 - Lc) (27)

  13. Maximization The Planner maximizes: ∫∞0U[T + μLc]e-δtdt (28) where U is the utility of the log of consumption Hamiltonian with p0 = 1 U[T + μLc]e-δt + p1aμr(1 - Lc) (29) U1[T + μLc]e-δt - p1aμr = 0 (30) The co-state variable condition dp1/dt = - U1[T + μLc]e-δt (31)

  14. An Optimal Condition Differentiating (30) totally with respect to time and taking into account (31) -(du/dt)/u = a(μr)/(μc) – δ (32) where u = U1 (32) Is like a Ramsey necessary condition but NB U is the utility of the log of consumption

  15. Translating the Optimal Condition Note that: dU[lnc]/dc = u/c (33) -[d/dt(dU[lnc]/dc)]/dU[lnc]/dc = (1/c)(dc/dt) + a(μr)/(μc) – δ (36) Consumption growth has the same effect as a reduction in the discount rate

  16. Try a Special Case U[lnc] = {1/(1-η)}e(1-η)lnc (37) This is the standard constant-elasticity function with its argument lnc Now (36) becomes: (1/c)(dc/dt) = (a(μr)/(μc) - δ)/η (38) The solution is always a steady-state

  17. Theorem 4 Theorem 4: Trade increases the steady state growth rate of the economy iff it increases the ratio μr/μc. Proof: By inspection of equation (23).□ To provide the intuition of this result it is only necessary to note that for trade to increase the growth rate it has to raise R&D efficiency relative to the efficiency of delivering current consumption. A similar point is made by Grossman and Helpman (1991), Innovation and Growth in the World Economy

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