Intertemporal Approach to CA

Intertemporal Approach to CA

1. Small 2-period Endowment Economy (Closed Economy)

   • U = u(C1) + bu(C2)
     • max(C1) u(C1) + bu[(1+r)(Y1-C1)+Y2]
       • bu'(C2)/u'(C1) = 1/(1+r)
         • MRS = Relative price
           • Equilibrium in Autarky: C* = Y*
             • b>1/(1+r) => C1<C2
             • b<1/(1+r) => C1>C2
             • b=1/(1+r) => C1=C2
   • C1 + C2/(1+r) = Y1 + Y2/(1+r)
     • C2 = (1+r)(Y1-C1) + Y2
   • CA
     • iin 2 period, CA deficit in T1 = CA surplus in T2
       • rA < r
         • CA1>0
           • Export in T1 Import in T2
       • rA > r
         • CA1<0
           • Import in T1 Export in T2
     • Y1 increase => rA decrease as they cannot save without lending abroad
       • Y2 increase => rA increase as they cannot consume more without borrowing from abroad
         • rA > r => CA<0
       • rA < r => CA>0
       • Temporary change in output

2. Investment

   • C1 + I1 + (C2+I2)/(1+r) = Y1 + Y2/(1+r)
     • F'(K2) = r
       • Producers maximise their profits if the marginal return on period 1 investment is equal to that on a foreign loan
         • Extra Investment, gains from trade with higher rA
     • Y = F(K)
     • Kt+1 = Kt + It

3. Two-Region World Economy

   • Walras' law
     • S1 + S1* = 0
       • AB(lend)= B*A*(borrow)
         • rA < r < rA*

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