Market Clearing in World Capital Markets PDF

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Market Clearing in World Capital Markets...

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Market Clearing in World Capital Markets In equilibrium the world current account balance has to be zero, that is, CAC1 + CAUS 1 = 0. (6.11) Can you verify that this equation implies that in equilibrium the world endowment of goods is equal to world wide absorption, that is, CUS 1 + CC 1= 3 2 Q and CUS 2 + CC 2 = 2Q.

6.6.2 Equilibrium Under Free Capital Mobility Consider first the case that there is free capital mobility in both countries. Then in equilibrium the interest rate must be the same in both countries, that is, r1 = rc1 . (6.12) In this case the world interest rate is determined as the solution to (6.11). Combining (6.10), (6.5), (6.12), and (6.11) yields: 1 2 Q r1 1 + r1 + Q 4− 1 2 Q 1 + r1 =0 Solving for r1, we obtain r1 = 1 3 . It follows that under free capital mobility the world interest rate is 33 percent. Using this information, we can find that CUS 1= 1 2 _ Q+ Q 1 + 1/3 _ =

7 8 Q CAUS 1 = Q − CUS 1= 1 8 Q Country US consumes 7 8 of its endowment and saves the rest. Hence it runs a current account surplus of 1 8Q. It follows that the current account deficit of country C must be equal to −1 8Q, that is, CAC1 =− 1 8 Q. And thus consumption in country C is given by CC 1= Q 2 − CAc 1= 5 8 Q. In period 2, country US consumes CUS 2 = QUS 2 + (1 + r1)BUS 1= Q + 4 3 1 8 Q= 7 6 Q. And country C consumes CC 2 = Qc 2 + (1 + r1)Bc1 =Q− 4 3 1 8 Q= 5 6 Q.

The level of welfare under free capital mobility can be found by evaluating the utility function at the respective equilibrium consumption levels: U(CUS 1 , CUS 2 ) = lnCUS 1 +lnCUS 2 = ln 7 8 Q+ln 7 6 Q = ln _ 49 48 Q2 _ = ln � 1.0208Q2_ (6.13) and welfare in country C is equal to U(Cc 1, Cc 2) = lnCc 1 + lnCc 2 = ln 5 8 Q + ln 5 6 Q = ln _ 25 48 Q2 _ = ln � 0.5208Q2_ Can you show that both countries are better off under free capital mobility than under financial autarky?...