Finance 475 

Solutions to Problem Set #6

1)   Both  the U.S. and Britain are both following a gold standard;  the US price of gold is $35 and the British price of gold is L25. The PPP implied exchange rate  between the US and Britain should be 35/25 = $ 1.40 per British pound.

2)   With a gold standard, the U.S. must be committed to buying/selling gold at the fixed price.

    1. If new gold deposits were discovered, the market price of gold would fall (due to increased supply). The US would be forced to buy up the extra gold. This would increase the US money supply causing higher prices.
    2. An increase in demand for gold would drive up the price of gold. To maintain a constant gold price, the US would be forced to sell gold. This would contract the US money supply and lower US prices.
    3.  If the US us the only country following a gold standard, then - in principle, nothing will happen.  If the US can' t attract enough capital inflow (i.e. selling US assets) to finance the deficit, the dollar will depreciate in currency markets which should correct the trade imbalance. However, if the world believes that the US will devalue (i.e. raise the dollar price of gold) in the near future, they will react by buying gold today (selling dollars). This will put a strain on the US central bank (they must continue supplying gold to the market to offset the increased demand. If the "run" on the dollar is big enough, the US will be forced to either devalue (thus reinforcing everyone’s expectations) or abandoning the gold standard all together. However, if other countries are also following a gold standard, the depreciation of the dollar in currency markets will create an arbitrage opportunity in gold (buy gold from the Treasury and sell it overseas).  The loss of gold and subsequent contraction of the money supply should lower US prices and correct the imbalance.
3) Suppose the recent depreciation of the dollar has prompted several interventions by the Federal Reserve.
    1. An intervention by the Fed in defense of the dollar would involve buying dollars with their stock of foreign reserves. Note that this would also reduce the quantity of dollars in circulation and hence, the  money supply.

      Assets                           Liabilities

      (-) Foreign Assets                 (-) Currency in circulation

    2. To sterilize the intervention, the Fed would have to offset the intervention with a domestic open market operation (a purchase of domestic assets)

Assets                          Liabilities

(-) Foreign Assets                 (-) Currency in circulation

(+) Domestic Assets             (+) Currency in circulation

4) The monetary model of exchange rates implies that a fixed exchange rate results in the following monetary policy rule:

M = (e)(M*)(Y/Y*)( i*/i)

    1. A recession in Saudi Arabia would result in a depreciation of the Riyal (as Y decreases). Therefore, the central bank would be required to decrease the Saudi money supply in response.
    2. A reduction in the world price of oil (a terms of trade deterioration) would result in a real (and, hence, nominal) depreciation of the Riyal. The Saudi government would again be forced to contract the money supply.
    3. The monetary model assumes that money supply has no repercussions on the domestic economy (i.e., reducing the money supply will not contract output, raise interest rates, etc), so there is no conflict between external balance and internal balance. However, note that each of the above events results in a loss of foreign reserve assets. If a recession or price change is persistent enough to use up all of the Saudi reserves, they will be forced to either devalue or abandon the fix.

5) When prices are fixed, we need to look to currency markets to understand the direction of the exchange rate. Lower income brought on by a recession will most likely increase domestic savings (while lowering domestic investment).  Assuming that the government deficit is fixed, this will lower domestic interest rates (this will hurt the ability of the US to attract foreign capital), but also reduce the trade deficit. 

  1. If capital is mobile, then the interest rate effect wins out and the Real depreciates.  The Bank of Brazil is forced to use foreign reserves to defend their currency. 
  2. If capital is immobile, then lower interest rates do not significantly influence capital flows and the lower trade deficit causes the Real to appreciate. The Bank of Brazil now must supply Real to the market to keep the Real from appreciating.
  3. While capital can be somewhat immobile in the short run, in the long run, capital is quite mobile. As in (4), fixed exchange rates are very difficult to maintain during bad economic times.