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Exercise: pegged exchange rate

  • Assume that the U.S government wants to start fixing its currency against the Mexican peso. Government officials estimate that the optimal exchange rate should be at one peso for $0.35.
  •  You are given the following information about the U.S market for Mexican peso:
  • Find how much peso does the U.S needs to buy or sell in order to achieve its targeted exchange rate.
    • Find the original equilibrium exchange rate: let the demand equal to the supply curve. Just like in the previous exercise, we see that one peso is worth half a U.S dollar and there are 6,250,000 pesos demanded at this price.
    • Now, in order to change the exchange rate, realize that the U.S government has access to U.S dollars (for the sake of the argument, assume the central bank is no longer independent). Then, it can only shift the demand for Mexican pesos in the U.S foreign exchange market.
    • Thus, there must only be a movement along the supply curve, set $=0.35 in the supply schedule and solve for p.
    • Now, calculate the gap between the new equilibrium exchange rate and the exchange rate given in the old demand:
    • Substract that gap from the original demand and obtain the new demand curve. Set the new demand curve equal to the supply curve and solve the system. We see that in order to obtain this new exchange rate, the U.S government needs to sell 1,500,000 worth of Mexican financial assets in order to buy back U.S dollars. This is the difference between the old and new equilibrium amount of Mexican pesos.
    • Note that since the Mexican peso is depreciating, it must be the case that the U.S dollar is appreciating. 
  • Let's graph that:

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