This question considers long-run policies in Mexico relative to the US. Assume Mexico's money growth rate is currently 14% and its growth rate of real income is 2%. The US's money growth rate is 6% and its growth rate of real income is 3.75%. The world real interest rate is 1.75%.
For the following questions, use the conditions associated with the general monetary model. Treat Mexico as the home country (define the exchange rate as Mexican pesos per US dollar).
a. Calculate the inflation rates in Mexico and the US.
b. Calculate the nominal interest rate in each country.
c. Calculate the expected rate of depreciation of the Mexican peso relative to the US dollar.
d. Suppose the Central Bank of Mexico increases the money growth rate from 14% to 19%. If nothing in the US changes, what is the new inflation rate in Mexico, and what is the new expected rate of depreciation of the Mexican peso relative to the US dollar?
e. Illustrate how the change in Mexico's money growth rate affects the time paths of the following variables: MM , PM , Mexico's real money supply, and E.
f. Suppose instead that the Mexico decreases the money growth rate from 14% to 9%. If nothing in the US changes, what is the new inflation rate in Mexico, and what is the new expected rate of depreciation of the Mexican peso relative to the US dollar?
g. Suppose the Central Bank of Mexico wants to implement a policy that would cause the Mexican peso to appreciate relative to the US dollar. What range of the money growth rate would achieve this objective? What range of values does this imply for Mexico's inflation rate?
i. Suppose that Mexico's central bank wants to maintain a fixed exchange rate against the US dollar. Assuming that nothing in the US changes, what must the central bank do to achieve this objective? What money growth rate for Mexico will make a fixed exchange rate feasible? Explain. j. Calculate Mexico's new inflation rate and nominal interest rate after this policy is implemented.
k. Suppose Mexico's growth rate of real income increases from 2% to 4%. If Mexico wants to maintain the fixed exchange rate with the US dollar, how must it change its policy?
l. Now suppose that the US's inflation rate increases by 1.5 percentage points. If Mexico wants to maintain the fixed exchange rate, what will happen to its inflation rate? What is the necessary change in Mexico's money supply growth rate?