The Argentine peso was fixed through a currency board at Ps$1\mathrm{.}00=$ $$1\mathrm{.}00$ throughout the $1990$s$.$ In January$2002,$ the Argentine peso was floated. On January$29,2003,$ it was trading at Ps$3\mathrm{.}19=$ $$1\mathrm{.}00.$ During that$$ one$-$year period,$$ Argentina's inflation rate was $21\%$ on an annualized basis. Inflation in the United States during that same period was $2\mathrm{.}5\%$ annualized.

Argentine Float. The Argentine peso was fixed through a currency board at Ps$1\mathrm{.}00=$$$1\mathrm{.}00$ throughout the $1990$s$.$ In January $2002,$ the Argentine

peso was floated. On January $29,2003,$ it was trading at $Ps3\mathrm{.}19=$$$1\mathrm{.}00.$ During that one$-$year period, Argentina's inflation rate was $21\%$ on an

annualized basis. Inflation in the United States during that same period was $2\mathrm{.}5\%$ annualized.

a$.$ What should have been the exchange rate in January $2003$ if PPP held?

b$.$ By what percentage was the Argentine peso undervalued on an annualized basis?

c$.$ What were the probable causes of undervaluation?