An economist studied a large data set of Mexican consumer prices covering episod

Question

An economist studied a large data set of Mexican consumer prices covering episodes of both high and low inflation. One of the goods in the study was milk. When the inflation rate was low, an average of 1.7 changes in the price of milk occurred each year. When the inflation rate was high, the price of milk changed more frequently-an average of 7.5 times each year. [Source: E. Etienne Gagnon, Price setting during low and high inflation: Evidence from Mexico, International Finance Discussion Papers, No. 896 (City: Board of Governors of the Federal Reserve System, 2007). The expected number of milk-price changes in a 1-month period is when inflation is low and when inflation is high. Assume that y, the number of price changes in any 1-month period, is described by a Poisson probability distribution with a mean equal to one of the values you just calculated (depending on whether the inflation rate is high or low). Then x, the number of months between consecutive price changes, is exponentially distributed with a mean of when inflation is low and a mean of when inflation is high Screen Shot 2018-07-01 at 3.21.58 PM Q Search The probability that the price of milk remains fixed for more than 3 months is when inflation is low and when inflation is high If the probability that the price of milk stays the same for 2 months or less is about 0.25, is Mexico's inflation rate high or low? O Low O High If Mexico is in a high inflation episode, the variance of x is

Explanation / Answer

the expected number of milk price change in a 1 mnth period is 1.7/12=0.1417 when inflation.........and 0.625 when inflation is high

exponential distribution with 7.0588(~7.06) months when inflation is low and a mean of 1.6 months when inflation is high

the probability...........is e-3/7.0588 =0.6538 when inflation is low and e-3/1.6 =0.1534 when inflation is high

if the probability.......................high

variance of x is =1.62 =2.56

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