USING EXTERNAL PRICE INDEXES$$PROBLEM $1$ In June $2012,$ a buyer entered into a three$-$year agreement with a supplier that provides plastic water pipe. Among other things, this agreement features fixed pricing over the life of the agreement. It is now March $2015,$ and the agreement with this supplier is up for review and possibly renewal. While the supplier$$s over$-$all performance has been excellent, the supplier has already indicated it intends to seek a $3\%$ price increase to cover what it calls escalating costs. The time has come to start thinking about renewing this contract. Please answer the following questions using the data in Table $10\mathrm{.}1.1.$ What is the average PPI for this item for $2012,2013,$ and $2014?$ Do you believe the price index for this item is relatively stable or volatile?$2.$ In retrospect, was the decision to pursue fixed pricing with this supplier a good economic decision from the buyer$$s perspective? Why or why not? Provide quantitative evidence.$3.$ What was the percent change in the index from June $2012$ to July $2012?$ What was the percent change from January $2014$ to April $2014?$ What could have caused these changes in prices and therefore, the index?$4.$ If the buyer intends to renew the agreement for another two years with this supplier, do you feel the $3\%$ price increase is reasonable? Why or why not? What other information might you need to know to make an informed decision?$5.$ What type of pricing arrangements or language would you propose for this contract if it is renewed?