\fPart a. (10 Marks) Assume there are four goods in the economy i.e. good 1' = 1, 2, 3, 4 PH = the market price of good i in month I 9;: = the quantity of good 1' produced in month 1' Show that the GDP deator is a weighted average of prices. Do the weights change over time? Why or why not? Part II). {10 Marks} Now assume that there are only three goods in the CPI basket i.e. good j=1,2,3 P]: = the market price of good 1 in month I Q; = amount of good j in the CPI's basket Show that the CF] is a weighted average of prices. Do the weights change over time? Why or why not