Question

The following table reports prices and usage quantities for two items in 2009 and 2011. (Round your answers to the nearest integer.) Quantity Unit Price ($) 2009 2011 Item A B 1,500 1,800 2009 2011 8.50 7.55 630.00 1,500.00 2 (a) Compute price relatives for each item in 2011 using 2009 as the base period. Item Price Relative А B (b) Compute an unweighted aggregate price index for the two items in 2011 using 2009 as the base period. 12011 = (c) Compute a weighted aggregate price index for the two items using the Laspeyres method using 2009 as the base period. 12011 = (d) Compute a weighted aggregate price index for the two items using the Paasche method using 2009 as the base period. 12011

Answer 1

Solution item we have to compute ptice delatives fore each poll wing 200g as the base period Xloo) Price relative Formwa! Σ Po N Chede obse&vation table (I) 2oog is the base period) Unit Peice ($) Price Zelotive Item 2011 P y 100 Quantity 200g 2011 ge 9 1,500 1,800 4 A Toss 200g Po P, Po 8.50 88.82 630.00 1,500.00 238.09 EL=638.5 3P=1507.55 (21.7100) = 326.91 B 2 Po Price delative I PT Pa here total no. items i.e. N=2 : Paice belatives 163.455 326.91 2 Price telative - 163.455 ñ 164 We have to compute unweighted aggdegate peice index fore the two items in 2011 wing 2009 as the base pesiod. Formwa: Wnweighted aggregative poire index is given by, EP, Izoll EPo Por

we know the : Por from the obseevation table (I) EPo = 638.5 & EP, = 1507.55 Unweighted aggdeg ate peice index is, ΣΡ 150%.55 X 100 - 2.36 v 3 ΣΡ. 638.5 :| Pol = 3 ic. I 2011=3 c) we have to compute a weighted agg&egate ptice index fore too items using the Laspeye es method wing 2009 as the base pesiod. X100 Formula: Laspeydes price index numbee is given by, s Pilo. I 2011 Por(La) = EPogo here 2009 is the base petiod. obsecvation table Quantity Unit Pere ($) Item 2009 2011 2009 9. Po Pi P,90 2011 9 Potlo A 11500 1800 8.50 7.55 11325 12750 4 2 630.00 1,500.00 B 6ooo 2520 EP,90=17325 EPogo=15270 .. Laspeyces poice index number is given by, ΣΡ 9ο I 2011 = Poilla) = I Polo X 100 17325 x 100 15270 Izoll Pol(La)= 113.45 % 114 : Laspeydes price index numbe & = 114

d) We have to compute weighted aggdegate price index fore two items wing the Paasche method wing 200g as the bale period. Formula! Paasche's peice index number is given by, Ep.9, Poia) x Too Poli here 2oog is the base pesod Item obsequation table Quantity Unit peice ($) 200g 2011 2009 2011 91 Po P 1500 18oo 8.50 7.55 Pixgi Poxa, A 135go 15300 B. 4 2 630.00 1500.00 3000 1260 EP,9,-16590 EPot=16560 . Paasche's price index numbee is, E Pigi Pol (pa) Epoqi 165go 16560 X 100 I 2011 | Pol (Pa) = 100.18 o lol

Hence, a) Item A Peire Belative 88.82 % 89 238.09 V 239 B b) I2011 = unweighted aggregate price index numbe & = 3 c) weighted aqaaegate parce index wing Laspeyces method, Izoll =114 d) weighted aggdegale peice index wing Paasche method I 2011 = lol