Question

In: Statistics and Probability

A certain manufacturing company has the following data on quantities shipped and unit costs for each...

A certain manufacturing company has the following data on quantities shipped and unit costs for each of its four products.

Products	Base-Period Quantities (Year 1)	Mean Shipping Cost per Unit ($)
Products	Base-Period Quantities (Year 1)	Year 1	Year 5
A	2,500	10.50	15.90
B	5,000	16.25	31.00
C	6,500	12.20	17.40
D	2,500	20.00	35.50

Use the price data to compute a Paasche index for the shipping cost if year 5 quantities are 4,000, 3,000, 7,000, and 3,000 for products A, B, C, and D, respectively. (Round your answer to the nearest integer.)

I₅ =

Products	Base-Period Quantities (Year 1)	Mean Shipping Cost per Unit ($)
Products	Base-Period Quantities (Year 1)	Year 1	Year 5
A	1,500	10.50	15.90
B	5,000	16.25	31.00
C	6,500	12.20	17.40
D	2,500	20.00	35.50

Use the price data to compute a Paasche index for the shipping cost if year 5 quantities are 3,500, 3,000, 7,000, and 3,000 for products A, B, C, and D, respectively. (Round your answer to the nearest integer.)

I₅ =

Expert Solution

Answer:

1)

Product	Quantity	Year 1, (base year)	Year 5, (Obs year)	*Quantityobs cost**	*QuantityBase cost**
A	2500	10.50	15.90	2500*15.9 = 39750	2500*10.5 = 26250
B	5000	16.25	31.00	5000*31 = 155000	5000*16.25 = 81250
C	6500	12.20	17.40	6500*17.4 = 113100	6500*12.2 = 79300
D	2500	20.00	35.50	2500*35.5 = 88750	2500*20 = 50000
Total				393600	236800

Price index = 393600/236800 *100 = 166.216 166

[OR]

1)

Paasche price index formula =

In our case we have our observational year as year 5 and base year as year 1.

Product	Year 5 (Obs qty)	Shipping Cost	obs qty * obs cost	Obs qty * Base cost
Year 1 (base year)	Year 5 (Obs year)
A	4000	10.5	15.9	400015.9 = 63600*	400010.5= 42000*
B	3000	16.25	31	93000	48750
C	7000	12.2	17.4	121800	85400
D	3000	20	35.5	106500	60000
Total				384900	236150

Passche index = 384900/236150 = 162.98 163

Final Answer : Paasche price index = 163

2)

Paasche price index formula =

In our case we have our observational year as year 5 and base year as year 1.

Product	Year 5 (Obs qty)	Shipping Cost	obs qty * obs cost	Obs qty * Base cost
Year 1 (base year)	Year 5 (Obs year)
A	3500	10.5	15.9	350015.9 = 55650*	350010.5= 36750*
B	3000	16.25	31	93000	48750
C	7000	12.2	17.4	121800	85400
D	3000	20	35.5	106500	60000
Total				376950	230900

Passche index =376950/230900 = 163.25 163

Final Answer : Paasche price index = 163

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