Related questions with answers

Seafood price and quantity data are reported by the U.S. Census Bureau. Data for the years 2000 and 2009 follow.

	2000 Qty. (000 lbs.)	2000 Price ($/pound)	2009 Price ($/pound)
Halibut	75,190	1.91	2.33
Lobster	83,180	3.62	3.09
Tuna	50,779	1.87	1.97

a. Compute a price relative for each type of seafood.

b. Compute a weighted aggregate price index for the U.S. domestic seafood catch. Comment on the change in seafood prices over the nine-year period.

An item with a price relative of 132 cost $\$10.75$ in 2011. Its base year was 1994.

a. What was the percentage increase or decrease in cost of the item over the 17-year period?

b. What did the item cost in 1994

The retail price of gasoline is influenced by a variety of factors. From 2011 to 2014, the average retail price for a gallon of regular grade gasoline is shown in the table below.

\begin{array}{cc}\text { Year } & \text{ Average Price (\$) } \\ 2011 & 3.521 \\ 2012 & 3.618 \\ 2013 & 3.505 \\ 2014 & 3.358\end{array}

a. Starting with 2011, create a price index for the retail price of a gallon of regular grade gasoline over a four-year period. b. Using 2012 as the starting point, create a price index for the retail price of a gallon of regular grade gasoline over the next four years.

Question

A large manufacturer buys an identical component from three different independent suppliers, each with a different unit price and quantity supplied. The pertinent data for 2012 and 2014 are provided here.

Unit Price ($) Unit Price ($)

Supplier Quantity (2012) 2012 2014

A 150 5.45 6.00

B 200 5.60 5.95

C 120 5.50 6.20

a. Separately compute the price relations for each component supplier. Compare the price increases by suppliers over the last two years. b. In 2014, compute an unweighted aggregate price index for the component part. c. Create a weighted aggregate price index for the component part in 2014. What is the manufacturing firm's interpretation of this index?

		Unit Price ($)	Unit Price ($)
Supplier	Quantity (2012)	2012	2014
A	150	5.45	6.00
B	200	5.60	5.95
C	120	5.50	6.20

Solution

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a. Let $P_{i0}$ and $P_{it}$ be the prices of item $i=A,B,C$ in the earlier year and in the later year, respectively. The relative prices of items with earlier year as the base period, are:

r_i=\dfrac{P_{it}}{P_{i0}}\cdot 100

As indicated by formula, it is the later year price in percentages of the earlier base year price. Substituting the knowns find:

r_A=\dfrac{6}{5.45}=110,\quad r_B=106,\ r_C=113

The third firm raised its price the most, but all increases are about the same.

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	Shipments		Price/Shipment
Commodity	2000	2015	2000
A	120	95	$1200
B	86	75	$1800
C	35	50	$2000
D	60	70	$1500

	Quantity		Unit Price ($)
Item	2009	2011	2009	2011
A	1500	1800	7.50	7.75
B	2	1	630.00	1500.00

	Shipments		Price/Shipment
Commodity	2000	2015	2000
A	120	95	$1200
B	86	75	$1800
C	35	50	$2000
D	60	70	$1500

	Quantity		Unit Price ($)
Item	2009	2011	2009	2011
A	1500	1800	7.50	7.75
B	2	1	630.00	1500.00

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