12 May ulia is interested in exploring the average consumption of sp
ulia is interested in exploring the average consumption of spirits in various regions over the past 10 years. She also wants to compare the percentage changes in consumption of spirits over time across regions.
She has information from many countries on the per capita consumption of various types of spirits (Brandy, Gin, Vodka, and Other spirits) from 2001 to 2011. She also has population figures for these countries over the same time period.
Use the following symbols:
Bij = Per capita Brandy consumption in country i in the year j
Gij = Per capita Gin consumption in country i in the year j
Vij = Per capita Vodka consumption in country i in the year j
Xij = Per capita consumption of other spirits in country i in the year j
Pij = Population of country i in the year j
Sj = Total consumption of spirits in Scandinavia in the year j
Bj = Total consumption of spirits in the Balkans in the year j
Yj = Average consumption of spirits in Scandinavia in the year j
Zj = Average consumption of spirits in the Balkans in the year j
m = the number of countries in the Balkans
Use 2001 as the reference year, that is, j = 0 in the year 2001
The first region Julia is interested in is Scandinavia. She knows that there are six countries generally considered to be Scandinavian (Sweden, Norway, Denmark, Finland, Iceland and Faroe Islands). In order to calculate the average consumption of spirits per person in Scandinavia, Julia will first need to calculate the total consumption of spirits in the region by adding the total consumption per capita in each country, multiplied by the population of that country.
a. Using summation notation, complete with the correct subscripts, give the formula for the total consumption of spirits in Scandinavia (for the year j). Use the symbols defined above.
b. To calculate the average consumption of spirits per person in Scandinavia Julia will need to divide the total consumption of spirits by the total population. Using summation notation, complete with the correct subscripts, give the formula for the average (per capita) consumption of spirits in Scandinavia (for the year j). Use the symbols defined above.
The second region Julia is interested in is the Balkans. She is not sure yet exactly which countries she is going to include as part of this region.
c. Give the formula for the average consumption of spirits per person for the Balkans, using the symbols defined below.
d. Using symbols defined below, give a formula for the percentage change in the average consumption of spirits in Scandinavia from the base year (2001) to the year j. (Define your own symbol to represent this percentage change.)
e. Julia would like to know how much higher the average consumption of spirits was in the Balkans than in Scandinavia in 2009. Using the appropriate subscripts and symbols defined below; give a formula for the percentage difference in average consumption of spirits in the Balkans as compared to Scandinavia in 2009.
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