smartphone ownership in Australia

Smartphone ownership in Australia increased from 11.1 million on 30 June 2013 to 15.3 million by the end of 2015. Assuming that Australian smartphone ownership will continue to expand at the same rate as it did between 2013 and 2015, calculate: Total smartphone ownership in Australia at the end of 2020. [5 marks]

In order to estimate smartphone ownership in Australia, we need to develop a prediction equation. We'd need to figure out the intercept for the equation as well as the rate or slope.

The intercept represents the initial smartphone ownership at the start of the prediction period. As a result, intercept = 11.1 million. To determine the rate of increase, we need to divide the increase in smartphone ownership by the length of time in months.

Increase in smart phone ownership = 15.3m – 11.1m = 4.2 million

Time = 5/2 years = 30 months

Rate = 4.2 million/30 = 140,000

Equation: Smartphone ownership = 11.1 million + 140,000 X where X is the number of months after 30th June 2013.

To determine the total smartphone ownership by the end of 2020 we need to determine the number of months first. There are 78 months between 30th June 2013 and 31st December 2020.

Therefore, total smartphone ownership by end of 2020 = 11.1 million + (140,000*78) = 22,020,000.

Smartphone ownership = 22.02 million

in which calendar year Australian smartphone ownership will reach 22 million. [5 marks

Using the equation, we would determine the number of months till the total smartphone ownership is 22 million.

22 million = 11.1 million + 140,000 X

140,000 X = 22 million -11.1 million

140,000 X = 10.9 million

X = 10.9 million / 140,000 = 77.86 months

Therefore, smartphone ownership will reach 22 million in 2020.

Given below is quintile distribution of average household weekly income in Town A and Town B.

Quintile

Number of households

Average weekly household income ($) in town A

Average weekly household income ($) in town B

Q1

200

500

900

Q2

200

900

1050

Q3

200

1250

1250

Q4

200

1450

1300

Q5

200

1800

1400

Calculate Gini Coefficient of average weekly household income in Town A and Town B (Please keep 4 decimal places for all percentages and 2 decimal places for Gini coefficients. You must show necessary working steps). [10 marks]

Quintile

Number of households

Average weekly household income ($) in town A

Share of total income (%)

Cumulative share of income

Cumulative share of total population

Area

Q1

200

500

8.4746%

8.47%

20%

84.7

Q2

200

900

15.2542%

23.7288%

40%

321.988

Q3

200

1250

21.1864%

44.9153%

60%

686.441

Q4

200

1450

24.5763%

69.4915%

80%

1144.068

Q5

200

1800

30.5085%

100.0000%

100%

1694.915

Total

5900

3932.112

Gini coefficient = [(100*100/2) – 3932.112]/[100*100/2]

Gini coefficient (Town A) = (5,000 – 3,932.112) / 5000 = 0.2136 or 21.36%

The table below shows the calculation of the gini coefficient for Town B

Quintile

Number of households

Average weekly household income ($) in town A

Share of total income (%)

Cumulative share of income

Cumulative share of total population

Area

Q1

200

900

15.2542%

15.2542%

20%

152.542

Q2

200

1050

17.7966%

33.0508%

40%

483.05

Q3

200

1250

21.1864%

54.2373%

60%

872.881

Q4

200

1300

22.0339%

76.2711%

80%

1305.084

Q5

200

1400

23.7288%

100.0000%

100%

1762.711

Total

5900

4576.268

Gini coefficient = [(100*100/2) – 4576.268]/[100*100/2]

Gini coefficient (Town B) = (5,000 – 4576.268) / 5000 = 0.0847 or 8.47%

The Gini coefficient for town A is greater than that for town B. This indicates a difference in the equality of income distribution between the two towns. Town A has a greater Gini coefficient than town B. Therefore, income inequality in town A is greater than in town B.

Presented below in the Table 1 are the OECD household expenditure equivalence units and in Table 2 are the average number of people in household and the annual household expenditure by the age of household head.

Table 1

Household size

OECD Household expenditure equivalence units

Increment

1

1

2

1.7

0.7

3

2.2

0.5

4

2.7

0.5

5

3.2

0.5

Table 2

Age of household head

Average number of people in household

Annual household expenditure ($)

Equivalent average annual household expenditure ($)

74

1.5

27,650

?

Using the OECD household expenditure equivalence units, estimate the equivalent average annual household expenditure in households headed by people in each age group, taking into account the average number of people in the household. [10 marks]

We need to predict the annual household expenditure for a household with one person.

Age of household head

Average number of people in household

Annual household expenditure ($)

OECD Household expenditure equivalence units

Equivalent average annual household expenditure ($)

74

1.5

27,650

1.35

$ 20,481

Comment on the rationale of using household expenditure equivalence units in estimating equivalent average annual household expenditure. [2 marks]

The use of household expenditure equivalence units in estimating equivalent average annual household expenditure helps in eliminating extreme high and extreme low values of household expenditure. Therefore, this method eliminates outliers from the data of household annual expenditure.