Income increased by 3.5% in the previous year. During that time total spending on three different goods changed. First good cost 2 PLN and total spending decreased from 345.000 to 305.000 units. Second good cost 5 PLN and total spending increased from 210.000 to 215.000. Third good cost 10 PLN and total spending increased from 500.000 to 600.000. What can you tell about those goods, provided the price remained unchanged during the previous year (use income elasticity of demand).

 

First good is income elastic and inferior good.

Second good is income inelastic and normal good.

Third good is income elastic and normal good.

 

Please find complete explanation in the explanation section.

Step-by-step explanation

Income elasticity of demand = Percentage change in quantity demanded of a good / Percentage change in income.

 

Percentage change in income = 3.5

 

First good.

Cost of first good = 2

Total spending decreased from 345.000 to 305.000 units

Quantity demanded before increase in income = 345.000 / 2 = 172.500

Quantity demanded after increase in income = 305.000 / 2 = 152.500

 

Percentage change in quantity demanded of first good = 152.500 - 172.500  / 172.500  * 100

Percentage change in quantity demanded of first good = -20.000 / 172.500 * 100

Percentage change in quantity demanded of first good = -0.1159  * 100

Percentage change in quantity demanded of first good = -11.59 %

 

Income elasticity of demand = Percentage change in quantity demanded of a good / Percentage change in income.

Income elasticity of demand = - 11.59 / 3.5

Income elasticity of demand = - 3.31

 

A negative Income elasticity of demand denotes that first good is an inferior good. Inferior goods are goods of which quantity demanded declines with increase in income and quantity demanded increases with decline in incomes.

And Income elasticity of demand is greater than 1, which suggests that first good's income elasticity of demand is elastic in nature.

 

First good is income elastic and inferior good.

 

Second good.

Cost of second good = 5

total spending increased from 210.000 to 215.000

Quantity demanded before increase in income = 210.000 / 5 = 42.000

Quantity demanded after increase in income = 215.000/ 5 = 43.000

 

Percentage change in quantity demanded of second good = 43.000 - 42.000 / 42.000 * 100

Percentage change in quantity demanded of second good = 1.000/ 42.000* 100

Percentage change in quantity demanded of second good = 0.02380  * 100

Percentage change in quantity demanded of second good = 2.38 %

 

Income elasticity of demand = Percentage change in quantity demanded of a good / Percentage change in income.

Income elasticity of demand = 2.38 / 3.5

Income elasticity of demand = 0.68

 

A positive Income elasticity of demand denotes that second good is a normal good. Normal goods are goods of which quantity demanded increases with increase in income and quantity demanded decreases with decline in incomes.

And Income elasticity of demand is less than 1, which suggests that second good's income elasticity of demand is inelastic in nature.

 

Second good is income inelastic and normal good.

 

Third good.

Cost of third good = 10

total spending increased from 500.000 to 600.000

Quantity demanded before increase in income = 500.000 / 10 = 50.000

Quantity demanded after increase in income = 600.000/ 10 = 60.000

 

Percentage change in quantity demanded of third good = 60.000 - 50.000/ 50.000* 100

Percentage change in quantity demanded of third good = 10.000/ 50.000 * 100

Percentage change in quantity demanded of third good = 0.2  * 100

Percentage change in quantity demanded of third good = 20 %

 

Income elasticity of demand = Percentage change in quantity demanded of a good / Percentage change in income.

Income elasticity of demand = 20 / 3.5

Income elasticity of demand = 5.7142

 

A positive Income elasticity of demand denotes that second good is a normal good. Normal goods are goods of which quantity demanded increases with increase in income and quantity demanded decreases with decline in incomes.

And Income elasticity of demand is greater than 1, which suggests that third good's income elasticity of demand is elastic in nature.

 

Third good is income elastic and normal good.