Question

2. The following table shows three demand schedules for a person who likes to play football and/or go swimming. In scenario S1, his income is $100,000 per year and swimming cost $18 each. In scenario S2, his income is also $100,000 per year, but the price of swimming rises to $22 per round. And in scenario S3, his income increases to $140,000 per year while swimming cost $22 per round.

A. Use data under S1 and S2 to calculate the cross elasticity of demand for football at all three prices. (Use the midpoint formula) Is the cross elasticity the same at all three prices? What type of goods are football and swimming? Why?

b. Use data under S2 and S3 to calculate the income elasticity of demand for football at all three prices. (Use the midpoint formula) Is the income elasticity the same at all three prices? Is football an inferior good? Why?

                                        Quantity Demanded

Price                    S1               S2               S3

$100                    30                20                30

70                          50                30                60

40                          80                40                100

Answer 1

a.

At $100, cross elasticity = (20-30)/(30+20)/2)÷(22-18)/(22+18)/2= -2

At $70, cross elasticity = (30-50)/(50+30)/2)÷(22-18)/(22+18)/2= -2.5

At $40, cross elasticity=( 80-40)/(80+40)/2÷(18-22)/(22+18)/2= -3.3

reason- Cross price elasticity of demand= % change in quantity demanded of Golf/ % change in price of movie ticket

No, cross price elasticity is different at all prices.

Complementary goods

reason- Since the cross price elasticity is negative, football and swimming are substitute goods.

b. At $100, income elasticity of demand = (30-20)/(20+30)/2)÷(140000-100000)/(140000+100000)/2= 1.2

At $70, income elasticity of demand = (60-30)/(60+30)/2)÷(140000-100000)/(140000+100000)/2= 2

At $40, income elasticity of demand = (100-40)/(100+40)/2÷(140000-100000)/(140000+100000)/2= 2.57

reason- Income elasticity of demand= % change in quantity demanded/ % change in income level

No, income elasticity of demand is different.

No, it is a normal good.

reason- football is not an inferior good. When income rises, demand for football rises, so football is a normal good.