Question

Lorena likes to play golf. The number of times per year that she plays depends on both the price of playing a round of golf as well as Lorena’s income and the cost of other types of entertainment—in particular, how much it costs to go see a movie instead of playing golf. The three demand schedules in the table below show how many rounds of golf per year Lorena will demand at each price under three different scenarios. In scenario D₁, Lorena’s income is $70,000 per year and movies cost $13 each. In scenario D₂, Lorena’s income is also $70,000 per year, but the price of seeing a movie rises to $15. And in scenario D₃, Lorena’s income goes up to $90,000 per year, while movies cost $15.

Scenario	D1	D2	D3
Income per year	$ 70,000	$70,000	$ 90,000
Price of movie ticket	$ 13	$15	$ 15

Price of Golf		Quantity Demand
$ 55	15	10	15
$ 40	25	15	30
$ 25	40	20	50

Instructions: Round your answers to 2 decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.

a. Using the data under D₁ and D₂, calculate the cross elasticity of Lorena’s demand for golf at all three prices. (To do this, apply the midpoints approach to the cross elasticity of demand.)     

At $55, cross elasticity =     .     

At $40, cross elasticity =  .     

At $25, cross elasticity =  .     

Is the cross elasticity the same at all three prices?        (Click to select)   Yes   No  .     

Are movies and golf substitute goods, complementary goods, or independent goods?        (Click to select)   Complementary goods   Substitute goods   Independent goods  .

b. Using the data under D₂ and D₃, calculate the income elasticity of Lorena’s demand for golf at all three prices. (To do this, apply the midpoints approach to the income elasticity of demand.)     

At $55, income elasticity of demand =  .     

At $40, income elasticity of demand =  .     

At $25, income elasticity of demand =  .     

Is the income elasticity the same at all three prices?        (Click to select)   No   Yes  .     

Is golf an inferior good?        (Click to select)   Yes   No  , it is   (Click to select)   a normal good   an inferior good  .

Answer 1

a.

At $55, cross elasticity = (10-15)/(15+10)/2)÷(15-13)/(15+13)/2= -2.8 .   

At $40, cross elasticity = (15-25)/(15+25)/2)÷(15-13)/(15+13)/2= -3.5.   

At $25, cross elasticity=( 20-40)/(20+40)/2÷(15-13)/(15+13)/2= -4.6

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, movies and golf are substitute goods.

b. At $55, income elasticity of demand = (15-10)/(15+10)/2)÷(90000-70000)/(90000+70000)/2= 1.6 .     

At $40, income elasticity of demand = (30-15)/(30+15)/2)÷(90000-70000)/(90000+70000)/2= 2.67.     

At $25, income elasticity of demand = (50-20)/(50+20)/2÷(90000-70000)/(90000+70000)/2= 3.43 .

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