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 $60,000 per year and movies cost $11 each. In scenario D₂, Lorena’s income is also $60,000 per year, but the price of seeing a movie rises to $13. And in scenario D₃, Lorena’s income goes up to $80,000 per year, while movies cost $13.

	Scenario D1 D2 D3 Income per year $60,000 $60,000 $80,000 Price of movie ticket $11 $13 $13 Price of Golf Quantity Demanded $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?      YesNo .     

Are movies and golf substitute goods, complementary goods, or independent goods? Independent goods Complementary goods Substitute 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? Yes No .     

Is golf an inferior good? Yes No , it is an inferior good, normal good .

Answer 1

Scenario	D1	D2	D3
Income per year	$60,000	$60,000	$80,000
Price of movie ticket	$11	$13	$13
Price of Golf	Quantity Demanded
$55	15	10	15
$40	25	15	30
$25	40	20	50

a) Cross elasticity of  Lorena’s demand for golf:

Formula for midpoint method of Cross elasticity of demand = [(Q2 - Q1)/(Q2+Q1)/2] / [(P2-P1)/(P2+P1)/2]

At price = $55: (-5/12.5) / (2/12) = -2.40

At price = $40: (-10/20) / (2/12) = -1.50

At rice = $25: (-20/30) / (2/12) = -4

Is the cross elasticity the same at all three prices? No

Are movies and golf substitute goods, complementary goods, or independent goods? Complementary (negative value of cross price elasticity indicates the two are complements. So increase in the price of one leads to decrease in the demand for the other good.)

b) Income elasticity:

Formula: [(Q2 -Q1)/ (Q2+Q1)/2] / [(P2-P1)/(P2+P1)/2

At $55, income elasticity of demand = . (10/12.5) / (20,000/70,000) = 2.8

At $40, income elasticity of demand = . (15/22.5) / (20,000/70,000) = 2.33   

At $25, income elasticity of demand = .(30/35) / (20,000/70,000) =   3

Is the income elasticity the same at all three prices? No .     

Is golf an inferior good? No , it is a normal good.

( when income elasticity is positive, the good demanded is a normal good indicating an increase in income leads to increase in the demand.)