Question

Lorena likes to play golf. How many times per year she plays depends on two things: (1) the price of playing a round of golf, and (2) Lorena’s income and the cost of other types of entertainment—in particular, how much it costs to 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.

Scenario:	D1	D2	D3
Income per year:	$50,000	$50,000	$70,000
Movie Ticket Price:	$9	$11	$11
Rounds of Golf:	Quantity Demanded	Quantity Demanded	Quantity Demanded
Price = $55	15	10	15
Price = $40	25	15	30
Price = $25	40	20	50

  
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.)

Instructions: Round your answer to two decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.  
Cross elasticity of Lorena’s demand at the price of $55 =

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

Cross elasticity of Lorena’s demand at the price of $40 =

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

Cross elasticity of Lorena’s demand at the price of $25 =

Is the cross elasticity the same at all three prices? (Click to select)NoYes

Are movies and golf substitute goods, complementary goods, or independent goods? (Click to select)complementary goodssubstitute goodsindependent 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.)

Instructions: Round your answer to two decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.  
Income elasticity of Lorena’s demand at the price of $55 =

Instructions: Round your answer to two decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.  
Income elasticity of Lorena’s demand at the price of $40 =

Instructions: Round your answer to two decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.  
Income elasticity of Lorena’s demand at the price of $25 =

Is the income elasticity the same at all three prices? (Click to select)NoYes

Is golf an inferior good? (Click to select)NoYes it is (Click to select)a normal goodan inferior good.

Answer 1

a. Using the data under D₁ and D₂, calculate the cross elasticity of Lorena’s demand using the formula:

Percentage change in quantity demanded of X/Percentage change in price of Y
So,Cross elasticity of Lorena’s demand at the price of $55 = [10-15/(10+15/2)] / [11-9/(11+9/2)] = [(-5/12.5) / (2/10)] = -2

Cross elasticity of Lorena’s demand at the price of $40 = [15-25/(15+25/2)] / [11-9/(11+9/2)] = [-10/20]/[2/10] = -2.5

Cross elasticity of Lorena’s demand at the price of $25 = [20-40/(20+40/2)] / [11-9/(11+9/2)] = [-20/30] / [2/10] = -3.33

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

Are movies and golf substitute goods, complementary goods, or independent goods? complementary good as the cross elasticity is negative in all three.

b. Using the data under D₂ and D₃, calculate the income elasticity of Lorena’s demand for golf at all three prices using the formula: percentage change in quantity demanded/percentage change in income
Income elasticity of Lorena’s demand at the price of $55 = [15-10/(15+10/2)] / [70000-50000/(70000+50000/2)] = [5/12.5] / [20000/60000] = 1.2

Income elasticity of Lorena’s demand at the price of $40 = [30-15/(30+15/2)] / [70000-50000/(70000+50000/2)] = [15/22.5] / [20000/60000] = 2

Income elasticity of Lorena’s demand at the price of $25 = [50-20/(50+20/2)] / [70000-50000/(70000+50000/2)] = [30/35] / [20000/60000] = 2.57

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

Is golf an inferior good? No it is a normal good because the elasticity is positive in all three.