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 $80,000 per year and movies cost $15 each. In scenario D₂, Lorena’s income is also $80,000 per year, but the price of seeing a movie rises to $17. And in scenario D₃, Lorena’s income goes up to $100,000 per year, while movies cost $17.

	Scenario D1 D2 D3 Income per year $80,000 $80,000 $100,000 Price of movie ticket $15 $17 $17 Price of Golf Quantity Demanded $60 15 10 15 $45 25 15 30 $30 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 $60, cross elasticity =    .     

At $45, cross elasticity =  .     

At $30, 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)  Independent goods  Substitute goods  Complementary 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 $60, income elasticity of demand =  .     

At $45, income elasticity of demand =  .     

At $30, income elasticity of demand =  .     

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

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

Answer 1

(a) Elasticity through mid point formula = ((Q2-Q1)/(Q2+Q1)/2)/((P2-P1)/(P2+P1)/2))

At $60, elasticity = ((10-15)/((10+15)/2))/((17-15)/((17+15)/2))

= (-5/25)*(2/32)

= -0.01

At $45, = ((15-25)/((15+25)/2))/((17-15)/((17+15)/2))

= (-10/40)*(2/32)

= -0.02

At $30, =  ((20-40)/((20+40)/2))/((17-15)/((17+15)/2))

=(-20/60)*(2/32)

= -0.02

Thus, cross-price elasticity is not the same across prices. Since it is negative, the goods are complementary goods.

(b) Income elasticity through mid point formula = ((Q2-Q1)/(Q2+Q1)/2)/((Y2-Y1)/(Y2+Y1)/2))

At $60, elasticity = ((15-10)/((10+15)/2))/((100000-80000)/((100000+80000)/2))

= (5/25)*(20000/180000)

= 0.02

At $45, = ((30-15)/((30+15)/2))/((100000-80000)/((100000+80000)/2))

= (15/45)*(20000/180000)

= 0.04

At $60 = ((50-20)/((50+20)/2))/((100000-80000)/((100000+80000)/2))

= (30/70)*(20000/180000)

= 0.05

No the income elasticity is not the same across prices. Since it is positive, so no golf is not inferior good, it is a normal good.