Question

The accompanying table shows the price and yearly quantity sold of souvenir T-shirts in the town of Crystal Lake according to the average income of the tourists visiting.

price of t-shirt	Quantity of t-shirts demanded when average tourist income is 20,000	Quantity of t-shirts demanded when average tourist income is 30,000
$4	3,000	5,000
$5	2,400	4200
$6	1,600	3000
$7	800	1000

(a) Using the midpoint method, calculate the price elasticity of demand when the price of a T-shirt rises from $5 to $6 and the average tourist income is $20,000.

(b) Using the midpoint method, calculate the price elasticity of demand when the price of a T-shirt rises from $5 to $6 and the average tourist income is $30,000.

(c) Explain the difference in the price elasticity of demand for each income level.

(d) Using the midpoint method, calculate the income elasticity of demand when the price of a T-shirt is $4 and the average tourist income increases from $20,000 to $30,000. Using the midpoint method, calculate the income elasticity of demand when the price of a T-shirt is $7 and the average tourist income increases from $20,000 to $30,000.

(e) Explain the difference in income elasticity of demand for each price.

Answer 1

Answer
a)
price elasticity of demand=(change in quantity demanded/average quantity)/(change in price/average price)
change in quantity demanded=1600-2400=-800
average quantity demanded=(1600+2400)/2=2000
change in price=6-5=1
average price=(6+5)/2=5.5
e=(-800/2000)/(1/5.5)
=-2.2
the demand is elastic at this price range
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b)
price elasticity of demand=(change in quantity demanded/average quantity)/(change in price/average price)
change in quantity demanded=3000-4200=-1200
average quantity demanded=(3000+4200)/2=3600
change in price=6-5=1
average price=(6+5)/2=5.5
e=(-1200/3600)/(1/5.5)
=-1.83333333
The demand is elastic

c)
The demand for both a and b is elastic but the elasticity decreases as the income increases because of the ability to pay increases the demand even if the increase in price.

d)
the income elasticity of demand when the price of a T-shirt is $4 and the average tourist income increases from $20,000 to $30,000

income elasticity of demand=(change in quantity demanded/average quantity)/(change in income /average income )
change in quantity demanded=5000-3000=2000
average quantity demanded=(5000+3000)/2=4000
change in income =30000-20000=10000
average income =(30000+20000)/2=25000

income elasticity of demand=(2000/4000)/(10000/25000)
=1.25
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the income elasticity of demand when the price of a T-shirt is $7 and the average tourist income increases from $20,000 to $30,000

income elasticity of demand=(change in quantity demanded/average quantity)/(change in income /average income )
change in quantity demanded=1000-800=200
average quantity demanded=(1000+800)/2=900
change in income =30000-20000=10000
average income =(30000+20000)/2=25000

income elasticity of demand=(200/900)/(10000/25000)
=0.555555556
=0.55
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e)
As for price increases the income elasticity of demand decreases.

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