The accompanying table shows the price and yearly quantity sold of souvenir t-sh

Question

The accompanying table shows the price and yearly quantity sold of souvenir t-shirts in the town of saint john according to the average income of the tourists visiting.

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. Also, calculate it when the average tourist income is $30 000.

B.) 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. Also, calculate it when the price is $7.

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 3000 5000 5 2400 4200 6 1600 3000 7 800 1800

Explanation / Answer

According to the mid-point formula, the price elasticity of demand for a product is given by:

Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]

A) Income is 20000 and we have

P1 = 5, P2 = 6, Q1 = 2400, Q2 = 1600

Ed = -2.20

Income is 30000 and we have

P1 = 5, P2 = 6, Q1 = 4200, Q2 = 3000

Ed = -1.83

B) According to the mid-point formula, the income elasticity of demand for a product is given by:

Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (M2 – M1) / [(M2 + M1)/2]

When price is $4,

M1 = 20000, M2 = 30000, Q1 = 3000 and Q2 = 5000

Em = 1.25

When price is $7,

M1 = 20000, M2 = 30000, Q1 = 800 and Q2 = 1800

Em = 1.92

Cases Q1 Q2 P1 P2 Q2-Q1 (Q2+Q1)/2 %Q P2-P1 (P1+P2)/2 %P Ed Income = 20000 2400 1600 5 6 -800 2000.00 -40.00 1 5.50 18.18 -2.20 Income = 30000 4200 3000 5 6 -1200 3600.00 -33.33 1 5.50 18.18 -1.83

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