Compute elasticities of demand and explain briefly for each

Compute elasticities of demand and explain briefly for each the relevance of this information in decision-making by the firm. The data has been generated in each case from recent market experience or from test markets.

1. Current p of dinner =$100, q=60; New p = $80, q=70

2. Current symphony ticket p=$90, q=2000; New p= $50, q=4000

3. Current monthly income =$10,000, monthly q=6 of dinners out; new income = $8000, q=4

4. Current p of good y = $50, q of good x=100; new p of y = $40,q of x=90 (p of x has not changed)

Solution

Price elasticity of demand = % change in quantity / %change in price.

1. Percentage change in price (-20% - decrease); Percentage change in quantity = +16.66

Price elasticity of demand = +16.66% / -20% = -0.83

The negative sign indicates that P and Q are inversely related. In this case the change in quantity demanded is proportionately smaller than the change in price.

2. Percentage change in price (-44.44% - decrease). Percentage change in quantity = +100%

Price elasticity of demand = 100 / (-44.44) = -2.25.

The negative sign indicates that P and Q are inversely related. In this case the change in quantity demanded is proportionately smaller than the change in price.

3. Percentage change in income (-20% - decrease). Percentage change in q dinners out (-33.33 – decrease)

Price elasticity of demand = (-33.33) / (-20%) = +1.66

In this case, the quantity demanded is proportionately larger than the change in price. This means that an increase in price would result in decrease in revenue and a decrease in price would result in an increase in revenue.

4. Percentage change in price of Y 20%. Percentage change in quantity X (-10%)

Price elasticity of demand = (-10%) / 20% = -0.5.

The negative sign indicates that P and Q are inversely related. In this case the change in quantity demanded is proportionately smaller than the change in price.

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