Question

Assume that a new theater is opening near campus. The theater owner wants lots of students to come to see movies, but is nervous about what influences their demand. Through masterful research, the theater owner discovers the following is true about demand for his theater tickets:

Own Price Elasticity    =   3.5      
Cross Price Elasticity    =   2.2      
Income Elasticity    =    4.7

If the owner lowers his price by 20%, by how much will quantity demand change? Show all work.

If the competing theater raises his price by 8%, by how much will quantity demand change at this new theater? Show all work.

If students at the Mount get 9% more income, by how much will demand for tickets change? Show all work.

If incomes fall by 5%, by how much does the theater owner need to lower his price to keep the same number of customers as before? (i.e. to keep quantity demand the same as before the drop in income). Show all work.

Answer 1

Given that,

Own price elasticity = 3.5      
Cross Price Elasticity = 2.2      
Income Elasticity = 4.7

(a) If the owner lowers his price by 20%,

(-3.5)*(-20) = Percentage change in quantity demanded

70% = Percentage change in quantity demanded

Therefore, the quantity demanded increases by 70% if the price lowers by 20%.

(b) If the competing theater raises his price by 8%,

(2.2) * (8) = Percentage change in quantity demanded for new theater

17.6 % = Percentage change in quantity demanded for new theater

Therefore, the quantity demanded for new theater increases by 17.6 % if the competing theater raises its price by 8%, as they are substitutes.

(c) If students at the Mount get 9% more income,

(4.7) * (9) = Percentage change in quantity demanded

42.3% = Percentage change in quantity demanded

Therefore, the quantity demanded for theater tickets increases by 42.3% if the income of the students increases by 9%.

(d) If incomes fall by 5%,

(4.7) * (-5) = Percentage change in quantity demanded

-23.5% = Percentage change in quantity demanded (Fall in quantity demanded demanded)

Percentage change in price = 6.71%

Therefore, the theater owner need to lower his price by 6.71% to keep the same number of customers as before.

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