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You are the manager of a firm that receives revenues of $60,000 per year from product X and $70,000 per year from product Y. The own price elasticity of demand for product X is -2.5, and the cross-price elasticity of demand between product Y and X is 1.7. How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 2 percent?

User Sixtytrees
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Final answer:

Increasing the price of product X by 2% in a firm with an own price elasticity of demand of -2.5 for product X and a cross-price elasticity of 1.7 with product Y will result in a decrease in total revenue of $620.

Step-by-step explanation:

The student is asking about the change in total revenue that would result from a price increase in product X, given its own price elasticity of demand and the cross-price elasticity of demand with product Y. Since the own price elasticity of demand for product X is -2.5, a 2% increase in the price will lead to a 5% decrease in quantity demanded for product X (as elasticity is the percentage change in quantity demanded divided by the percentage change in price).

Revenue change for product X = (Percentage change in quantity demanded) x (Original revenue)
Revenue change for product X = (-5%) x ($60,000) = -$3,000.

Additionally, with a cross-price elasticity of 1.7 between products Y and X, the price increase of product X will lead to a 3.4% increase in quantity demanded for product Y (as cross-price elasticity is the percentage change in quantity demanded of one good due to a percentage change in price of another good).

Revenue change for product Y = (Cross-price elasticity of demand) x (Price change of product X) x (Original revenue)
Revenue change for product Y = 1.7 x 2% x $70,000 = $2,380.

Summing the changes of both products, total revenue change = Revenue change for product X + Revenue change for product Y
Total revenue change = (-$3,000) + $2,380 = -$620.

Hence, with a price increase of 2% for product X, the firm's total revenues will decrease by $620.

User James Dunne
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