Final answer:
When the price of product X is increased by 2%, the revenue from product X will decrease by $3,000 due to an own price elasticity of -3. However, because product Y has a cross-price elasticity of 1.8 with product X, its revenue will increase by $2,880. The net change in total revenue for the firm will be a decrease of $120.
Step-by-step explanation:
As a manager of a firm, you need to predict how revenue will change if you adjust prices, taking into account elasticity of demand for your products. To calculate the expected revenue change for product X when increasing its price by 2%, you use the own price elasticity of demand, which for product X is −3. This means that a 1% increase in price would lead to a 3% decrease in quantity demanded. So, for a 2% price increase:
Revenue Change for X = $50,000 × (% change in price × elasticity) = $50,000 × (2% × −3) = $50,000 × (−0.06) = −$3,000
For product Y, using the cross-price elasticity of demand between product Y and X, which is 1.8, we know that as X's price increases, Y's demand also increases. For a 2% price increase in X:
Revenue Change for Y = $80,000 × (cross-price elasticity × % change in price of X) = $80,000 × (1.8 × 0.02) = $80,000 × 0.036 = $2,880
Total Revenue Change = Revenue Change for X + Revenue Change for Y = −$3,000 + $2,880 = −$120
The firm's total revenues will decrease by $120 if the price of product X is increased by 2%. It is important to round this response to the nearest dollar, so the change is −$120.