Final answer:
If the firm increases the price of product X by 1%, the total revenues of the firm will decrease by $2,160.
Step-by-step explanation:
The price elasticity of demand measures the responsiveness of demand for a product to a change in its price. In this case, the price elasticity of demand for product X is -2. This means that for a 1% increase in the price of product X, the quantity demanded will decrease by 2%. To calculate the change in total revenues, we need to consider the price effect and the quantity effect.
The price effect refers to the change in revenues due to the change in price while holding the quantity constant. Since the own price elasticity is -2, a 1% increase in price will lead to a 2% decrease in quantity demanded. Therefore, the price effect will be -2%.
The quantity effect refers to the change in revenues due to the change in quantity while holding the price constant. To calculate the quantity effect, we need to consider the cross-price elasticity of demand between product Y and product X. The cross-price elasticity measures the responsiveness of demand for one product to a change in the price of another product. In this case, the cross-price elasticity of demand between product Y and product X is -1.7. This means that a 1% increase in the price of product X will decrease the quantity demanded of product Y by 1.7%. Since the firm receives $80,000 per year from product Y, a 1.7% decrease in quantity demanded will result in a decrease in revenues of 1.7%× $80,000 = $1,360.
To calculate the total change in revenues, we need to sum the price effect and the quantity effect. The price effect is -2% ×$40,000 = -$800, and the quantity effect is -$1,360. Therefore, the total change in revenues will be -$800 + (-$1,360) = -$2,160. So, if the firm increases the price of product X by 1%, the total revenues of the firm will decrease by $2,160.