You are the manager of a firm that receives revenues of $40,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -1.5, and the cross-price elasticity of demand between product Y and X is -1.8.

How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 2 percent?

To calculate the change in the firm's total revenues resulting from a 2 percent increase in the price of product X, we need to consider the elasticities of demand for both product X and product Y.

1. Calculate the percentage change in the price of product X:
Percentage Change in Price = 2%
= 2/100
= 0.02

2. Calculate the new price of product X:
New Price of X = Current Price of X + (Percentage Change in Price * Current Price of X)

For example, if the current price of X is $10:
New Price of X = $10 + (0.02 * $10)
= $10 + $0.20
= $10.20

3. Calculate the percentage change in the quantity demanded of product X using the price elasticity of demand for X:
Percentage Change in Quantity Demanded of X = Own Price Elasticity of X * Percentage Change in Price

For example, if the own price elasticity of X is -1.5:
Percentage Change in Quantity Demanded of X = -1.5 * 0.02
= -0.03

4. Calculate the new quantity demanded of product X:
New Quantity Demanded of X = Current Quantity Demanded of X + (Percentage Change in Quantity Demanded of X * Current Quantity Demanded of X)

For example, if the current quantity demanded of X is 1,000:
New Quantity Demanded of X = 1,000 + (-0.03 * 1,000)
= 1,000 - 30
= 970

5. Calculate the change in total revenues from product X:
Change in Revenues from X = Current Price of X * (New Quantity Demanded of X - Current Quantity Demanded of X)

For example, if the current price of X is $10:
Change in Revenues from X = $10 * (970 - 1,000)
= $10 * (-30)
= -$300

6. Calculate the change in total revenues from product Y using the cross-price elasticity of demand between product Y and X:
Change in Revenues from Y = Current Price of Y * (Cross-Price Elasticity of Y * Percentage Change in Price of X)

For example, if the current price of Y is $15 and the cross-price elasticity of Y and X is -1.8:
Change in Revenues from Y = $15 * (-1.8 * 0.02)
= $15 * (-0.036)
= -$0.54

7. Calculate the change in total revenues:
Change in Total Revenues = Change in Revenues from X + Change in Revenues from Y

For example, using the calculated values from steps 5 and 6:
Change in Total Revenues = -$300 + (-$0.54)
= -$300 - $0.54
= -$300.54

Based on these calculations, increasing the price of product X by 2 percent would result in a decrease in the firm's total revenues by approximately $300.54.