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?
Using the change in revenue formula for two products, ΔR = [$40,000(1 - 1.5) + $90,000(-1.8)] (0.02) = -$3,640. Thus, a 2 percent increase in the price of good X would cause revenues from both goods to change by $3,640.
Ah, the wonderful world of elasticities and revenue calculations! Let me put on my clown nose and juggle some numbers for you.
To determine the change in total revenues, we need to consider the own price elasticity of demand for product X and the cross-price elasticity of demand between product Y and X.
Now, to get started, we know that the own price elasticity of demand for product X is -1.5. So, if we increase the price of good X by 2 percent, we can expect the quantity demanded to decrease by approximately 3 percent (1.5 times 2).
As for the cross-price elasticity of demand between product Y and X, which is -1.8, it tells us that a 1 percent increase in the price of product X will result in a 1.8 percent decrease in the quantity demanded for product Y. However, since we're dealing with a price increase for product X, we don't need to worry about the cross-price elasticity in this case.
Time to do some revenue math! Let's use the midpoint formula to estimate the change in total revenues:
Change in quantity demanded for product X = -3% of 40,000 = -1,200
Change in revenue for product X = -1,200 x 2% (price increase) = -$24
With a price increase of 2% for product X, the revenue from product X will decrease by $24.
Now, to calculate the change in total revenues, we need to take into account the revenue from product Y. Since the price increase for product X doesn't affect the cross-price elasticity for product Y, we can assume no change in quantity demanded for Y.
Therefore, the change in total revenues will be the change in revenue for product X, which is -$24.
So, all jokes aside, the firm's total revenues will decrease by $24 if the price of product X is increased by 2 percent.
To calculate the change in total revenues when you increase the price of good X by 2 percent, you need to consider the own price elasticity of demand for product X.
The own price elasticity of demand measures the responsiveness of quantity demanded to a change in the price of the same product. In this case, the own price elasticity for product X is -1.5. Since it is negative, it implies that an increase in price will result in a decrease in quantity demanded.
To calculate the percentage change in quantity demanded of product X, we need to multiply the percentage change in price by the own price elasticity:
Percentage change in quantity demanded of product X = Percentage change in price of product X * Own price elasticity of demand for product X
Given that the percentage change in price is 2 percent, we can calculate the change in quantity demanded for product X:
Percentage change in quantity demanded of product X = 2% * -1.5 = -3%
Now, we need to calculate the change in revenue for product X. Since the revenue is given as $40,000 per year, we can calculate the change in revenue for product X as:
Change in revenue for product X = Percentage change in quantity demanded of product X * Current revenue for product X
Change in revenue for product X = -3% * $40,000 = -$1,200
Thus, if the price of product X increases by 2 percent, the firm's revenue from product X would decrease by $1,200.
Next, we need to consider the cross-price elasticity of demand between product Y and X. The cross-price elasticity measures the responsiveness of quantity demanded of one product to a change in the price of another related product. In this case, the cross-price elasticity between product Y and X is -1.8, which indicates that the two products are substitutes.
Now, to calculate the percentage change in quantity demanded of product Y in response to a change in the price of product X, we multiply the percentage change in price of product X by the cross-price elasticity:
Percentage change in quantity demanded of product Y = Percentage change in price of product X * Cross-price elasticity of demand between product Y and X
Since the percentage change in the price of product X is 2 percent, we can calculate the change in quantity demanded for product Y:
Percentage change in quantity demanded of product Y = 2% * -1.8 = -3.6%
To calculate the change in revenue for product Y, we multiply the change in quantity demanded of product Y by the current revenue for product Y:
Change in revenue for product Y = Percentage change in quantity demanded of product Y * Current revenue for product Y
Given that the revenue for product Y is $90,000 per year, we can calculate the change in revenue for product Y as:
Change in revenue for product Y = -3.6% * $90,000 = -$3,240
Therefore, if the price of product X increases by 2 percent, the firm's revenue from product Y would decrease by $3,240.
Finally, we can calculate the overall change in total revenue for the firm by summing up the changes in revenue for both products:
Change in total revenue = Change in revenue for product X + Change in revenue for product Y
Change in total revenue = (-$1,200) + (-$3,240) = -$4,440
Hence, if the firm increases the price of good X by 2 percent, the firm's total revenue from both products would decrease by $4,440.
To calculate the change in total revenues, we need to consider the own price elasticity of demand for product X and the cross-price elasticity of demand between product Y and X.
First, let's define the own price elasticity of demand. It measures the responsiveness of the quantity demanded of a product to a change in its own price. In this case, the own price elasticity of demand for product X is given as -1.5.
The formula for calculating the percentage change in quantity demanded based on the own price elasticity of demand is:
% Change in Quantity Demanded = Own Price Elasticity of Demand * % Change in Price
Since we want to increase the price of product X by 2 percent, the % Change in Price would be 2.
% Change in Quantity Demanded = -1.5 * 2
Here, we multiply the own price elasticity of demand by the % Change in Price to find the percentage change in quantity demanded.
Now, let's calculate the change in the quantity demanded for product X:
Change in Quantity Demanded for Product X = % Change in Quantity Demanded * Current Quantity Demanded for Product X
To calculate the current quantity demanded for product X, we need more information. Unfortunately, the quantity demanded is not given in the question. Could you provide that information, or is there any other information you would like to input?