Opera CD buyers are located in New York and Los Angeles. At the current price for a CD, $25 in both New York
and Los Angeles, aggregate demand for Opera CD is 10,000 units (i.e. the sum of the demand in New York and Los Angeles); and the price elasticity of demand for Opera CD in New York and Los Anglees are -3 and -7 respectively. If the slope of each demand curve in New York is the same as in Los Angeles, then the quantity of Opera CDs demanded in Los Angles is?
To find the quantity of Opera CDs demanded in Los Angeles, we need to determine the price elasticity of demand for Opera CDs in Los Angeles.
Given that the price elasticity of demand for Opera CDs in New York is -3 and in Los Angeles is -7, and that the slope of each demand curve in New York is the same as in Los Angeles, we can assume that the price elasticity of demand in Los Angeles is also -3.
Now, using the concept of price elasticity of demand, we can calculate the quantity of Opera CDs demanded in Los Angeles. The price elasticity of demand formula is as follows:
Price elasticity of demand = % change in quantity demanded / % change in price
Since the price elasticity of demand is -3 and we have a 1% change in price, we can use this formula to find the corresponding percentage change in quantity demanded for Opera CDs in Los Angeles:
-3 = % change in quantity demanded / 1
Rearranging the equation, we find that the percentage change in quantity demanded is -3.
Therefore, the quantity of Opera CDs demanded in Los Angeles can be calculated as follows:
Quantity of Opera CDs demanded in Los Angeles = Initial quantity * (1 + Percentage change in quantity demanded)
Given that the initial quantity is 10,000 units, we can substitute the values into the equation:
Quantity of Opera CDs demanded in Los Angeles = 10,000 * (1 + (-3/100))
Calculating the equation, we find:
Quantity of Opera CDs demanded in Los Angeles = 10,000 * (1 - 0.03)
Quantity of Opera CDs demanded in Los Angeles = 10,000 * 0.97
Quantity of Opera CDs demanded in Los Angeles ≈ 9,700 units
Therefore, the quantity of Opera CDs demanded in Los Angeles is approximately 9,700 units.
To answer this question, we need to calculate the quantity of Opera CDs demanded in Los Angeles. We know that the aggregate demand for Opera CDs is 10,000 units, and we have the price elasticity of demand for Opera CDs in both New York and Los Angeles.
The price elasticity of demand measures the responsiveness of quantity demanded to changes in price. In this case, we are given that the price elasticity of demand for Opera CDs in New York is -3, and the price elasticity of demand for Opera CDs in Los Angeles is -7.
The formula for price elasticity of demand is:
Price elasticity of demand = (% change in quantity demanded) / (% change in price)
Since we are given that the slope of each demand curve in New York is the same as in Los Angeles, we can assume that the price changes by the same percentage in both cities.
Now, let's solve for the quantity of Opera CDs demanded in Los Angeles.
First, let's calculate the percentage change in price. We are told that the current price for a CD is $25 in both New York and Los Angeles. So if the price changes by a certain percentage, it will be the same for both cities.
Let's assume the price increases by x%. Therefore, the new price in both cities will be:
New price = $25 + ($25 * x/100) = $25 + $0.25x
Next, let's calculate the percentage change in quantity demanded using the price elasticity of demand formula.
For New York:
-3 = (% change in quantity demanded in New York) / (% change in price)
-3 = (% change in quantity demanded in New York) / (x/100)
-300 = (% change in quantity demanded in New York) / x
For Los Angeles:
-7 = (% change in quantity demanded in Los Angeles) / (% change in price)
-7 = (% change in quantity demanded in Los Angeles) / (x/100)
-700 = (% change in quantity demanded in Los Angeles) / x
Since the slope of each demand curve in New York is the same as in Los Angeles, the percentage change in quantity demanded will be the same in both cities. Therefore, we can set the equations for the percentage change in quantity demanded equal to each other:
-% change in quantity demanded in New York = -% change in quantity demanded in Los Angeles
-300/x = -700/x
300 = 700
This equation is not possible since 300 is not equal to 700. Therefore, there must be an error in the given information or assumptions.
In conclusion, based on the given information and assumptions, we cannot determine the quantity of Opera CDs demanded in Los Angeles.