The demand for a Laptop in Adama is estimated to be QD= 250,000 –35P if this relationship remains approximately valid in the future. What is the point price elasticity of demand at price of $2000? Interpret your result.
Well, to calculate the point price elasticity of demand, we need to use the formula:
E = (% change in quantity demanded) / (% change in price)
But since we are given a specific price of $2000, we'll need to use some imagination for the % change in price. So let’s just pretend that the price changes to $4000, then we can calculate the elasticity.
Now, the original quantity demanded at $2000 is QD1 = 250,000 – 35(2000) = 180,000.
If the price increases to $4000, the new quantity demanded is QD2 = 250,000 – 35(4000) = 110,000.
Using these values, we can calculate the % change in quantity demanded:
% change in quantity demanded = (QD2 - QD1) / QD1 * 100
= (110,000 - 180,000) / 180,000 * 100
= -39%
Now, let’s calculate the % change in price:
% change in price = (4000 - 2000) / 2000 * 100
= 100%
Now, substituting these values into the elasticity formula:
E = (-39%) / (100%)
= -0.39
Interpreting the result: Since the elasticity is negative, we know that the demand for laptops in Adama is price elastic. In other words, a 1% increase in price will lead to a 0.39% decrease in quantity demanded. So, it seems that clown noses and squirting flowers might need to be thrown in for free to boost laptop sales! *honk honk*
To calculate the point price elasticity of demand, we need to use the formula:
E = (%ΔQD) / (%ΔP)
Where:
E = Elasticity of demand
%ΔQD = Percentage change in quantity demanded
%ΔP = Percentage change in price
In this case, we are given the equation for quantity demanded as QD = 250,000 - 35P. To calculate the percentage change in quantity demanded, we will differentiate the equation with respect to P:
dQD/dP = -35
To find the value of %ΔQD, we need to divide the differential value by the original value of QD at the given price:
%ΔQD = (dQD/dP) / QD
= -35 / (250,000 - 35 * 2000)
= -35 / (250,000 - 70,000)
= -35 / 180,000
= -0.0001944
Next, we need to calculate the percentage change in price. Since the price is $2000 and there is no change given, we can substitute the values directly:
%ΔP = (ΔP / P) * 100
= (0 / 2000) * 100
= 0
Now we can substitute the percentage change values into the formula for point price elasticity of demand:
E = %ΔQD / %ΔP
= -0.0001944 / 0
= undefined
Interpretation:
Since the calculated point price elasticity of demand is undefined, it suggests that the demand for laptops in Adama is perfectly inelastic at a price of $2000. This means that a change in price will not have any effect on the quantity demanded.
To calculate the point price elasticity of demand, we need to use the following formula:
E = (dQ / Q) / (dP / P)
Where:
E = point price elasticity of demand
dQ = change in quantity demanded
Q = quantity demanded
dP = change in price
P = price
In this case, the demand function is given as:
QD = 250,000 - 35P
To find the point price elasticity of demand at a price of $2000, we need to calculate dQ/dP and P/Q.
dQ/dP = -35 (since -35P is the coefficient of price)
To calculate P/Q, we substitute the given price P=2000 into the demand function:
Q = 250,000 - 35(2000)
Q = 250,000 - 70,000
Q = 180,000
Now, we can calculate the point price elasticity of demand at a price of $2000:
E = (dQ / Q) / (dP / P)
E = (-35 / 180,000) / (0 / 2000)
E = (-35 / 180,000) / 0
E = -∞
Interpretation:
The point price elasticity of demand at a price of $2000 is negative infinity (-∞). This means that an increase in price from $2000 would lead to an infinitely small decrease in the quantity demanded. In other words, the demand is perfectly inelastic at this price, indicating that consumers in Adama are not very sensitive to price changes and would still buy laptops even if the price increases significantly.