The demand function for a cola-type soft drink in general is Q = 20-2P, where Q stands for quantity and P stands for price.
At which price would a change in price and quantity result in approximately no change in total revenue? Why?
Demand function for a cola-type soft drink in general is q= 20 – 2P, where Q stand
for quantity and P stands for price.
<br>a. Calculate point elasticities at prices of 5 and 9. Is the demand curve elastic or inelastic at these points?
To find the price at which a change in price and quantity would result in approximately no change in total revenue, we need to calculate the total revenue at different price levels.
Total revenue (TR) is calculated by multiplying the quantity sold (Q) by the corresponding price (P). So, TR = Q * P.
Let's analyze the scenario when there is no change in total revenue: ΔTR ≈ 0.
We can write the change in total revenue as:
ΔTR = (Q2 - Q1) * P
Since we want ΔTR to be approximately zero, it implies that (Q2 - Q1) also needs to be close to zero.
Let's substitute the demand equation Q = 20 - 2P into the change in total revenue equation:
ΔTR = (20 - 2P2 - 20 + 2P1) * P
Simplifying this equation further gives:
ΔTR = 2(P1 - P2) * P
Since we want ΔTR to be close to zero, it implies that (P1 - P2) also needs to be close to zero.
Therefore, for a change in price and quantity to result in approximately no change in total revenue, the difference in prices (P1 - P2) should be close to zero.
In other words, if the change in price is small, the change in quantity will also be small, resulting in an approximately constant total revenue.
Hence, when the difference in prices (P1 - P2) is close to zero, the change in price and quantity will result in approximately no change in total revenue.
Please note that this analysis assumes a linear demand function and a small change in price and quantity. In practice, demand functions can be more complex, and factors like consumer preferences, competition, and market conditions can also affect total revenue.