I need help with price of demand.
Question 3. A certain commodity satisfies the demand equation relating price, p, and quantity demanded, q,q =1000/p^2 .
If the price of this commodity is lowered, will the revenue generated by its sales increase?
4. The price p (in dollars) and the demand q for a product are related by p^2 + 2q^2 = 1100.
If the current price per unit is $30, will revenue increase or decrease if the price is raised slightly?
To determine whether the revenue generated by a commodity will increase or decrease with a change in price, you need to analyze the demand equation and consider the concept of revenue.
For Question 3, the demand equation is q = 1000/p^2. To calculate revenue, we multiply the price (p) by the quantity demanded (q). So, the revenue equation can be written as R = p*q.
To determine whether the revenue will increase or decrease with a decrease in price, we need to examine the relationship between price and quantity demanded. In this case, as the price decreases, the quantity demanded will increase according to the inverse relationship in the demand equation.
To calculate the new revenue, we need to find the new quantity demanded after the price is lowered. Let's assume the original price is p1 and the new price is p2. We know that q = 1000/p^2. Therefore, the new quantity demanded after the price decrease is q2 = 1000/p2^2.
Comparing the revenue before and after the price decrease, we have:
R1 = p1 * q1
R2 = p2 * q2
Since q2 > q1 (quantity demanded increases when the price decreases), we can conclude that the revenue, R2, will increase when the price is lowered.
Moving on to Question 4, the demand equation is given as p^2 + 2q^2 = 1100. Similar to earlier, we calculate the revenue as R = p*q.
To determine the effect on revenue with a slight price increase, we need to analyze the relationship between price and quantity demanded. In this case, we have a specific value for the current price, which is $30.
To calculate revenue, we substitute the given price (p = 30) into the demand equation. Solving for q, we can determine the quantity demanded.
p^2 + 2q^2 = 1100
30^2 + 2q^2 = 1100
900 + 2q^2 = 1100
2q^2 = 200
q^2 = 100
q = 10
So, the current quantity demanded is q = 10.
Now, if the price is raised slightly, the new price can be represented as p2 = 30 + Δp (where Δp represents the slight increase in price).
To determine the effect on revenue, we need to calculate the new quantity demanded (q2) after the slight price increase. We substitute p2 into the demand equation and solve for q:
p2^2 + 2q2^2 = 1100
(30 + Δp)^2 + 2q2^2 = 1100
Using this equation, we can solve for q2.
Once we have q2, we can calculate the new revenue R2 = p2 * q2.
By comparing the original revenue (R1 = p1 * q1) with the new revenue (R2 = p2 * q2), we can determine whether revenue will increase or decrease with the slight price increase.
Please note that specific calculations to find q2 and R2 will depend on the value of Δp provided in the question.