3.) The demand equation for a certain product is
q=500-40p+p^2
where p is the price per unit (in dollars) and q is the quantity of units demanded (in thousands). Find the point elasticity of demand when p = 15. If this price of 15 is increased by ½%, what is the approximate change in demand?
where p is the price per unit (in dollars) and q is the quantity of units demanded (in thousands). Find the point elasticity of demand when p = 15. If this price of 15 is increased by 1/2%, what is the approximate change in demand?
I don't know why it put an A there... sorry.
So if I plug 15 into p. I get q(demand) = 125
Half of 15 is 7.5. Thus the price would be 22.5.. I think.
I replace p with 22.5 and I get q= 106.25
Q/P =8.33 for 15
Q/P = 4.722 for 22.5
Is the change in demand 3.608?
Please i need answer
To find the point elasticity of demand at a specific price, we need to differentiate the demand equation with respect to price (p) and then calculate the derivative at that price. The point elasticity of demand is given by the formula:
E(p) = - (p * dq/dp) / q
where dq/dp is the derivative of the demand equation with respect to price and q is the quantity demanded.
First, let's differentiate the demand equation:
dq/dp = -40 + 2p
Now, we can calculate the derivative at p = 15:
dq/dp = -40 + 2(15)
= -40 + 30
= -10
Next, we need to calculate the quantity demanded (q) at p = 15. Plugging p = 15 into the demand equation:
q = 500 - 40(15) + (15^2)
= 500 - 600 + 225
= 125
Now, we can calculate the point elasticity of demand at p = 15:
E(15) = - (15 * (-10)) / 125
= 150 / 125
= 1.2
The point elasticity of demand at p = 15 is approximately 1.2.
To calculate the approximate change in demand when the price of 15 is increased by ½%, we need to multiply the point elasticity by the percentage change in price. Since the price is being increased by ½%, the percentage change is 0.5%. Therefore:
Approximate change in demand = E(15) * 0.005
Approximate change in demand = 1.2 * 0.005
Approximate change in demand = 0.006
So, the approximate change in demand is approximately 0.006 units.