demand = (p+1)sqroot(q+1)=1000. Find elasticity of demand at a price of $39 per unit.

I am really struggling with this problem is there anyone that can help me?

i am not familiar with the terminology, but if you are trying to solve for p, it is not that hard

(p+1)√(p+1) = 1000
(p+1)^(3/2)=1000
raise both sides to the 2/3 power
to get
p+1=1000^(2/3)
.
.
p=

I am trying to solve for q not p.

sorry, I didn't mind my p's and q's, read them as p

(q+1)^(1/2)=1000/(p+1)

q+1 = [1000/(p+1)]^2

q = [1000/(p+1)]^2 - 1

thank you!

No problem! Now that you have solved for q, you can proceed to find the elasticity of demand at a price of $39 per unit.

To calculate elasticity of demand, you'll need to differentiate the demand function with respect to price, and then plug in the given price to find the corresponding quantity demanded.

Let's start by differentiating the demand function with respect to price p:

d/dp [(q+1)^(1/2)] = d/dp [1000/(p+1)]

To simplify the differentiation, we can rewrite the demand function as:

(q+1)^(1/2) = 1000*(p+1)^(-1)

Now, differentiate both sides with respect to p:

(1/2)(q+1)^(-1/2) * d(q+1)/dp = -1000/(p+1)^2

Simplify further:

(q+1)^(-1/2) * d(q+1)/dp = -2000/(p+1)^2

Now, let's plug in the given price p = $39 and find the quantity demanded q:

q = [1000/(p+1)]^2 - 1
q = [1000/(39+1)]^2 - 1
q = [1000/40]^2 - 1
q = (25)^2 - 1
q = 625 - 1
q = 624

Now substitute the found quantity q into the differentiation equation to calculate the elasticity:

(q+1)^(-1/2) * d(q+1)/dp = -2000/(p+1)^2
(624+1)^(-1/2) * d(624+1)/dp = -2000/(39+1)^2
625^(-1/2) * d(625)/dp = -2000/40^2
(1/625^0.5) * 1 = -2000/1600
1/25 = -5/4

The negative sign indicates that the elasticity of demand is negative, which means demand is elastic.

So, the elasticity of demand at a price of $39 per unit is -5/4 or -1.25 (approximately).

I hope this helps! Let me know if you have any further questions.