P2-2''' 2(P2-2)
________=_______=0.5
(P2+2)/2 P2+2
The answer to this should be 0.5. I am not getting this answer. I am not sure
What I am doing wrong.
I do not understand your notation. That is why I did not respond to your previous post of the same question. You said it had something to do with price change and demand elasticity.
The question is from my microeconomics course. What I am having trouble remembering is how to simplify the Algebra portion of the problem.
The question deals with Price eleasticity of demand.
Q Quantitiy
P Price
This formula is:
{Q2-Q1)/[Q2-Q1)/2]
__________________
(P2-P1)/[P2+P1/2]
This is the question again:
Studies indicate that the price elasticity of demand for cigaretts is about 0.4. If a pack of cigarettes currently costs $2.00 and the govenment wants to reduce smoking by 20 percent, by how much should the govenment increase the price?
I understand that only the price portion (P2-P1)/[(P2-P1)/2]of the foumula is being used and that $2.00 is P1.
I have the calculation for the answer. That is what I submitted to your board.
When I try to simplify the algebra protion of the problem, I do not get the 0.5 and 3.33 as my answers.
Here is the calculation for the answer again. I will see if I can post it so it reads clearer at your end. Any help you could be in explaining how this was simplied would be greatly appreciated.
P2-2
_______ =
(P2+2)/2
2(P2-2)
________=0.5
P2+2
2P2-4=0.5P2+1
1.5P2=5
P2=3.33
Are you sure you copied the formula for demand elasticity correctly?
{Q2-Q1)/[Q2-Q1)/2] = 2, whatever Q2 and Q1 are
I suspect that you should have written
{Q2-Q1)/[Q2+Q1)/2]
which is the change in Q divided by the average value.
In the denominator,
(P2-P1)/[(P2+P1)/2]
is the change in P divided by the average value, but you omitted some parentheses around P1 + P2.
I also think there should be a minus sign in the elasticity definition, since Q should decrease when P increases.
Sorry I did write in a minus sign in two places by mistake.
This following is the correct formula. I don't know if you need to know this formula is for the midpoint method:
(Q2-Q1)/[Q2+Q1]/2
__________________
(P2-P1)/[(P2+P1)/2]
The following is the answer of 0.5 I came us with and that the price would be increased to $2.50.
.20 Quanity/.4 Price Eleasticity of Demand
.20/.4
=0.5
When I received the lesson back the instructor wrote out the answer. It seemed he used just second line of the formula (P2-P1)/[(P2-P1)/2] to calculate the answer.
P2-2
________=
(P2+2)/2
2(P2-2)
_________=0.5
P2+2
2P2-4=0.5P2+1
1.5P2=5
P2-3.33
I still am not clear how this is simplifing to 3.33?
To simplify the given expression, let's break it down step by step.
First, let's simplify the numerator:
P2 - 2''' can be written as (P2 - 2) * (P2 - 2). Applying the exponent rule, we get:
(P2 - 2)*(P2 - 2) = (P2 - 2)^2
Next, let's simplify the denominator:
(P2 + 2)/2 can be written as 1/2*(P2 + 2). Multiplying both the numerator and denominator by 2, we get:
1/2*(P2 + 2) = (1/2)*(2*(P2 + 2)) = (1/2)*(2*P2 + 4) = (1/2)*(2*(P2) + 4) = P2 + 2
Now, let's substitute the simplified numerator and denominator back into the main expression:
(P2 - 2)^2 / (P2 + 2)
= (P2 - 2)*(P2 - 2) / (P2 + 2)
= ((P2 - 2)*(P2 - 2)) / ((P2 + 2)/2)
= ((P2 - 2)*(P2 - 2)) * (2/(P2 + 2))
= (2*(P2 - 2)*(P2 - 2)) / (P2 + 2)
Now, applying the distributive property, we get:
= (2*(P2)*(P2) - 2*(P2)*2 - 2*(P2)*2 + 4*2) / (P2 + 2)
= (2P2^2 - 4P2 - 4P2 + 8) / (P2 + 2)
= (2P2^2 - 8P2 + 8) / (P2 + 2)
Now, let's set this expression equal to 0.5:
(2P2^2 - 8P2 + 8) / (P2 + 2) = 0.5
To solve for P2, we can multiply both sides by (P2 + 2):
(2P2^2 - 8P2 + 8) = 0.5*(P2 + 2)
Expanding the right side:
2P2^2 - 8P2 + 8 = 0.5P2 + 1
Subtracting 0.5P2 + 1 from both sides:
2P2^2 - 8P2 + 8 - 0.5P2 - 1 = 0
Combining like terms:
2P2^2 - 8.5P2 + 7 = 0
Now, we have a quadratic equation. We can solve this using factoring, completing the square, or the quadratic formula. Once we find the values of P2 that satisfy this equation, we can substitute them into the original expression to verify if the answer is indeed 0.5.