about the elasticity of demand, please help..

guest:

Dear All,

Please help to check my answer for below questions :

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the demand function of a product is : Q = 500 - 40P + P²

P : price/unit (dollar), and Q : the amount of production.

questions :

a. Determine the elasticity of demand when the price is = 15.
b. If the price is increased by 5%, what will happen to the demand?

my answer :

a. Q = 500 - (40x15) + 15²
= 500 - 600 + 225
= 125

if Q = 500 - 40P + P², then Q₁ = 2P - 40, and P₁ = - 1/40 + 1/P
if Q = 500 - 40P + P², then dQ/dP = 2P - 40, and where did you get P' from?
So I guess Q'=2*15-40=-10

E = dQ/dP x P/Q
= -10 x 15/125
= -1,2 (Do you use commas instead of decimal points?)

b. If the price is increased by 5%, the demand will be decrease to = 1,2 x 5 = 6 (I don't think so)

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Thank you very much for the correction..

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I have never done this before, I just googled it then to see if I could help you.
I think that part a is correct except for the coloured changes/ additions that I did.

Now part b
E = -1.2
I think this means that if price goes up by 1.2%, the demand will go down by 1%
You want to know what will happen to demand if the price goes up by 5%
so let the change in demand be d%
so this is the equation that you have to solve.
1.2% / 1% = 5% / d%

1.2 = 5/d
d = 5/1.2
d = 4.2 (1 dec places)

so if the price increases by 5% I think that the demand will decrease by 4.2%

Like I said, I hadn't even heard these terms before I googled them for you just a moment ago.
But that's what I think.

Dear Melody,

Thank you very much for your correction, so I just have to state --> if Q = 500 - 40P + P2, then Q1 = 2P - 40, without P1 = - 1/40 + 1/P right?


Thanks.

guest:

Dear Melody,

Thank you very much for your correction, so I just have to state --> if Q = 500 - 40P + P2, then Q1 = 2P - 40, without P1 = - 1/40 + 1/P right?


Thanks.

--> if Q = 500 - 40P + P ², then Q ' = 2P - 40, without P1 = - 1/40 + 1/P right? right

I much prefer the notation dQ/dP but if you must use shorthand it is Q' (quotation mark - referred to as Q dash) not Q1

I have no idea where you even got the P1 (P') from. Some things are just a mystery to me.

Dear Melody,

Thank you very much for your answer.