Help with algebra/economics (maths cleverness needed)

[The Guid]

Hello, I have come to the people on the board who are better at maths than me in supplication. A formula has defeated a once proud warrior.

My textbook has asked me to find the "price elasticity of demand" in terms of Q only for the following linear demand functions:

i) P = a-bQ (where b is the slope and a is also typically the y intercept if that helps)
ii) Q = c-dP (where d is the slope and c is also typically the y intercept)

If there are maths awesome people who want to try this but don't know a few economics things (and why should you) the formula for the Elasticity of Demand is:

Elasticity of Demand = 1/slope (so b in formula i, d in formula ii) x P/Q

The answers are:
i) Elasticity of Damand = 1-a/b x 1/Q
ii) Elasticity of Demand = 1-c/Q

I just have failed to get from the first formula to the later formulas. Its making me feel quite stupid ...

I would prefer not to hear mocking of my mathematical ability... but I am willing for that to be the price I pay for help.

Thanks in advance!

[General Zod]

Edit: Eh, nevermind.

[Steel]

i) P = a-bQ (where b is the slope and a is also typically the y intercept if that helps)
ii) Q = c-dP (where d is the slope and c is also typically the y intercept)

Major point and minor point here: b is not the slope, the slope is -b.

Minor point, it a is not "typically" the y (here actually P) intercept, it is always exactly the 'y' intercept.

If there are maths awesome people who want to try this but don't know a few economics things (and why should you) the formula for the Elasticity of Demand is:

Elasticity of Demand = 1/slope (so b in formula i, d in formula ii) x P/Q

The answers are:
i) Elasticity of Damand = 1-a/b x 1/Q
ii) Elasticity of Demand = 1-c/Q

I just have failed to get from the first formula to the later formulas. Its making me feel quite stupid ...

I would prefer not to hear mocking of my mathematical ability... but I am willing for that to be the price I pay for help.

Thanks in advance!

Well lets use eq i)

Slope is -b, so we juts plug it in and get

E= 1/(-b) * P/Q


what is P/Q? Its a/Q - b

So

E = -a/(bQ) + 1

or as the answer you have puts it

E = 1 - a/b *1/Q

Part ii)

Rearrange the formula to get P = (c-Q)/d

So here the slope is -1/d

You should be able to do the rest of this now.

[The Guid]

Hiya Steel, thanks for your help. Unfortunately you underestimated my own capacity for stupidity so I'm going to have ask another question to the world of people who are smarter than I am at this. Sorry!

Well lets use eq i)

Slope is -b, so we juts plug it in and get


E= 1/(-b) * P/Q

I'm good so far.

what is P/Q? Its a/Q - b

This was new to me, and I am not sure why this is true, but I am willing to just accept it (I tested it a couple of times and was baffled to see it work!), learn it and move on!

So

E = -a/(bQ) + 1

I'm confused. I go:

E = 1/-b * P/Q

E = 1/-b * a/Q-b (as per substitution)

And this is where I get stuck. I can't work out why it doesn't end up as:

E = a/bq+bsquared

I'm getting this by multiplying top by top and bottom by bottom and I know I am nowhere near right now. I also can't work out where the "1" comes from in the final answer.

I will keep working on this myself.

(Incidentally if anyone has a question relating to my degree in Drama, I will happily answer it.... Hello? Anyone got any Drama related problems? Why is everyone lauging?)

[Steel]

Hiya Steel, thanks for your help. Unfortunately you underestimated my own capacity for stupidity so I'm going to have ask another question to the world of people who are smarter than I am at this. Sorry!

Well lets use eq i)

Slope is -b, so we juts plug it in and get


E= 1/(-b) * P/Q

I'm good so far.

what is P/Q? Its a/Q - b

This was new to me, and I am not sure why this is true, but I am willing to just accept it (I tested it a couple of times and was baffled to see it work!), learn it and move on!

Ok, so we have an expression for P

P = a-bQ

so to find P/Q we just divide the whole line above by Q

So the left hand side becomes P/Q (looks quite like what we wanted to get)

The right hand side is

(a-bQ)/Q

which is

a/Q - bQ/Q

which is

a/Q -b

and so as the left hand side equals the right hand side (!)

P/Q = a/Q -b

So

E = -a/(bQ) + 1

I'm confused. I go:

E = 1/-b * P/Q

E = 1/-b * a/Q-b (as per substitution)

And this is where I get stuck. I can't work out why it doesn't end up as:

E = a/bq+bsquared

Theres a bit of bracketing confusion going on here (plain text is terrible for maths)

P/Q is a/Q -b

NOT

a/(Q-b)

so 1/(-b) * P/Q

is 1/(-b) * ( (a/Q) - b )

so we get one term

-a/(bQ)

and then the other term is

-(1/b) * (-b)

which gives us

1

as you want

I'm getting this by multiplying top by top and bottom by bottom and I know I am nowhere near right now. I also can't work out where the "1" comes from in the final answer.

I will keep working on this myself.

(Incidentally if anyone has a question relating to my degree in Drama, I will happily answer it.... Hello? Anyone got any Drama related problems? Why is everyone lauging?)

I spent 4 hours this afternoon giving the first demonstration to 250 first year biologists in their maths course and how to use a (shitty) maths program.

Only had one girl totally break down crying. Good day.