a WTF economics ?

[thespeakerbox]

In the gasoliine market the Equill. price is $2 and the Equill. quantity is 100m gallons a day. Supposed the Gov. set a 1.80 maximum price. The price elasticity of supply of gas is 2.0 and the price elasticity of demand is 1.

There is a shortage... i firgured this out..
but i am asked how much of a shortage ?

I dont want the answer itself, but can someone help explain it. Can i just set up a simple proportion or something?

 

[BigJ]

Yes.

 

[everman]

Indeed I am.

 

[BigJ]

If you don't want an answer, read up here:

http://en.wikipedia.org/wiki/Price_elasticity

 

[thespeakerbox]

ok then, can someone show me how to get an answer. Wikipedia is just the concept

 

[Nebor]

I don't believe a simple proportion will give you your answer. It will give you one of the things you need to determine the answer, but the problem is more complicated than that.

 

[JS80]

Government price controls don't work. Don't even try.

 

[Nebor]

Ok, stick with me. I've had about a decade since my last economics course, but I'll give it my best shot.

First off, set up your proportion $2 over 100 = $1.8 over x. Work that out and you get 90.

Now it may be helpful to draw a graph with your supply and demand curves, that's what I did. Make your equilibrium point, then draw a dotted line representing your price ceiling at $1.80. Go ahead and mark your other point of $1.80, 90 on your supply curve. Now the shortage is the difference between that point, and wherever your price ceiling intersects your demand curve.

Graphing math has sort of fell from my brain over the years, but I think because the price elasticity is 1, which is basically 1 over 1, that you can assume that the X value on the demand curve where Y equals $1.80 is 110m.

So that would mean the answer is 20 million barrels. Again, I'm not certain on that last part.

EDIT: Ok, the math came back to my brain after a moment. Plus you'll need a real answer and not a guess to do a problem where price elasticity is not equal to 1. So to determine the X value when Y = $1.80, set up your price elasticity formula as follows, keeping in mind that price elasticity is equal to the percentage change in x over the percentage change in y. And that I am putting in 1 as the value for price elasticity, as that was a given.

1 = ((x-100)/x)/(2 - 1.8)/2))

So solve that for X.

 

[Nebor]

Sorry for the delays in my replies, I'm halfway relearning this as I'm doing it. I came up with the X value to be 111.11. So that would leave you with a shortage of 21.11 million barrels.