University Economics Question Help?

Question

I have an exam tomorrow and there is a question that I cannot work out. It is as follows:

The demand schedule for a particular good is P = 400-2Q

Where P is the Price and Q is the quantity demanded.

What is the price elasticity of demand when Q is 100?

I have worked out that at Q = 100, P = 200.

I know that the formula for working these out is

Change in Quantity / Change in Price

X

Price / Quantity.

But my problem is knowing what the original figures are in order to calculate the change. I have tried using random original quantities but the answers are always different.

The second part of the question is whether the demand is elastic or inelastic at this point?

Many thanks in advance for any help

Answer 1

You need to use point elasticity method here (requires some calculus)

E=δQ*P/δP*Q

Q=100 P=400-200=200

P/Q=200/100=2

P=400-2Q

Q=200-P/2

δQ/δP=(200-P/2)'= -1/2

E= -2/2 = -1

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