IAI's May, 2015 exam Q5

[Hemant Rupani]

case of inverse relation between Quantity Supplied and Price.

If P is price and Q is quantity supplied, then which of the following equations gives a price elasticity of supply of 1 at all quantities.?
A. P = x – Q (for x > Q)
B. P = 1/Q
C. P = x + Q

here answer is B, so is there any case where Quantity Supplied and Price inversely related?

 

[Whippet1]

No, because we always assume that quantity supplied increases with price and so the supply curve slopes upwards.

P = 1/Q gives a downward-sloping curve. It is actually the equation of a downward-sloping demand curve with an elasticity of -1 at all points along it.

elasticity = dQ/dP * P/Q

So, for P=1/Q, Q=1/P and dQ/dP = -1/P^2

and:

elasticity = -1/P^2 *P/(1/P) = -1

Seems like a bit of an "odd" question!

 

[Hemant Rupani]

Thanks Whippet!
So, now I can say it was just mathematically correct but illogical.