Help: elasticity?

Question

Consider the following non-linear demand curve:

(i)What is the slope of this demand curve? dP/dQ = -2AQ^-3

(ii)When what is the slope at P=1, P=4, and P=9?

(iii)What is the elasticity for the above values?

(iv)Suppose this were the demand curve facing your firm, and you were the only supplier of this product. Would you increase the price from $1 to $2? Would you increase prices from $4 to $5?

i think i did the first part wrong b/c i asked my teacher, but i didn't understand what she said to do... can someone help me? please??

Answer 1

are u sure the equation is correct?

Answer 2

(i)

Slope of demand curve will change over all range.

If δP/δQ=-2AQ^-3

So slope of demand function will be (reversed from above):

δQ/δP=1/(-2AQ^-3)

(ii)

P=1 Slope=-(2A)^1/3

P=4 Slope=-(A/2)^1/3

P=9 Slope=-(2A/9)^1/3

(iii)

To find elasticities you should give primary demand functions - not derivatives, because E=P*δQ/Q*δP since P is given then Q would be find from primary functions.

(iv)

You should give 'A' variable and supply equation mentioned in (iii) for right answer.