Question

Given the demand equation 180 q +15 where 15sqs75, for what value of q is In a maximum? For what value is it a minimum? The absolute value of the elasticity of demand has a maximum value at q Enter your answer in the answer box and then click Check Answer 1 Clear All remaining to (Use commas to separate answers. Round to the nearest ox)-4x-2x-9 the graph of t) -3x 4 and is vse in the same plane Use the graphing tool to graph the lines Click to enlarge Clear All

Answer 1

Q.1.

Demand equation:

180 where 15 S 75 + 15

Price elasticity of demand is given by:

$\eta = \frac{\frac{\mathrm{d} q}{q}}{\frac{\mathrm{d} p}{p}}p = \frac{p}{q}\frac{\mathrm{d} q}{\mathrm{d} p} = \frac{p}{q}\frac{1}{\frac{\mathrm{d} p}{\mathrm{d} q}}$

180 180 dp

Absolute value of elasticity:

p 1 180/(q15) 180/(15)2 15 15 where 15 <qK 75

Hence absolute value of elasticity is maximum when q = 75 and the value is 1 + 15/75 = 1.2

And absolute value of elasticity is minimum when q = 15 and the value is 1 + 15/15 = 2