Question

The arc advertising elasticity is 1.5 as advertising expenditure increase from $10 to $12 million. If demand is 50 at an advertising expenditure of $12 million, what will demand be at an advertising expenditure of $10 million?

Answer 1

Arc elasticity is the measure of elasticity between two point on curve by using midpoints:

elasticity=1.5

midpoint expenditure=$\frac{p1+p2}{2}$

=$\frac{10+12}{2}$ =

p=11

%change in expenditure=

$\frac{12-10}{11}$

=0.18

midpoint quantiy=$\frac{q1+q2}{2}$

Where,q₁=X,q₂=50

midpoint q=$\frac{X+50}{2}$

=0.5x+25

%change in quantity=

$\frac{50-X}{0.5X+25}$

Arc elasticity=$\frac{change in quantity}{change in expenditure}$

1.5$\times0.18$ =$\frac{50-X}{0.5X+25}$

0.27=$\frac{50-X}{0.5X+25}$

0.27(0.5x+25)=50-X

0.135X+6.75=50-X

1.135X=43.25

X=38.10

therefore the demand of advertising at $10 is

Q₁=38.10