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?
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
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