Answer to Question #312217 in Microeconomics for Pat

Question #312217

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?


1
Expert's answer
2022-03-18T11:59:58-0400

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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