Algebra 2 Honors

Question

If the price per ticket is $150, what would be the predicted amount of lost revenue to the nearest dollar?

Answer 1

price per ticket = $150

this type of problem usually gives additional information, such as the supply and demand curves (functions)

supply is upward sloping, demand downward sloping

for simple linear functions

such as demand: x = -P +300

supply x = P

set them equal to solve for equilibrium price (market clearng price where quantity sold = quantity supplied)

2P = 300

P = $150

revenue = R= Px = -P^2 +300P

revenue maximizing price is when derivatie R'=0 = -2P+300

2P=300

P =$150

max R =-150^2 +300(150) = 150x150 = $22,500

raise price by $5

and new Revenue =-155^2+300(155) =145(155)= 22475

and lost Revenue = 22500-22475 = $25

sort of a "surprise" is that if you raise or lower price, you lose revenue