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ID: 2887062 • Letter: 2
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20(Sp18) Live Streaming/At @HomelCheggcom x- #x www.webassign.net pos 38dep- 18510516 function for a certain make of replacement cartridges for a water purifier is given by the following equation where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. p-0.01r-0.1r +35 Determine the consumers' surplus if the market price is set at s5/cartridge. (Round your answer to two decimal places) ori points alc10 6 Used My Notes Ask Your Teach The demand function for a certain brand of CD is given by p-0.01x-o.2x41 where p is the wholesale unit price in dollars and x is the quantity demanded each week measured in units of a thousand Determine the consumers surplus·f the market pnce is se s0/disc. (Round your answer to two decimal places) $34375000 Submit Answer Save Progress -(2 points 67010 0/100 Submissions k Your Teacher where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is p36+1 dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. (Round your answers to the nearest dollar.) consumer's surplus +7 10.22.-Explanation / Answer
Solution:(1)
Demand function: P = -0.01x2 - 0.1x + 35
P(0) = 35
Given P = 5;
5 = -0.01x2 - 0.1x + 35
0.01x2 + 0.1x - 30 = 0
x2 + 10x - 3000 = 0
x2 + 60x - 50x - 3000 = 0
x(x + 60) - 50(x + 60) = 0
(x + 60) (x - 50) = 0
x = -60, 50
But x should be positive so, x = 50
Consumer's surplus is the integral of P minus 5.
Consumer's surplus = ?050 P(x) dx - ?050 5 dx
= ?050 (-0.01x2 - 0.1x + 35 - 5) dx
= [-0.01x3/3 - 0.1x2/2 + 30x]050
= [(-0.01*503/3 - 0.1*502/2 + 30*50) - 0]
= -1250/3 - 125 + 1500
Consumer's surplus = $958.33333 in thousands / week
or say
Consumer's surplus = $958333.33 / week
Solution:(2)
Demand function: P = -0.01x2 - 0.2x + 41
P(0) = 41
Given P = 6;
6 = -0.01x2 - 0.2x + 41
0.01x2 + 0.2x - 35 = 0
x2 + 20x - 3500 = 0
x2 + 70x - 50x - 3500 = 0
x(x + 70) - 50(x + 70) = 0
(x + 70) (x - 50) = 0
x = -70, 50
But x should be positive so, x = 50
Consumer's surplus is the integral of P minus 6.
Consumer's surplus = ?050 P(x) dx - ?050 6 dx
= ?050 (-0.01x2 - 0.2x + 41 - 6) dx
= [-0.01x3/3 - 0.2x2/2 + 35x]050
= [(-0.01*503/3 - 0.2*502/2 + 35*50) - 0]
= -1250/3 - 250 + 1750
Consumer's surplus = $1083.33333 in thousands / week
or say
Consumer's surplus = $1083333.33 / week
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