10. CONSUMERS' AND PRODUCERS' SURPLUS The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires per week is related to the unit price p by the relation p = 144 - - x? where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires avail- able in the market if the unit price is 1 p = 48 + 2 dollars, Determine the consumers' surplus and the pro- ducers' surplus when the market unit price is set at the equilibrium price.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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10. CONSUMERS' AND PRODUCERS' SURPLUS The management of
the Titan Tire Company has determined that the quantity
demanded x of their Super Titan tires week is related
per
to the unit price p by the relation
p = 144 – x2
where p is measured in dollars and x is measured in units
of a thousand. Titan will make x units of the tires avail-
able in the market if the unit price is
1
p = 48 +
dollars. Determine the consumers' surplus and the pro-
ducers' surplus when the market unit price is set at the
equilibrium price.
Transcribed Image Text:10. CONSUMERS' AND PRODUCERS' SURPLUS The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires week is related per to the unit price p by the relation p = 144 – x2 where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires avail- able in the market if the unit price is 1 p = 48 + dollars. Determine the consumers' surplus and the pro- ducers' surplus when the market unit price is set at the equilibrium price.
Expert Solution
Step 1

The demand equation is given as:

p=144-x2

The supply equation is:

p=48+x22

Step 2

At equilibrium, demand = supply:

144-x2=48+x22

144-48=x22+x296=3x22x2=9623x2=64x=±8

Equilibrium point will be (8,80)

Step 3

Consumer Surplus will be:

Calculus homework question answer, step 3, image 1

It will be given as:

CS=08144-x2-80dx

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