Aboat tour company finds that if the price p , charged for an one-hour harbor tour, is $20, the average number of passengers per week, x , is 300. when the price is reduced to $18, the average number of passengers per week increases to 360.the demand and supply curves of a certain brand of running shoes are given by
p=0(x)=1 1 2-0.04x, and p-s(x)-0.06x+42, where p is the price in dollars and x is the quantity sold.
(a) assuming that the demand curve p d(x) is linear, find its formula: p-d(x)
(b) assuming that the equilibrium price is $22 per tour, the equilibrium demand is e
(c) the consumers' surplus at that demand is $ . (use a fraction for the coefficient.)

Answer

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Explanation  

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a)  p(x) = (-1/30)*x + 30

b) xe = 240

c) The consumers' surplus at that demand is $ 960.00

Step-by-step explanation:

Given info

p₁ = 20

x₁ = 300

p₂ = 18

x₂ = 360

a) We can apply the following equation

p - p₁ = m*(x - x₁)

where

m is the slope, which can be obtained as follows

m = (p₂-p₁) / (x₂-x₁)

⇒ m = (18-20) / (360-300) = -2/60 = -1/30

then

p-20 = (-1/30)*(x-300)

⇒ 30*p - 600 = -x + 300

⇒ p(x) = (-1/30)*x + 30

b) If p(x) = 22

⇒  22 = (-1/30)*x + 30

⇒  xe = 240 passengers

c) If x = 0   ⇒  p(0) = (-1/30)*(0) + 30 = 30

then

we can get h as follows

h = p(0) - p(240) = 30 - 22 = 8

if b = x(equlibrium) = 240

we apply

A = b*h/2  ⇒  A = 240*8/2 = 960

The consumers' surplus at that demand is $ 960.00

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