What is the consumers' surplus if the selling price is set at $150/unit? (Round your answer to the nearest dollar.)

Question

Consumers' Surplus, The demand function for a certain model of Blu-ray player is given by

p=450/0.5x+2

where p is the unit price in dollars and x (in units of a thousand) is the quantity demanded per week. What is the consumers' surplus if the selling price is set at $150/unit? (Round your answer to the nearest dollar.)

Answer 1

p=450/.5x^2 =900/x^2

p=150 = 900/x^2

1=6/x^2

x^2 =6

x =sqr6 (thousand)

CS = integral of 900/x^2 - 150 = -900/x -150x

evaluated from 0 to sqr6

= -900/sqr6-150sqr6 -(-infinity)

= -900sqr6/6-150sqr6 + infinity

= -150sqr6 -150sq6+ infinity

=-300sqr6+infinity

=about infinity -$734.85

= infinite number of dollars

the Consumer Surplus is infinite

since the integral is divergent

the demand curve has consumers still buying some small amount even as price approaches infinity

It's not a realistic demand curve, at some finitely high price, all consumers get priced out of the market and stop buying.