You only need to complete either (a) or (b) below. Circle the letter at the star

Question

You only need to complete either (a) or (b) below. Circle the letter at the start of the question to show which problem should be graded out of 10 points. The other question may be completed for 5 extra credit points. Mark that one for extra credit. It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding unit price is p = square root 260 - 4x dollars. Determine the consumer's surplus if the market price is set at $10/unit. Round your answer to the nearest dollar.

Explanation / Answer

p = (260 -4x)

given po = $10

==> 10 = (260 -4x)

==> 100 = 260 -4x

==> 4x = 160

==> x = 40

Consumer surplus = [0 to x] p - po dx

==> Consumer surplus = [0 to 40] (260 -4x) - 10 dx

= [0 to 40] (260 -4x)1/2 - 10 dx

= [0 to 40] (260 -4x)1/2 +1/[(1/2 +1)(-4)] - 10x

= [0 to 40] -(260 -4x)3/2/6 - 10x

= -(260 -4(40))3/2/6 - 10(40) - [-(260 -4(0))3/2/6 - 10(0)]

= -1000/6 -400-[-698.73]

= 132.06

Hence consumer surplus = 132.06

==> consumer surplus = $132

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