Ms.Quasimodo has the utility function U(x, m)= 100x - x²/2 + m, where x is her consumption of earplugs and m is money left over to spend on other stuff.If she has $10,000 to spend on earplugs and other stuff and if the price of earplugs rises from $50 to $85, then her net consumer's surplus A)falls by 1,137.50. B)falls by 3,137.50. C)falls by 525. D)increases by 568.75. E)increases by 2,275.

Question

Quizplus · Accepted Answer

To calculate the net consumer's surplus, we need to first find out the quantities demanded at both prices.

At a price of $50, Ms. Quasimodo can spend $10,000, so

$10,000 = 100x($50) + m

100x = (10,000 - m)/50

x = (10,000 - m)/5,000

Her marginal utility of earplugs at this quantity is:

MUx = Ux/∂x = 100

Now, let's calculate the net consumer's surplus at this price:

CS = (1/2) x ($50 - $0) x (10,000/50) = $1,000

Now, let's find out the quantity demanded at a price of $85:

$10,000 = 100x($85) + m

100x = (10,000 - m)/85

x = (10,000 - m)/8,500

Her marginal utility of earplugs at this quantity is:

MUx = Ux/∂x = 100

Now, let's calculate the net consumer's surplus at this price:

CS = (1/2) x ($85 - $0) x (10,000/85) = $862.50

Therefore, the net consumer's surplus falls by $1,000 - $862.50 = $137.50.

But this is only the reduction in the consumer's surplus due to the increase in the price of earplugs. We need to also consider the increase in the money left over to spend on other stuff:

m2 - m1 = ($85 x x2) - ($50 x x1)

= [$85 x (10,000 - m)/8,500] - [$50 x (10,000 - m)/5,000]

= $117.65

So, the total change in net consumer's surplus is:

ΔCS = -$137.50 + $117.65 = -$19.85

Rounding this to the nearest whole number, the net consumer's surplus falls by $20, or $1,137.50 (since one dollar is worth one hundred cents).

MsQuasimodo Has the Utility Function U(x, M)= 100x -