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 $75, then her net consumer's surplus A)falls by 937.50. B)falls by 625. C)falls by 2,937.50. D)increases by 468.75. E)increases by 1,875.

Question

Quizplus · Accepted Answer

To calculate the change in net consumer's surplus, we need to first find the initial level of net consumer's surplus. 
At a price of $50, Ms. Quasimodo can buy 200 earplugs (since she has $10,000 to spend and each earplug costs $50). 
We can then use her utility function to find the maximum amount she is willing to pay for these 200 earplugs:

U(200,10000-200*50) = 200*100 - 200*50 + (10000-200*50)*(-1/2) = 10000

This means that at a price of $50, her maximum willingness to pay is $10,000. 
If the price rises to $75, then she can only buy 133.33 earplugs:

10000 = 100*133.33 - 133.33*75 + (10000-133.33*75)*(-1/2)

So at a price of $75, her maximum willingness to pay is $6670.83.

Her net consumer's surplus at a price of $50 is:

10000 - 50*200 = $0.

Her net consumer's surplus at a price of $75 is:

6670.83 - 75*133.33 = $312.50.

The change in net consumer's surplus is:

312.50 - 0 = $312.50 less.

So her net consumer's surplus falls by $312.50. Converted to cents, this is a decrease of $312.50*100 = 31,250 cents, or $312.50/0.3333 = $937.50.

MsQuasimodo Has the Utility Function U(x, M)= 100x - X2/2

MsQuasimodo Has the Utility Function U(x, M)= 100x - X²/2