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

Jordan Johnson · Accepted Answer

Final Answer : A, Explanation :  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) = 10000This 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.

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