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 $70, then her net consumer's surplus A)increases by 400. B)falls by 2,800. C)falls by 600. D)falls by 800. E)increases by 1,600.

Question

Quizplus · Accepted Answer

To find the net consumer's surplus, we need to first find the utility-maximizing consumption bundle before and after the price increase. The utility-maximizing consumption bundle can be found by setting the marginal utility per dollar of each good equal to each other. Mathematically, it can be represented as:

MUx/Px = MUm/Py

where MUx is the marginal utility of earplugs, Px is the price of earplugs, MUm is the marginal utility of other goods, and Py is the price of other goods.

So, the utility-maximizing consumption bundle before the price increase can be found by setting MUx/Px = MUm/Py = 100/50 = 2. And, we know that Ms. Quasimodo has $10,000 to spend, so she can buy 200 earplugs and have $0 left over for other stuff.

After the price increase, the new price of earplugs is $70. So, the new marginal utility per dollar of earplugs becomes:

MUx/Px = 100/70 = 10/7

Setting MUx/Px = MUm/Py, we can find the new optimal consumption bundle as:

10/7x = Umx = 1000 - m

m = 1000 - (10/7)x

Total spending is $10,000, so we have:

70x + m = 10,000

Substituting m from above, we get:

70x + 1000 - (10/7)x = 10,000

Solving for x, we get:

x = 105

So, Ms. Quasimodo can now buy 105 earplugs and have $1,450 left over for other stuff.

To find the net consumer's surplus, we need to find the difference between the total utility before and after the price increase and subtract the increase in spending:

Net consumer's surplus = U(200, 0) - U(105, 1450) - (70-50)*105

Net consumer's surplus = 20,000 - 19,200 - 2100 = 700

Therefore, Ms. Quasimodo's net consumer's surplus falls by $800 (option D).

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