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Consumer Surplus Mathematical Methods Model Analysis Notes

Economics Notes > Advanced Microeconomics Notes

This is an extract of our Consumer Surplus Mathematical Methods Model Analysis document, which we sell as part of our Advanced Microeconomics Notes collection written by the top tier of University Of Leeds students.

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X=

I I Y=
2PX, 2PY

A consumer has the utility function u=x0.5y0.5.

100 = 50 2(1) 100 Y=
= 25 2(2) X=

(i) Find the consumers Marshallian demand curves for x and y Max Z = X 0.5 Y 0.5 - l[PX X + PY Y - I]
dZ U
= 0.5 - lPX = 0
dX X

(i)

dZ U
= 0.5 - lPY = 0
dY Y

(ii)

dZ
= PX X + PY Y - I = 0
dl
P Y
[?] = X X PY

(iii) from (i) and (ii)) (from (iii))

PX X + PX X = I Thus

X=

I I Y=
2PX, 2PY

(ii) Suppose that initially the consumer has an income of 100, and faces Px = 1 and Py = 2. What will be the consumption of x and y?

(iii) Suppose that the price of y is now reduced to 1. Find an approximate value for the consumer surplus resulting from this price change, using the `rule of a half' If the price of Y is reduced to 1 then Y=50. Using the 'rule of a half' Marshallian Consumer Surplus (MCS) = 0.5(P1-P2)(Y1+Y2)

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