# Consumer Surplus Mathematical Methods Model Analysis Notes

This is a sample of our (approximately) 4 page long Consumer Surplus Mathematical Methods Model Analysis notes, which we sell as part of the Advanced Microeconomics Notes collection, a 1st Class package written at University Of Leeds in 2013 that contains (approximately) 14 pages of notes across 3 different documents.

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### Consumer Surplus Mathematical Methods Model Analysis Revision

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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 − λ[PX X + PY Y − I]
δZ U
= 0.5 − λPX = 0
δX X

(i)

δZ U
= 0.5 − λPY = 0
δY Y

(ii)

δZ
= PX X + PY Y − I = 0
δλ
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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