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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.

* The following is a more accessble plain text extract of the PDF sample above, taken from our Advanced Microeconomics Notes.
Due to the challenges of extracting text from PDFs, it will have odd formatting:
*

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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