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## Pareto Optimality Mathematical Methods & Model Analysis Notes

This is an extract of our Pareto Optimality 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:

PARETO OPTIMALITY ANSWER An economy is composed of consumers with identical incomes and an identical utility function U=x1 0.5x20.5. There is a single input labour, of which 100 units are available. Production of x 1 requires 2 units of labour per unit of output; production of x2 requires 3. (i) Find an expression for the slope of the set of indifference curves of the consumers MRS = -

?[?] ?
[?]U [?]U
/
=? X2/
[?]X 1 [?]X 2 ?[?]X 1 ?

[?]U

0.5 = 0.5 X -0.5 X2 1
[?]X 1
[?]U

0.5 = 0.5 X -0.5 X1 2
[?]X 2
[?]MRS = - X 2 / X 1

(ii) What is the slope of the PPF Slope of the PPF is given by 100 = 2 X 1 + 3 X 2
[?]X 2 = 33 31 [?]X 2
=[?]X 1

2 3

X1

2 3

(PPF Function/ budget constraint for production)

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