Economics Notes Advanced Microeconomics Notes

Pareto Optimality Mathematical Methods & Model Analysis Notes

Updated Pareto Optimality Mathematical Methods & Model Analysis Notes

Advanced Microeconomics

Approximately 14 pages

These notes provide detailed exam essay structures on various topics within advanced microeconomics such as: general equilibrium; welfare economics and the theory of cost-benefit analysis. Two Notes include the mathematical models of pareto optimality and consumer surplus, with detailed essay structures analysing the models in context. The third set of notes analyses the trade off between different measurements of welfare; compensation tests and social welfare function.

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Pareto Optim...

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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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