#4970 - Pareto Optimality Mathematical Methods & Model Analysis - Advanced Microeconomics

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)