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Week3 Handout (6pp) - Rational Choice The principal...

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Choice Ch 5: Choice Ch 6: Demand (sec. 2,5,6,8 & appendix) Ch 15: Market Demand (sec. 1& 2) 2 Rational Choice The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it. In terms of our model, this means choosing a bundle from the highest indifference curve that can be reached without exceeding the budget set. 3 Rational Constrained Choice x 1 x 2 Affordable bundles 4 Rational Constrained Choice Affordable bundles x 1 x 2 More preferred bundles 5 Rational Constrained Choice x 1 x 2 x 1 * x 2 * (x 1 *,x 2 *) is the most preferred affordable bundle. 6 Rational Constrained Choice The most preferred affordable bundle is called the consumer‟s ORDINARY DEMAND at the given prices and budget. Ordinary demands will be denoted by x 1 *(p 1 ,p 2 ,m) and x 2 *(p 1 ,p 2 ,m).
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7 Choice with monotonic preferences Supposed preferences are monotonic, i.e. more is better; Then the consumer will always choose a bundle that exhausts the budget. The chosen bundle is “interior” if it contains strictly positive quantities of both goods. 8 Rational Constrained Choice When preferences are monotonic, indifference curves are smoothly convex and the chosen bundle is interior, (x 1 *,x 2 *) satisfies two conditions: (a) the budget is exhausted; p 1 x 1 * + p 2 x 2 * = m (b) the slope of the budget constraint, - p 1 /p 2 , and the slope of the indifference curve containing (x 1 *,x 2 *) are equal at (x 1 *,x 2 *). 9 Choice: The canonical case x 1 x 2 x 1 * x 2 * (x 1 *,x 2 *) is interior . (a) (x 1 *,x 2 *) exhausts the budget; p 1 x 1 * + p 2 x 2 * = m. (b) The slope of the indiff. curve at (x 1 *,x 2 *) equals the slope of the budget constraint. 10 Solving for the optimum bundle If the budget is exhausted, then the optimum bundle must satisfy the budget constraint with equality: p 1 x 1 * + p 2 x 2 * = m If the optimum bundle is interior, then it must be a point at which the slope of the budget line equals the slope of the indifference curve, i.e.: - p 1 /p 2 = MRS We can use these two equations to solve for the two variables x 1 *and x 2 * . 11 Computing Ordinary Demands - a Cobb-Douglas Example. Suppose that the consumer has Cobb-Douglas preferences. Then U x x x x a b ( , ) 1 2 1 2 MU U x ax x a b 1 1 1 1 2 MU U x bx x a b 2 2 1 2 1 12 Computing Ordinary Demands - a Cobb-Douglas Example. So the MRS is At (x 1 *,x 2 *), MRS = -p 1 /p 2 so MRS dx dx U x U x ax x bx x ax bx a b a b       2 1 1 2 1 1 2 1 2 1 2 1 / / .   ax bx p p x bp ap x 2 1 1 2 2 1 2 1 * * * * . (A)
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