# econ wk 3 - Rational Choice The principal behavioral...

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Choice Ch 5: Choice Ch 6: Demand (sec. 2,5,6,8 & appendix) Ch 15: Market Demand (sec. 1& 2) Rational Choice The principal behavioral postulate is that a decision maker chooses its most preferred alternative from those available to it. 2 In terms of our model, this means choosing a bundle from the highest indifference curve that can be reached without exceeding the budget set. Rational Constrained Choice x 2 3 x 1 Affordable bundles Rational Constrained Choice x 2 More preferred bundles 4 Affordable bundles x 1 Rational Constrained Choice x 2 (x 1 *,x 2 *) is the most preferred affordable bundle. 5 x 1 x 1 * x 2 * 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 6 x 1 *(p 1 ,p 2 ,m) and x 2 *(p 1 ,p 2 ,m).

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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. 7 The chosen bundle is “interior” if it contains strictly positive quantities of both goods. 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: 8 (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 *). Choice: The canonical case 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 9 x 1 x 1 * x 2 * ,x ) equals the slope of the budget constraint. 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, 10 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 * . Computing Ordinary Demands - a Cobb-Douglas Example. Suppose that the consumer has Cobb-Douglas preferences. Ux x x x ab ( , ) 1 2 1 2 11 Then MU U x ax x 1 1 1 1 2  MU U x bx x 2 2 12 1 Computing Ordinary Demands - a Cobb-Douglas Example. So the MRS is MRS dx dx Ux ax x bx x bx 2 1 1 2 1 1 2 1 2 1 2 1  / / . 12 At (x 1 *,x 2 *), MRS = -p 1 /p 2 so   ax bx p p x bp ap x 2 1 1 2 2 1 2 1 * * ** . (A)
Computing Ordinary Demands - a Cobb-Douglas Example. So now we know that MRS = slope of budget line: x bp x 2 1 1 ** (A 13 budget constraint is satisfied with equality ap 2 (A) px m 11 22 .  (B) Computing Ordinary Demands - a Cobb-Douglas Example.

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econ wk 3 - Rational Choice The principal behavioral...

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