05_Ch05_Choice.pdf

X am a b p 1 1 computing ordinary demands a cobb

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x am a b p 1 1 * ( ) .

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Computing Ordinary Demands - a Cobb-Douglas Example. x bm a b p 2 2 * ( ) . Substituting for x 1 * in p x p x m 1 1 2 2 * * then gives x am a b p 1 1 * ( ) .
Computing Ordinary Demands - a Cobb-Douglas Example. So we have discovered that the most preferred affordable bundle for a consumer with Cobb-Douglas preferences U x x x x a b ( , ) 1 2 1 2 is ( , ) ( ) , ( ) . * * ( ) x x am a b p bm a b p 1 2 1 2

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Computing Ordinary Demands - a Cobb-Douglas Example. x 1 x 2 x am a b p 1 1 * ( ) x bm a b p 2 2 * ( ) U x x x x a b ( , ) 1 2 1 2
Rational Constrained Choice When x 1 * > 0 and x 2 * > 0 and (x 1 *,x 2 *) exhausts the budget, and indifference curves have no kinks , the ordinary demands are obtained by solving: (a) p 1 x 1 * + p 2 x 2 * = y (b) the slopes of the budget constraint, -p 1 /p 2 , and of the indifference curve containing (x 1 *,x 2 *) are equal at (x 1 *,x 2 *).

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