Chapter five Choice 消费者最优选择
Chapter Five Choice 消费者最优选择
Where Are We doing in This Chapter? After modeling a consumer's choice set and his preference(represented by utility functions), we now put them together and model how he/she makes optimal choice In mathematical terms this is a constrained maximization problem In economics this is a rational choice problem
Where Are We Doing in This Chapter? After modeling a consumer’s choice set and his preference (represented by utility functions), we now put them together and model how he/she makes optimal choice. In mathematical terms, this is a constrained maximization problem; In economics, this is a rational choice problem
Rational Constrained choice More preferred bundles Affordable bundles
Rational Constrained Choice Affordable bundles x1 x2 More preferred bundles
Rational Constrained choice The most preferred affordable bundle is called the consumers ordinary DEMAND at the given prices and budget Ordinary demands will be denoted by X, (p1,P2, m) and X2 (p1,p2, m)
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 x1 *(p1 ,p2 ,m) and x2 *(p1 ,p2 ,m)
Rational constrained choice When x*>0 and x* >o the demanded bundle is Interior If buying (x,* x2 *)costs Sm then the budget is exhausted
Rational Constrained Choice When x1 * > 0 and x2 * > 0 the demanded bundle is INTERIOR. If buying (x1 *,x2 *) costs $m then the budget is exhausted
Rational Constrained choice (X,*, X2 * )is interior. (a(x,*, x2 )exhausts the budget; p p2X 大 m
Rational Constrained Choice x1 x2 x1 * x2 * (x1 *,x2 *) is interior. (a) (x1 *,x2 *) exhausts the budget; p1x1 * + p2x2 * = m
Rational Constrained choice (X,*, X2 )is interior (b The slope of the indiff curve at ( X,* X2 * )equals the slope of the budget constraint
Rational Constrained Choice x1 x2 x1 * x2 * (x1 *,x2 *) is interior . (b) The slope of the indiff. curve at (x1 *,x2 *) equals the slope of the budget constraint
Rational Constrained choice (X*,x2*)satisfies two conditions (a the budget is exhausted; p11+p2X2=m (b the slope of the budget constraint p1/p2, and the slope of the indifference curve containing(X,* X2 * are equal at X,*, x2*)
Rational Constrained Choice (x1 *,x2 *) satisfies two conditions: (a) the budget is exhausted; p1x1 * + p2x2 * = m (b) the slope of the budget constraint, -p1 /p2 , and the slope of the indifference curve containing (x1 *,x2 *) are equal at (x1 *,x2 *)
Computing Ordinary Demands a Cobb-Douglas Example Suppose that the consumer has Cobb-Douglas preferences U(x1,X2)=X1x2
Computing Ordinary Demands - a Cobb-Douglas Example. Suppose that the consumer has Cobb-Douglas preferences. U x x x x a b ( , ) 1 2 = 1 2
Computing Ordinary Demands a Cobb-Douglas Example Suppose that the consumer has Cobb-Douglas preferences U(XI, X2)=xix Then MU Ox,axd-xb U MU- OU Ox2bx月x21
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 = = −
