[经济学]Micro Ch05.ppt

Chapter 05 Choice 消费者最优选择 Where Are We in the Course? 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 Rational Constrained Choice 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 byx1*(p1,p2,m) and x2*(p1,p2,m). 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 Rational Constrained Choice Computing Ordinary Demands - a Cobb-Douglas Example. Suppose that the consumer has Cobb-Douglas preferences. Then Computing Ordinary Demands - a Cobb-Douglas Example. So the MRS is At (x1*,x2*), MRS = -p1/p2 so Computing Ordinary Demands - a Cobb-Douglas Example. (x1*,x2*) also exhausts the budget, so Computing Ordinary Demands - a Cobb-Douglas Example. Computing Ordinary Demands - a Cobb-Douglas Example. Rational Constrained Choice When x1* 0 and x2* 0 and (x1*,x2*) exhausts the budget,and indifference curves have no ‘kinks’, the ordinary demands are obtained by solving: (a) p1x1* + p2x2* = y (b) the slopes of the budget constraint, -p1/p2, and of the indifference curve containing (x1*,x2*) are equal at (x1*,x2*). Rational Constrained Choice But what if x1* = 0? Or if x2* = 0? If either x1* = 0 or x2* = 0 then the ordinary demand (x1*,x2*) is at a corner solution to the problem of maximizing utility subject to a budget constraint. Examples of Corner Solutions -- the Perfect Substitutes Case Examples of Corner Solutions -- the Perfect Substitutes Case Examples of Corner Solutions -- the Perfect Substitutes Case Examples of Corner Solutions -- the Perfect S