Rational Constrained Choice (Xy* x2 )is interior. (a(x,*, x2 )exhausts the budget; p,X,*+ p2X2= m X1
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 X1
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; p1X1 p2X2 m b tangency: the slope of the budget constraint,-p,p2, and the slope of the indifference curve containing(,*, x2*) are equal at (x, * X2*)
Rational Constrained Choice (x1 *,x2 *) satisfies two conditions: (a) the budget is exhausted; p1x1 * + p2x2 * = m (b) tangency: the slope of the budget constraint, -p1 /p2 , and the slope of the indifference curve containing (x1 *,x2 *) are equal at (x1 *,x2 *)
Meaning of the Tangency Condition Consumer's marginal willingness to pay equals the market exchange rate Suppose at a consumption bundle x1, x2), MRS=2,1/P2=-1 The consumer is willing to give up 2 unit of x2 to exchange for an additional unit of x1 The market allows her to give up only 1 unit of x2 to obtain an additional x1 (X1, x2) is not optimal choice She can be better off increasing her consumption of x1
Meaning of the Tangency Condition Consumer’s marginal willingness to pay equals the market exchange rate. Suppose at a consumption bundle (x1, x2), MRS=-2, -P1/P2=-1 – The consumer is willing to give up 2 unit of x2 to exchange for an additional unit of x1 – The market allows her to give up only 1 unit of x2 to obtain an additional x1 (x1, x2) is not optimal choice She can be better off increasing her consumption of x1
x2 X
x 1 x 1 x 2