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( x,, x2) MRS=2,P1P2=-1 The consumer is willing to give up 2 unit of x to exchange for an additional unit of X, The market allows her to give up only 1 unit of x to obtain an additional x (X1, X2)is not optimal choice She can be better off increasing her consumption of x
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