Topic 4 – Choice

(Lecture 2 – Sept 23rd)

Assume: x1,x2; p1,p2;

x2

x1

Math: Constrained Optimization

-- U(x1,x2); Max(x1,x2) s.t. p1x1+p2x2=Y

-- Solve: 3 first-order conditions;

1.

2.

3.

-- Intuition:

MUx1 =

= ;

MUx2 =

=

left: MRS (“internal” marginal valuation)

right: OC (“external” marginal valuation)

Budget Constraint: x1p1 + x2p2 = Y

Intuition:

-- Points on the budget constraint represent choices

that fully exhaust individual’s income;

-- Every bundle on the budget constraint is associated

with an indifference curve and defines a level of utility;

-- The individual has to choose the bundle on the

constraint that maximized the individual’s utility;

-- The max is given by a tangency.

## Document Summary

Topic 4 choice (lecture 2 sept 23rd) - points on the budget constraint represent choices that fully exhaust individual"s income; - every bundle on the budget constraint is associated with an indifference curve and defines a level of utility; - the individual has to choose the bundle on the constraint that maximized the individual"s utility; - the max is given by a tangency. x1. - at point a, the slope of the indifferent curve is mrs; - at point a, the slope of the budget constraint is oc; - clearly at point a, mrs > oc; - msr>oc: how much x2 the individual is willing to give up for an additional unit of x1 (msr) is more than what they have to (oc). - move down the budget line until x2 x1. Problem: there are a lot of tangencies that satisfy this equation (a. k. a. Solution: foc 3 the tangency must lie on the budget line.