The Consumer Problem and the Budget Constraint Overheads

The fundamental unit of analysis in consumption economics is the individual consumer

The underlying assumption in consumption analysis is that all consumers possess a preference ordering which allows them to rank alternative states of the world.

The behavioral assumption in consumption analysis is that consumers make choices consistent with their underlying preferences

The main constraint facing consumers in determining which goods to purchase and consume is This is called the budget constraint the amount of income that they can spend

The Consumer Problem The consumer problem is to maximize the consumer has to spend. the satisfaction that comes from the consumption of various goods subject to the amount of income

The Consumer Problem Maximize satisfaction subject to income

Definition of the budget constraint A consumer’s budget constraint identifies which combinations of goods and services the consumer can afford with a limited budget, at given prices

Notation Income - I Quantities of goods - q 1, q 2,... q n Prices of goods - p 1, p 2,... p n Number of goods - n

Budget constraint with 2 goods

Budget constraint with n goods

Example Income = I = $1.20 q 1 = Reese’s Pieces p 1 = price of Reese’s Pieces = $0.30 q 2 = Snickers p 2 = price of Snickers = $0.20

Graphical Analysis of Budget Set Snickers Reese’s

Graphical Analysis of Budget Set q2q2 q1q1

q2q2 q1q1 4 Reese’s -- 0 Snickers Cost = 4 x x 0.20 = $1.20

Graphical Analysis of Budget Set q2q2 q1q1 0 Reese’s -- 6 Snickers Cost = 0 x x 0.20 = $1.20

Graphical Analysis of Budget Set q2q2 q1q1 2 Reese’s -- 3 Snickers Cost = 2 x x 0.20 = $1.20

Graphical Analysis of Budget Set q2q2 q1q1 2 Reese’s -- 1 Snickers Cost = 2 x x 0.20 = $.80

Graphical Analysis of Budget Set q2q2 q1q1 3 Reese’s -- 3 Snickers Cost = 3 x x 0.20 = $1.50

Graphical Analysis of Budget Set q2q2 q1q1 There are many different combinations Only some combinations are feasible

Graphical Analysis of Budget Set q2q2 q1q1 Some combinations exactly exhaust income

Graphical Analysis of Budget Set q2q2 q1q1 We say these points lie along the budget line

Graphical Analysis of Budget Set q2q2 q1q1 Or on the boundary of the budget set

Graphical Analysis of Budget Set q2q2 q1q1 Points inside or on the line are affordable

Graphical Analysis of Budget Set Budget Set q2q2 q1q1 Points outside the line are not affordable

Slope of the Budget Constraint - q 1 = h(q 2 ) So the slope is -p 2 / p 1

Graphical Analysis of Budget Set q2q2 q1q1 0 Snickers -- 4 Reese’s  q 2 = Snickers -- 2 Reese’s q1q1  q 1 = 2

Graphical Analysis of Budget Set q2q2 q1q1 0 Snickers -- 4 Reese’s 3 Snickers -- 2 Reese’s  q 1 = 2  q 2 = - 3

Numerical Example I = $1.20, p 1 = 0.30, p 2 = 0.20

Budget Constraint - 0.3q q 2 = $1.20 Affordable Not Affordable q1q1 q2q2

Budget Constraint - 0.3q q 2 = $1.20 Affordable Not Affordable q2q2 q1q1 Double prices and income Budget Constraint - 0.6q q 2 = $2.40

Budget Constraint - 0.6q q 2 = $1.20 Affordable q2q2 q1q1 Not Affordable Double p 1 from 0.3 to 0.6 Budget Constraint - 0.3q q 2 = $1.20

Just to review how to solve Budget Constraint - 0.6q q 2 = $1.20

Budget Constraint - 0.3q q 2 = $1.20 Affordable q2q2 q1q1 Raise p 2 from 0.2 to 0.3 Not Affordable Budget Constraint - 0.3q q 2 = $1.20

q1q1 q2q2 Change in Income Budget Constraint q q 2 = $1.20 Budget Constraint q q 2 = $0.60

Change in Price of Good 1 (price rises) Budget Constraint q q 2 = $ q1q1 q2q2 Budget Constraint q q 2 = $1.20

Change in Price of Good 1 (price falls) Budget Constraint q q 2 = $1.20 Budget Constraint q q 2 = $ q1q1 q2q2

Change in Price of Good 2 (price rises) Budget Constraint q q 2 = $1.20 Budget Constraint q q 2 = $ q1q1 q2q2

The End

Graphical Analysis of Budget Set Budget Set q2q2 q1q1

Graphical Analysis of Budget Set Budget Set q2q2 q1q1