Microeconomics

Consumer Theory: Budget Constraint

Basic principle: Agents choose the best bundle of goods they can afford

2 components:

1. best: depends on preferences

2. can afford: depends on prices and wealth

We start from (2): what can subjects afford? Consumer Theory

A consumption choice set is the collection of all consumption choice available to the consumer

What constrains consumption choice?

Budgetary

Time

Other resource limitations

Bundles

A consumption bundle with:

x1 units of commodity 1

x2 units of commodity 2

xn units of commodity n

is denoted by the vector (x1, x2, , xn)

We denote the commodity prices by p1, p2, , pn

Denote by m the disposable income/wealth of the consumer

Budget Constraints:

Question:

When is a consumption bundle (x1, , xn) affordable at given prices p1, , pn? Budget Constraints

-Question:

- When is a consumption bundle (x1, , xn) affordable at given prices p1, , pn?

- Answer: When p1x1 + + pnxn m

Budget Set and Budget Constraint:

- The consumers budget set is the set of all affordable bundles

B(p1, , pn, m) = { (x1, , xn) | x1 0, , xn 0 and p1x1 + + pnxn m }

- The budget constraint is the set of bundles that are only just affordable

- { (x1,,xn) | x1 0, , xn 0 and p1x1 + + pnxn = m }.

- It is the upper boundary of the budget set