The budget constraint and choice

The budget constraint and choice The problem of limited resources and its effect on choice

The budget constraint and choice • Last week: • We saw that preferences can be represented by utility functions ... • That indifference curves can be used to map a utility function into “consumption space” • But we still don’t know how consumers choose amongst the different bundles... • This week: • We introduce the concept of a budget, • This is the 2nd half of consumer theory

The budget constraint and choice The budget constraint The optimal consumer choice Income and substitution effects

The budget constraint • The basic concept is really straightforward: • The consumer has a limited income (I) to purchase different goods • Each type of good has a defined price (p) per unit • We assume that the consumer does not save and spends all his income • This possibility will be examined later

The budget constraint • The general budget constraint for n goods is: • If we only look at 2 goods (Same simplification as last week), it can be expressed as:

The budget constraint • Imagine the following “student entertainment budget” • You have 50 € • The price of a meal is 10 € • The price of a cinema ticket is 5 € • Your budget constraint is:

Meals Maximum amount of meals you can buy  Cinema The budget constraint Diagram in “consumption space”

Maximum amount of cinema tickets you can buy  The budget constraint Meals  Cinema

The budget constraint Meals  Budget constraint  Cinema

The budget constraint The budget constraint is Dividing by p1 and rearranging: Meals intercept  slope  Cinema

H E C G F D The budget constraint Any bundle within the budget constraint is affordable , but not all the budget is spent (C,D). Meals  Any bundle beyond the budget constraint cannot be afforded (H,G). Any bundle on the budget constraint is affordable and ensures all the budget is spent (E,F).  Cinema

The budget constraint Meals Budget set  Budget constraint  Cinema

The budget constraint • The position of the budget constraint depends on • The income of the agent (I) • The price of the two goods (p1 and p2)

The budget constraint Effect of a fall in income (I) Meals   Cinema

The budget constraint Increase in the price of cinema tickets Meals   Cinema

The optimal consumer choice • This requires bringing in the two elements of the theory • The indifference curves, which show how agents rank the different bundles • The budget constraint, which shows which bundles are affordable, and which are not • Both of these are defined over the “consumption space”, so they can be superposed easily

Optimal bundle F  The optimal consumer choice Which is the best bundle ? Meals  A C   B D   E   Cinema

Definition of the MRS at F !!!  The optimal consumer choice The budget constraint is tangent to the indifference curve at F Meals  F  Cinema

The optimal consumer choice • The optimal bundle is on the tangency between the budget constraint and the indifference curve. • This means that for the optimal bundle the slope of the indifference curve is equal to the slope of the budget constraint MRS = ratio of prices

The optimal consumer choice • This condition gives a central result of consumer theory: • The optimal bundle is the one which equalises the marginal utility per € spent • If you were to receive an extra € of income, your marginal utility will be the same regardless of where you spend it

 The optimal consumer choice Example of optimal choice with concave preferences The optimal solution is a “corner solution” Meals  F  G   Cinema

Income and substitution effects • Consumer theory is used to understand how choice is affected by changes in the environment • These can be complex, and the theory helps to isolate these different effects • The separation of income and substitution effects is a good illustration of the concept of “ceteris paribus” • Each variable is isolated and analysed separately from the others

Income and substitution effects An increase in the price of cinema tickets has 2 effects : • 1: A change in real income • A previously affordable bundle (A) is no longer affordable • 2: A relative price change • The slope of the budget constraint changes, and meals become relativelycheaper Meals  A   Cinema

Income and substitution effects Effect of an increase in the price of cinema tickets on consumer choice • Fall in the consumption of cinema • Increase in the consumption of meals • Question: How can we separate the effect of the change in real income from the effect of the change in relative prices ? Meals   A B   Cinema

Income and substitution effects In order to separate the 2 effects, we add animaginarybudget constraint • Parallel to the new budget constraint • Tangent to the original IC • There is only a single curve that satisfies these two requirements • This gives an imaginary optimal bundle (Im) Meals  Im   A B   Cinema

Income and substitution effects The substitution effect • From A to Im, real income is held constant • We are still on the same indifference curve, so utility is the same • The change of bundle is due entirely to the change in relative price • This is the substitution effect Meals  Im   A B   Cinema

Income and substitution effects The income effect • From Im, to B, relative prices are held constant • The two budget constraints are parallel, so the slope is the same • The change of bundle is due entirely to the fall in income. • This is the income effect Meals  Im   A B   Cinema

Income and substitution effects The overall effect • By combining the two, one gets the overall effect • One can see that the interaction is different for the two goods • The 2 effects can work against each other, or add up • Depending on the relative strength of the effects, this can lead to increases or falls in consumption Meals  Im   A B   Cinema

Income and substitution effects • This type of approach is fundamental to micro-economic analysis • Anyprice change is always accompanied by income and substitution effects. • So this helps understand the effects of taxation, shocks to prices, taste changes, etc. • Look at the complex effects of oil price increases on consumption • Price change ⇒ Complex change in bundle • Clearly, this will also help understand how demand curves are built (next week)

The budget constraint and choice