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 2 nd 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:

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

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

The budget constraint   Cinema Meals Budget constraint

The budget constraint   Cinema Meals The budget constraint is Dividing by p 1 and rearranging: slope intercept

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

The budget constraint   Cinema Meals Budget constraint Budget set

The budget constraint The position of the budget constraint depends on The income of the agent (I) The price of the two goods (p 1 and p 2 )

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

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

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

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

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

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

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

The budget constraint and choice The budget constraint The optimal consumer choice 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   Cinema Meals An increase in the price of cinema tickets has 2 effects :  A 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 relatively cheaper

Income and substitution effects   Cinema Meals  A  B 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 ?

Income and substitution effects   Cinema Meals  A  B In order to separate the 2 effects, we add an imaginary budget 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)  Im

Income and substitution effects   Cinema Meals  A  B 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  Im

Income and substitution effects   Cinema Meals  A  B 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  Im

Income and substitution effects   Cinema Meals  A  B 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  Im

Income and substitution effects This type of approach is fundamental to micro- economic analysis Any price 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)