ECON 356 - Outline Five

Individual  Demand

Now let's look at, still using the same consumer choice model, how changes in the budget constraint affect actual purchase decisions - or in other words, we will use this model to generate an individual consumer's demand curve for a good and see how individual demand varies with income.

Total effect from a price change can be separated into two different effects:

1.  Substitution effect - comes about because a change in price makes other goods more or less attractive

2.  Income effect - comes about from the change in purchasing power caused by the price change.

Then we will derive the market demand curve from individual demand curves.

Some interesting concepts we will use:

a.  price elasticity of demand

b.  income elasticity of demand

c.  the importance of the distribution of income (not simply average value)

d.  cross price elasticity of demand (substitutes and complements)

The Effects of the Changes in Price

The Price-Consumption Curve (PCC):  holding income and the price of Y (or the composite good) constant, the PCC for a good X is the set of optimal bundles traced on an indifference map as the price of X varies.

Graph:

The Individual Consumer's Demand Curve:  quantities consumers will buy at various prices (ceteris paribus).

We can derive this from the price-consumption curve.

Simply record the quantities of x that correspond to the x prices on each budget constraint.

Assume x = shelter.  Consider the following data:

Then simply Graph the data:

The Effects of Changes in Income

The Income-Consumption Curve (ICC):  holding the prices of X and Y (or composite good) constant, the ICC for a good x is the set of optimal bundles traced on an indifference map as income varies.

Graph:

Engel curve:  plots the relationship between the quantity of x consumed and income.

    Normal good:

    Inferior good:

Assume x = shelter.  Consider the following data:

Plot the individual consumer's Engel Curve.  Remember that preferences and relative prices are being held constant.

Graph:

Engel Curves for Normal and Inferior Goods:

The Income and Substitution Effects of a Price Change

Extra Reading on Income and Substitution Effects

Link to Some Examples of Showing the Income and Substitution Effects

Substitution Effect:  that part of the total effect of a price change that results from the associated change in the relative attractiveness of other goods.

Income Effect:  that part of the total effect of a price change that results from the associated change in real purchasing power (real income)

Graph (normal good):

Graph (inferior good):

Giffen Good:  one for which the quantity demanded rises as its price rises.

    Does this exist?  Much-cited example:  potato during the Irish potato famine in the nineteenth century -- the idea was that potatoes were such a large part of poor people's diets to begin with that an increase in their price had a severe adverse effect on the real value of purchasing power.  Having less real income, many families responded by cutting back on meat and other more expensive foods, and buying even more potatoes. Or the story goes ....

Whether you believe it or not -- the story does illustrate what a Giffen good would look like if it did exist.

Graph:

Deriving the Individual Demand Curve

Just take a normal good:

Graph:

Now an inferior good:

Graph:

Giffen Good:

Graph:

Application - Excise Subsidy vs. Lump Sum Subsidy

Excise subsidy:  the government pays part of the per-unit price of a good and allows the consumer to purchase as many units as desired at the subsidized price.  For example, the government might pay half a consumer's housing costs, which effectively lowers the price of housing services by 50%.  Often found in the tax code with tax credits -- a tax credit for child care expenses, for example, effectively lowers the price of child care. 

Lump Sum subsidy (or transfer):  a fixed amount subsidy.  For example, the government simply gives people $200/month instead of paying half the housing costs.

Let's look at health care - first an excise subsidy.

Suppose that Sickly has a weekly income of $100, the market price of health care is $5 per unit, and Sickly will purchase 9 units of health care without any subsidy. 

Graph:

To subsidize Sickly's health care consumption, suppose that the government pays $2 of the $5 per-unit cost of health care.  So basically the cost to Sickly goes to $3 per unit and her budget constraint rotates and she will consume more.  Let's assume that her preferences are such that she will now consume 15 units of health care (and stay with 55 units of the composite good).  That way she is still using her $100 budget 15 x $3 = $45 + $55 = $100.

What is the total cost to the government of supplying this subsidy?  Because the subsidy is $2 per unit, and Sickly purchases 15 units per week, the total cost is $30 per week. 

So far so good -- the price of health care lowers and she buys more.  But how does this analysis differ from a lump sum subsidy?

Assume that instead of using an excise subsidy, the government gives the consumer the same amount of assistance, $30 per week, in the form of a cash grant to be spent any way the recipient wants. 

How will this change Sickly's consumption pattern and will she be better or worse off?

Graph:

This will shift the consumer's budget constraint in a different way.  It shifts out parallel to the old one.  Note that the new budget constraint passes through Sickly's optimal point when she received the excise subsidy.  Both subsidies cost the government the same amount --  So the new budget line lies exactly $30 above the old one.  The consumer can stay with the same optimal consumption bundle if she chooses.

But the consumer can now get to a higher indifference curve and purchases less health care and more of other goods and is better off.

In other words -- the excise subsidy analysis includes a substitution effect since the price effectively changed that stimulates more health care consumption.  But the lump sum analysis does not.  The only reason to buy more health care is a higher income -- it is not also relatively cheaper than other goods.

So generally speaking, again, the consumer is better off given a cash grant then with an excise subsidy linked to the consumption of a particular good.  This is why some economists would convert welfare programs such as Medicaid, food stamps, and housing subsidies into outright cash grants.    Consumers could still buy the same amount of the subsidized good but if something is more valuable to them -- they could change their consumption pattern.

So is having the recipients better off the goal?  Some would take a more "paternalistic" view and disagree.