Tutorial 5: Consumer choice (cont.)
The Budget Constraint
In the first part of Tutorial 5
we learned that a consumer seeks a bundle of goods, a market
basket, the consumption of which generates the maximum
happiness (utility). Graphically, such a basket is found
on the indifference curve as far from the origin as possible.
Of course these goods are not free, and one's money income
is not limitless. So one's goal of maximizing utility is
subject to the constraint imposed by one's budget. In this
tutorial we will develop a model of the consumer's budget
constraint.
Suppose a consumer has a fixed periodic money income, represented
by I, and must pay a price, Pf, for each unit
of food, and a price, Pc, for each unit of clothing.
The consumer's budget can be represented by the identity
shown in equation (1),
,
where Pf*F indicates the amount of money income I
spent on food, and Pc*C is the amount of money income
spent on clothing. Equation (1) simply indicates that the
sum of spending on food and clothing must equal the amount
of money income available.
To add this constraint to our model, we need to rewrite
it in a form that can be plotted in (F, C) space. We can
do that by simply rewriting equation (1) so that C is the
dependent variable.

...subtracting Pc*C from both sides.
...multiplying both sides by 1.
...dividing both sides by Pc.
...rearranging terms. 
Now we have an equation that can be plotted in (F, C) space,
where C is the dependent variable, F is the independent
variable, and I, Pf, and Pc are parameters with known values:
Let's read equation (2). First of all, C(F) tells us that
the amount of clothing one can buy depends on the amount
of food one has purchased. The yintercept term, I/Pc, indicates
the amount of clothing that may be purchased, given income
and the price of clothing, if one buys no food (i.e., if
F = 0). The slope term, Pf/Pc, indicates the amount
of clothing that must be given up in order to free up enough
money to buy one more unit of food.
Let I = $80 per period, Pc = $2 per unit,
and Pf = $5 per unit. Given these parameter values,
equation (2) would be written
,
which is an equation of a straight line (e.g., y = a +b*x),
where a = I/Pc, and b = Pf/Pc. A graph of this equation
is shown as B1 in Figure 6 below. The vertical intercept
is 40 units/t. It is the amount of clothing that may be
purchased given an income of $80 and a price of clothing
equal to $2 per unit (e.g., 40 = $80/$2). How is the horizontal
intercept, 16, calculated? [Hint: The horizontal intercept,
16, is the amount of food that may be purchased with an
income of $80 and a price of food of $5 per unit.]
Figure 6
The slope is equal to 5/2 = 2.5 units. It tells us that
one must give up 2.5 units of clothing in order to free
up enough cash to buy one unit of food. How's that? Well,
a unit of clothing is priced at $2. So, "selling off" 2.5
units of clothing would bring you $5:
2.5 * $2 = $5,
which is the price of a unit of food. Thus, selling 2.5
units of clothing gives you enough money to buy 1 unit of
food.
Changes in Parameter
Values
Now let's explore what happens to the budget line when
income or the prices of the goods changes.
Increases (decreases) in income result in an outward (inward)
shift in the budget line parallel to the original. This
is because more (less) income expands (contracts) the set
of affordable baskets of food and clothing. On the
graph, as income rises (falls), both the vertical intercept,
I/Pc, and horizontal intercept, I/Pf, rise
(fall). Why? Because each intercept term shows the maximum
amount of a good one can by given one's income and the price
of the good. Thus as income rises (falls), the maximum amount
of a good one can afford to buy rises (falls), assuming
the prices of the goods remain constant.
A decrease (increase) in the price of food lowers (raises)
the slope of the budget line (Pf/Pc) by raising (lowering)
the horizontal intercept (I/Pf), leaving the vertical
intercept (I/Pc) unaltered. Similarly, decreases
(increases) in the price of clothing raise (lower) the slope
of the budget line by raising (lowering) the vertical intercept,
leaving the horizontal intercept unaltered. In both cases,
a decrease (increase) in price expands (contracts) the set
of affordable baskets of food and clothing.
Now it's time to
"do the thing".
Click on the following link
to download the Consumer
Choice Workbook. Work through Tutorial
5 Questions 4 and 5a  5f to improve your
understanding of the budget constraint model.
Return here when you have finished.
Need help
downloading the Excel file? 

Special Issues: Inkind Gifts
and Product Rationing
There are several other factors that alter the consumer's
budget constraint, two of them are inkind gifts
and product rationing. As the name implies, inkind
gifts are units of a good, food for example, that are given
to the consumer free of charge. They serve to expand the
amount of goods that may be purchased by providing the consumer
a certain number of units without the sacrifice of any income.
Contrariwise, when a good is rationed, the consumer is
barred from buying beyond the ration limit regardless the
amount of income the consumer has. This serves to contract
the amount of goods that may be purchased by limiting the
quantities of one good available.
To see how gifts and rationing affect the budget constraint,
work through the rest of Tutorial 5 Question 5 now.
Now it's time to
"do the thing".
Click on the following link
to download the Consumer
Choice Workbook. Work through Tutorial
5 Questions 5g  5h to continue improving
your understanding of the budget constraint
model.
Return here when you have finished.
Need help
downloading the Excel file? 

Now we are ready to put both of the parts of this consumer choice model together.
We will use the completed model to analyse how consumer's
choose to maximize the satisfaction they receive from the
consumption of a bundle of goods, subject to the constraint
imposed on their choice by their income and the prices of
the goods they buy.
Continues...
