Tutorial 5: Consumer choice (cont.)
Finding the Consumer's Optimal Choice
In Tutorial 5a we learned
that a consumer seeks a market basket of goods which generates
the maximum level of utility. In Tutorial 5b
we learned that one's goal of maximizing utility is subject
to the constraint imposed by one's money income and the
prices of the goods.
Stated formally, the consumer's objective is to
maximize utility subject to a budget constraint.
That is,
The function u(F, C) describes the level of satisfaction
("utility") received when the bundle of goods (F*, C*) is
consumed. This form of the utility function allows us to
manipulate the relative strength of the consumer's preference
for F or C by changing the parameters a
and b. [Review Tutorial 5
Question 3 in the Consumer
Choice Workbook.]
Stating the consumer choice problem this way makes explicit
the fact that, whereas one desires to maximize the
satisfaction from a bundle of goods (Max u(F, C)), one is
constrained in that quest by one's income and the
prices of the goods (i.e., by one's budget).
The complete model of consumer choice is shown in Figure
7 below. Graphically, the consumer's utilitymaximizing
choice must meet two conditions:
 The market basket chosen must place the consumer on
the highest indifference curve attainable;
 The market basket must be located on the budget line
(i.e., no "saving").
By the Axiom of Greediness, any basket on U1 is
preferred to any basket on U or U0. But attainment of U1
is blocked by the budget constraint.
At points C or D, for example, the budget constraint is
satisfied, but U0 is not the highest level of utility attainable.
There are a number of indifference curves higher than U0.
In fact any point on B1 that lies between bundles
C and D would place the consumer on a higher indifference
curve.
Market basket A exhausts the consumer's income ($5*8 + 20*$2
= $80) and results in a higher level of utility than bundles
C, D, or any other.
Figure 7
Therefore, this graphical model shows that the maximum
attainable level of satisfaction takes place when
the budget line and indifference curve are tangent. At the
point of tangency, A, income is exhausted, and:
The
slope of the budget line 
= 
The slope
of the highest IC attainable 
Pf/Pc 
= 
MRS_{fc} 
The
rate at which one can trade C for F 
= 
The rate
at which one is willing to trade C for F 
MC
(of one more unit of F) 
= 
MB (of
one more unit of F) 
In contrast, at point C, MRS_{fc} > Pf/Pc.
So the rate at which the consumer is willing to trade
C for F, exceeds the amount s/he is required (by
the market) to trade. So if 15 units of C is traded for
6 units of F  that's 2.5C for 1F, what the market requires
 the consumer will be better off as they move to point
A on indifference curve U1.
Similarly, at point D, MRS < Pf/Pc. The rate at
which the consumer is willing to trade F for C, exceeds
the amount s/he is required (by the market) to trade.
So if 6 units of F is traded for 15 units of C  that's
1C for 2/5F, what the market requires  the consumer will
be better off as they move to point A on indifference curve
U1.
Some "Mathemagics"
Remember that the consumer's objective is
to maximize the satisfaction received from the consumption
of a market basket of goods, subject to the constraint that
spending on the goods does not exceed income, i.e.,
Graphically, we were able to determine that
this constrained maximum occurs at the point where the slope
of the budget line, Pf/Pc, equals the slope of the
indifference curve, referred to as the marginal rate
of substitution (MRS). In this section we will learn
how to calculate the MRS.
Once again, the function u(F, C) describes
the level of satisfaction ("utility") received when the
bundle of goods (F*, C*) is consumed. An indifference curve
simply describes all the combinations of F and C that generate
a constant level of utility, U_{1}, to the consumer.
So, the change in utility along an indifference curve is
equal to zero. But as you give up some clothing, for example,
your utility level changes (drops). The change in utility
from a one unit change in clothing is called marginal
utility (MU_{c}). So the size of the change
in total utility from a reduction in C depends on
the size of the change in C and on the consumer's MU_{c},
e.g., DC*MU_{c}.
Similarly, when you get more food, your utility
level changes again (rises). This time the change in total
utility from an increase in F is equal to DF*MU_{f}.
Mathematically, the two changes cancel each
other out:
.
Now all we have to do is figure out how to
calculate marginal utilities. As mentioned above, marginal
utility measures the additional satisfaction one receives
from consumption of another unit of a good. Mathematically,
marginal utility is the partial derivative of a total utility
function. Starting with the utility function noted above:
,
differentiating with respect to F, gives
us MU_{f} = 

differentiating with respect to C, gives
us MU_{c} = 

To calculate MRS = MU_{f}/MU_{c}
Now you can see the importance of the terms a
and b from your answers to Tutorial
5 Question 3 in the Consumer Choice Workbook.
Now it's time to
"do the thing".
Click on the following link
to download the Consumer
Choice Workbook. Work through Tutorial
5 Questions 6  7 to improve your understanding
of the consumer choice model.
Return here when you have finished.
Need help
downloading the Excel file? 

This is a good time to check your understanding of the
consumer choice model by working through the Applications
in Tutorial 5 Questions 810. Answer the questions
without the use of the consumer choice template, and hand
draw the graphical model you use to illustrate your answer.
[If you give yourself some time pressure to answer the three
questions, this will be excellent practice for the Literacy
Test and the end of the semester...]
Now it's time to
"do the thing".
Click on the following link
to download the Consumer
Choice Workbook. Work through Tutorial
5 Questions 8  10 to improve your understanding
of the consumer choice model.
Return here when you have finished.
Need help
downloading the Excel file? 

Now we are ready to use the consumer choice model to derive
the individual consumer's demand curve.
Next: Tutorial 6  Consumer
and Market Demand
