Page 37 - Microeconomics, Fourth Edition

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1.2 THREE KEY ANALYTICAL TOOLS 11

TV ads, it makes sense in light of your objective to split your budget between radio
and TV advertising.
This example highlights a theme that comes up repeatedly in microeconomics:
The solution to any constrained optimization problem depends on the marginal im-
pact of the decision variables on the value of the objective function. The marginal im-
pact of money spent on TV advertising is how much new beer sales go up for every
additional dollar spent on TV advertising. The marginal impact of money spent on
radio advertising is the rate at which new beer sales go up for every additional dollar
spent on radio advertising. You want to allocate some money to radio advertising be-
cause once you have allocated $800,000 of the $1,000,000 budget to TV, the marginal
impact of an additional $100,000 spent on TV advertising is less than the marginal im-
pact of an additional $100,000 spent on radio advertising. Why? Because the rate at
which new beer sales increase when we allocate that next $100,000 to TV advertising

is (24,750 24,000) 100,000, or 0.0075 barrels per additional dollar spent on TV ad-
vertising. But the rate at which new beer sales increase when we allocate the next

$100,000 to radio advertising is (24,000 950 24,000) 100,000 or 0.0095 barrels
per additional dollar spent on radio advertising. Thus, the marginal impact of radio
advertising exceeds the marginal impact of TV advertising. In light of that, we now
want to allocate this additional $100,000 of our advertising budget to radio, rather
than TV. (In fact, as we already saw, you would want to go even further and allocate
the last $200,000 in your budget to radio spots.)
In our advertising story, marginal reasoning leads to a not-so-obvious conclusion
that might make you uncomfortable, or perhaps even skeptical. That’s fine—that’s
how students often react when they first encounter marginal reasoning in microeco-
nomics classes. But whether or not you realize it, we all use marginal reasoning in our
daily lives. For example, even though pizza may be your favorite food and you may
prefer to eat it rather than vegetables like carrots and broccoli, you probably don’t
spend all of your weekly food budget on pizza. Why not? The reason must be that at
some point (perhaps after having eaten pizza for dinner Monday through Saturday
nights), the additional pleasure or satisfaction that you get from spending another $10
of your food budget on a pizza is less than what you would get from spending that $10
of your budget on something else. Although you may not realize it, this is marginal
reasoning in a constrained optimization problem.
The term marginal in microeconomics tells us how a dependent variable changes as
a result of adding one unit of an independent variable. The terms independent variable
and dependent variable may be new to you. To understand them, think of a relationship be-
tween two variables, such as between production volume (what economists call output)
and the total cost of manufacturing a product. We would expect that as a firm pro-
duces more, its total cost goes up. In this example, we would classify total cost as the
dependent variable because its value depends on the volume of production, which we
refer to as the independent variable.
Marginal cost measures the incremental impact of the last unit of the independent
variable (output) on the dependent variable (total cost). For example, if it costs an
extra $5 to increase production by one unit, the marginal cost will be $5. Equivalently,
marginal cost can be thought of as a rate of change of the dependent variable (again,
total cost) as the independent variable (output) changes. If the marginal cost is $5,
total cost is rising at a rate of $5 when a new unit of output is produced.
We will use marginal measures throughout this book. For example, we will use it
in Chapters 4 and 5 to find the solution to the consumer choice problem described in
Learning-By-Doing Exercise 1.2.