An economic approach to design efficient transportation systems involves maximizing an objective function that reflects both goals and costs. A demand curve can be derived by finding the quantities of a good that solve the maximization problem as one varies the price of that commodity, holding income and the prices of all other goods constant. A supply curve is derived by applying the idea of profit maximization of firms. The production function determines the relationship between input and output

Tideman, T. N.

English

NASA Technical Reports Server

Basic Economic Principles 
T. Nicolaus Tideman 
Economics shares with engineering a concern with solving problems: 
problems like how to produce shoes efficiently or how to control pollu-
tion--or how to design an efficient transportation system. However, the 
economic approach to solving problems differs from the engineering 
approach in one crucial way: In an economic context every problem has a 
solution. Economists achieve this miracle by defining their goals in 
such a way that doing without something is the correct "solution" if it 
is too expensive or impossible to obtain it. Thus if pollution can be 
eliminated only at a prohibitive cost, economists will seek the optimal 
amount of pollution. If Lockheed loses money no matter what it does, 
the economic solution is for Lockheed to go out of business. 
Formally, the economic approach involves maximizing an objective 
function that reflects both goals and costs. This idea is sometimes 
stated incorrectly as, for example, "getting the most pollution control 
for the least amount of money." A correct statement in words is somewhat 
cumbersome: The goal is to control pollution at whatever level in a 
cost-minimizing manner, and to choose the level of pollution control that 
is most worthwhile considering its minimum cost. Similsrly, economists 
look at the behavior of a consumer as solving a problem in the allocation 
of time snd money. The goal for a consumer is to spend whatever money is 
earned in the manner that maximizes his satisfaction, or "utility," and 
to esrn that amount of money that is most satisfying considering the 
disagreeableness of working harder and the satisfaction to be obtained from 
what the earnings from extra work will buy. Considering for the moment a 
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choice between just two goods, say wine and cheese, we can associate 
any pair of quantities of the two goods cheese 
with a point in the first quadrant of a 
graph with Cartesian co-ordinates. Thus 41-__ ~ 
point A may represent 2 glasses of wine 
and 4 ounces of cheese. The other 
combinations of wine and cheese that 
2 wine 
would be equally satisfying to a con-
sumer will, under reasonable assumptions, be on a curve through A that 
is convex to the origin. Economists call such a curve an "indifference 
curve." Combinations that are preferred over A lie on indifference 
curves farther from the origin. If the prices of wine and cheese are 
given, the other combinations that can be bought for the same amount of 
money as A will be on a straight line through A (the budget line), the 
slope of which is determined by the relative prices of wine and cheese. 
If A is preferred to all other combinations that can be bought with the 
same amount of money, then the indifference curve through A must be 
tangent to the budget line at A. Thus a graphical depiction of a process 
of consumer maximization involves finding where the boundary of attainable 
points is tangent to an indifference curve. In a more formal formulation 
a continuous variable called "utility" is assumed to depend on the 
quantities of wine and cheese in such a way that each indifference curve 
corresponds to a different level of utility, with higher levels of utility 
associated with indifference curves further from the origin. The consumer's 
problem is then one of maximizing 
(1) 
I VI . ~) 
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subject to the constraint that 
i.e., that expenditure be equal to income. To solve this kind of 
problem economists use Lagrangian constrained maximization techniques. 
Generalization to more than two commodities is straightforward. 
A demand curve can than be derived by finding the quantities of a 
good that solve the maximization problem as one varies the price of that 
commodity, : .. )lding income and the prices of all other goods constant. 
Or, more directly, one can say that a demand curve expresses the quantity 
of a good that a utility-maximizing person will want to buy as a function 
of the price, assuming that income and all other prices are fixed at 
given levels, and assuming that the person has no way of affecting the 
price he pays. For reasons of consistency p 
with historical diagrams, economists always 
put quantity on the horizontal axes of 
their graphs and price on the vertical axes, 
even though they usually think of quantity D 
as the dependent variable. Market demand 
~-----------------q 
at any price is obtained by summing the 
quantities demanded by all persons in the market at that price. Economists 
are often concerned with the "elasticity of demand," by which they mean 
k. l!. 
dp q , the limit of the ratio of percentage changes in quantity to 
percentage changes in price along the demand curve. 
A supply curve is derived by applying the idea of profit maximization 
of firms. Technology determines a relationship between inputs and output. 
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Economists call that relationship a "production function," but we won't 
delve into it. Suffice it to say that the production function and the 
prices of inputs determine a "total cost function," C(q) which gives 
the minimum cost at which any quantity of output can be produced. The 
profit, n, that a firm makes can be considered the difference between 
revenues and costs, each of which depend on the quantity of output: 
n = R(q) - C(q) (3) 
If a firm cannot affect the price at which it sells its output (as in 
the economists' model of perfect competition), then revenue is simply 
the product of quantity and that inflexible price: 
n = p • q - C(q) (4) 
The condition for profit maximization can be obtained by differentiating 
with respect to q and setting that derivative equal to 0: 
dn de o. = p = dq dq (5) 
Thus 
dC 
-
p. dq (6) 
Economists refer to the derivative of total cost with respect to quantity 
as "marginal cost," that is, the cost of producing one addition unit. 
Similarly, the derivative of revenue with respect to quantity is called 
marginal revenue. Profit maximization involves equating marginal revenue 
and marginal cost, which, in the cost of a competitive firm means choosing 
that output where marginal cost is equal to the price received. This is 
efficient because it means that the prices by which consumers choose how 
much to buy correspond to the costs of producing what they buy. 
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There is a second-order condition of profit maximization: Marginal 
cost must be rising. And one further condition: reVenue must be greater 
than "variable costs," that is the costs that could be avoided by not 
producing. This condition may also be stated as the condition that price 
be greater than average variable cost. All three conditions are summarized 
in the statement that a competitive firm's supply curve is that part of 
its marginal cost curve that is greater than average variable cost and 
rising. 
A market supply curve is obtained by summing the quantities that all 
firms would supply at each price. If all firms have the same cost func-
tions, then in the long run, when all costs are variable, a competitive 
market will supply unlimited quantities at a price that just covers costs. 
Profit, exclusive of an ordinary return to capital and entrepreneurial 
effort, is exactly zero. 
The competitive result may be contrasted with the profit maximizing 
outcome when a firm can affect the price of its output by varying the 
quantity it produces. Then (2) may be written as 
~ a p(q) • q - C(q). 
Differentiating and setting the result to zero, 
d~ ~ q + P dC o. (8) _ D -- = dq dq dq 
Rearranging. 
dC +££. (9) 
- -
q, dq P dq 
or 
-++ ) dC 1 (10) dq .<!q .E. dp q 
Jzq 
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In words, a profit-maximizing producer who can affect the price of his 
product will choose a level of output where marginal cost is equal to 
price multiplied by one plus the reciprocal of the elasticity of demand. 
Since the elasticity of demand is negative, this means that marginal 
cost will be less than price, so that consumers will be economizing on 
this output inefficiently, treating it as if it were more valuable than 
it is in terms of resources used in production. 
A regulated firm might have no control over the price of its product, 
but it could affect both revenues and costs through such variables as 
advertising ana frequency of service. An economic analysis would 
predict that regulated firms would maximize with respect to the variables 
they did control, setting them at levels where their marginal contribu-
tions to revenues equaled their marginal contributions to costs, with 
appropriate second-order conditions. 
For further reading 
R. G. Lipsey and P. O. Steiner, Economics (Harper & Row). 
P. A. Samuelson, Economics (McGraw-Hill) 
Kelvin Lancaster, Introduction to Modern Microeconomics (Rand McNally)--
a more theoretical treatment. 
J. M. Henderson and R. E. Quandt, Microecono~ic Theory (McGraw-Hill)--
a mathematical treatment. 


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