Transcript Consumer Surplus - West Virginia University

Consumer Surplus
Math 150: Spring 2004
Basic Idea
• Consumers have “extra cash” if the price of
an item is kept artificially low
• Example: The price of a bottled Coke is
kept at $1.00 even though high demand
might allow $1.50 to be charged. In this
case you (the consumer) have a “surplus” of
50 cents.
Changing Prices
• Prices probably wouldn’t stay constant,
though (at say $1.50) so the difference
between the artificial price and the actual
price will vary (say p(x) – 1.00)
• To find the actual Consumer Surplus, we
need to “add up” all these different
surpluses using an integral
Consumer Surplus
• The Consumer Surplus for a
product with demand curve
p(x) at a fixed price B=p(A) is
the area between the graphs
y=p(x) and y=B from x=0 to
x=A
• Written as an integral, this is
Example
•
•
EX: Suppose a product has demand curve p(x) = 50 - .6x in dollars and that
the price is held artificially low at p=$20. What is the consumer surplus for
this product?
Solution: The price is held at p=20 and this occurs when 50 - .6x = 20 so
when x = 50 units. Then the consumer surplus is
Review for Final Exam
•
Derivatives (About 25 questions total; about 15 from here)
–
Basic Derivatives
•
•
•
•
•
•
•
–
Polynomials
Exponential and logarithmic functions
Product rule, quotient rule
Chain rule
Slopes of tangents (evaluate at a point)
Equations of tangents
Continuity and differentiability
Applications of derivatives
•
•
Rates of change (velocity, marginal cost, marginal revenue, marginal profit)
Maxima and minima
–
–
–
–
–
Graphing
•
•
•
–
Maximize profit, minimize cost
Maximize area, minimize perimeter
Economic Order Quantities
others
Increasing and decreasing functions, extrema
Concavity, Points of inflection
Behavior as x!1, asympotes, behavior as f(x)\rightarrow\infty
Implicit Differentiation
More Topics for Final
• Integrals (about 10 from here)
–
–
–
–
Anti-derivatives (general and finding C)
Definite Integrals and the FTC
Riemann Sums (right and left hand sums)
Applications
•
•
•
•
Average value of a function
Future value of an income stream
Consumer surplus
Others
– Distance from velocity
– Total consumption/usage from rate of consumption/usage
– The Method of Substitution