Download Project 1

Project 1
Price Discrimination and
Consumer Surplus
Debi Bosselman
Heather Isenhart
Erin Meredith
Samantha McGlennen
Assumptions

A fundamental assumption is when calculus
is applied to economics, functions of
interest can be approximated with

We are assuming only
(price
and quantity) and that economics is as rigid
as calculus, which it is not. Many other
variables are involved, but not considered
here.
Supply and Demand
Debi Bosselman
Supply and Demand Equilibrium
The equilibrium
price,p*, and
quantity, q*, occur
when the quantity
at which the price
offered (demand)
and the price asked
(supply) are equal:
p*= D(q)=S(q).
Approximation of Demand
Function

When we use a
continuous function,
we are implicitly
assuming that the
jumps in these
functions are small
enough so that the
continuous functions
approximate the
discrete ones very
closely.
Price Discrimination and
Consumer Surplus
Heather Isenhart
Business Goals

Maximize revenue……

How do they maximize revenue?
Perfect Price Discrimination

hypothetical situation
Value to the Consumer
n
  D(q¡)q¡
i=1
Consumer Surplus
Value
beyond the price paid
Producer Surplus;
The Effect of the Elasticities of
Supply and Demand
Erin Meredith
Producer Surplus

The area below p = p* and above the supply
curve. The integral below is used to find
the producer surplus.
Linear Supply and Demand
Curves
These curves can be approximated by the
following linear functions:
 D(q) = A – Bq
 S(q) = Cq
 A, B, C are positive constants

Elasticity of Demand
The elasticity of demand for D(q) is the
quantity (1/B)(p/q).
 A smaller B means that small changes in the
price give a large change in the quantity
demanded. The demand is highly elastic.
 When the demand has a small elasticity, or
is inelastic, B is large, a large change in
prices means a small change in demand.

Elasticity of Supply
The elasticity of supply for S(q) is the
quantity (1/C)(p/q).
 If elastic, a small change in price means a
large change in the quantity supplied.
 If inelastic, a large change in price means a
small change in supply.

Problem: Comparing Elasticities
of Supply and Demand
C.S./P.S.= B/C =
Elasticity of Supply/Elasticity of Demand
 The larger this proportion, the greater the
surplus.
 This happens if producers are more
sensitive to price changes than the
consumers are.

Two-Tier Price Discrimination
and Maximum Revenue
Samantha McGlennen
Two-Tier Price Discrimination

A seller charges two prices
– The higher price, p¹
– The competitive price, p*

Total Revenue = p¹  q¹ + p*(q*- q¹)
Problem: Choosing p¹ to
maximize revenue
The revenue
function, f(q), is
(p¹  q¹) + p*(q*- q¹)
The critical point for
f(q) can be used to
find
p¹ = D(q¹)
How do our assumptions affect
our conclusions?
This model works well for companies that
deal in very large quantities of supply and
demand, such as Wal-Mart.
 However, this model would not work for
smaller companies, such as Oley’s Pizza.
