Chapter 7 – Empirical Demand
Functions
 Optimal pricing is critical to the success of
any business.
 Given the stakes, it is frequently worth
investing significant resources in
determining the optimal price.
 Large firms have pioneered the use of
econometrics in estimating demand
functions to serve as the base for
determining the best price.
7.1
Empirical Demand Functions
 Empirical demand functions are demand
equations derived from actual market data.
 There are two basic methods for demand
estimation
– Direct Methods
• Consumer Interviews
• Market Studies and Experiments
– Indirect Methods (econometrics/regression
techniques)
7.2
Consumer Interviews
 Estimation of demand is based on asking
individual consumers about their “potential”
purchase decisions. Essentially playing the “what
if” game – If the price is $10, how many units
would you purchase? However, if price is
decreased to $8, how many units would you now
purchase?
 Sample must be representative of population.
– Random samples
 Response bias occurs when hypothetical answers
are given to hypothetical questions.
– “People Lie”
– Sometimes unable to accurately answer the question
7.3
Market Studies and Experiments
 Market studies & experiments are the
economists attempt to control or hold
constant many of the factors affecting the
amount purchased.
 All factors except price are held constant
and the amount purchased is observed in
response to variation in price.
7.4
Market Studies
 Use the market to directly react to changes
in price
– M&M/Mars changed size of product and held
price constant(effectively reduced price per oz).
Response was positive and substantial
– Must be careful or may lose consumer goodwill
especially if price was low during study and
higher after research
7.5
Experiments
 Simulate market experience. Give income
and make purchases(subject to price
variation). Often known probabilities that
you can keep your purchases - providing an
incentive to make optimum choices.
7.6
Specification of the Empirical
Demand Function
 Specification of the relationship includes
two critical elements
– Choosing the correct set of independent
variables
– Choosing appropriate functional form for the
relationship
7.7
Choosing the Independent
Variables
Best guide to choosing IVs is to turn to theory.
Qd  f ( P, M , PR , T , Pe , N )
Price expectations and tastes and preferences are often
dropped due to the difficulty of measuring or estimating them.
Qd  f ( P, M , PR , N )
7.8
Choosing the Appropriate
Functional Form
 Choices we consider are
– Linear: Q=a+bP+cM+dPR+eN
– Log-linear: Q=aPbMc(PR)dNe
7.9
Linear Demand
 Q=a+bP+cM+dPR+eN
– Coefficient b yields the change in Q in response to a 1
unit increase in Price(b should be negative)
– Coefficient c can be positive(normal) or
negative(inferior). It yields the change in Q in response
to a 1 unit increase in incoMe.
– Coefficient d can be positive(substitutes) or
negative(complements). It yields the change in Q in
response to a 1 unit increase in the Price of a Related
good.
– Coefficient e should be positive and yields the change
in Q in response to a 1 unit increase in Number of
buyers( proxy is often population)
7.10
Elasticities for Linear
Specification
P
ˆ
ˆ
Ep  b
Q
Own Price Elasticity
M
ˆ
ˆ
EM  c
Q
Income Elasticity
PR
ˆ
ˆ
E PR  d
Q
Cross Price Elasticity
7.11
Log-linear Demand
 Q=aPbMc(PR)dNe
 Converted into logs yields
lnQ = ln a + b ln P + c ln M + d ln PR + e ln N
 Elasticites are constant and equal to th
estimated coefficients
7.12
Control of Price
 Market-determined price - For some products and
firms, managers have no control over price. Price
is set in the market and firms must accept it as a
given.
 Manager-determined price – For other products
and firms, mangers do have control over price and
set price to achieve their goal.
 Estimating demand for these two cases is quite
different, as we will see.
7.13
Endogenous versus Exogenous
Variables
 An endogenous variable is a variable determined
by a system of equations. If price is marketdetermined, it is an endogenous variable since it is
determined simultaneously by S and D.
 An exogenous variable is a variable in a system of
equations that is determined outside the system. If
price is manager-determined, it is an exogenous
variable since it is determined outside the S and D
simultaneous equation model.
7.14
Estimating Demand for PriceTaking Firms
 The problem of estimating demand when
price is market-determined is often referred
to as the simultaneity problem.
 See Figure 7.1 as base for the simultaneity
discussion.
7.15
Reduced Form EquationsMarket for Gas
 Demand: Q = a + bP + cM + d
 Supply: Q = h + kP + lPc + s
Pc is the price of crude oil
 Endogenous variables are P and Q.
 Demand: Q = A + bP, where A=a+cM+d
 Supply: Q = H + kP, where H= lPc+s
 PE= f(M,Pc, d ,s) & QE = g(M,Pc, d ,s)
 The above are the reduced-form equations, which express
the endogenous variables as a function of the exogenous
variables and the random errors.
7.16
Reduced-Form Equations
 The reduced-form equations indicate
– The observed values of the endogenous variables, P &
Q, are determined by all the exogenous variables and
random errors in both the supply and the demand
equations.
– The observed values of price are correlated with
(depend on) the random errors in both S and D.
 Ordinary Least Squares(OLS) cannot be used if
the observed values of price are correlated with
the random errors.
7.17
Two-Stage Least Squares(2SLS)
 To estimate demand where price is endogenously
determined by D & S, we must perform the
following steps:
– Identification of demand – make sure the sample data
will properly estimate the true demand relationship.
– Using data, estimate parameters(coefficients) of
industry demand equation with 2SLS. 2SLS deals with
simultaneous equation bias, in which endogenous
variable is determined simultaneously by “two”
relationships. If OLS had been used simultaneous
equation bias would have resulted.
7.18
Identification of Demand
 A demand equation is identified when the
true demand function can be estimated from
sample data on equilibrium points.
 The above occurs when Supply includes at
least one exogenous variable not in demand.
In our example supply included Pc, the price
of crude oil which was not in the demand
function.
7.19
Estimating Demand for PriceSetting Firms
 When prices are manager-determined, the
problem of simultaneity vanishes and single
equation OLS can be used for estimating the
parameters of the demand function without
any regard for supply.
7.20