Managerial Economics
Consumer Demand
Aalto University
School of Science
Department of Industrial Engineering and Management
January 12– 28, 2016
Dr. Arto Kovanen, Ph.D.
Visiting Lecturer
Demand curve
 Demand curves can be estimated
 Estimation involves:
 Model specification (essential)
 Actual estimation using econometric tools
 Interpretation of the results and possible modifications of
the empirical model
 A basic understanding of regression analysis is needed
to perform these types of estimations (this course,
however, is not an econometrics course)
 There are software packages available (e.g., Eviews)
Factors affecting demand
 Let’s assume the following demand function:
Q = f(P, L, A, D, Y, …)
where P = price
L = quality
A = advertising expenses
D = distribution spending
Y = average income of consumers
 How do we obtain the demand function?
 Management can control some of the factors while
others are beyond of its direct control
Factors affecting demand
 Controllable factors:
 Price (to a degree)
 Product characteristics (to a degree)
 Marketing expenses: promotions, advertisement, place of
sale, and so on
 Uncontrollable factors:
 Consumer income
 Consumer preferences, demographics
 Government policies (e.g., taxations and other means to
discourage tobacco and alcohol products)
 Competitive forces
 Macroeconomic factors (e.g., economic cycle)
Consumer choice
 How do consumers make decisions?
 Behavioral assumption: consumers act in their best
interest
 Interest = measured by utility or preferences
 Best interest = maximize utility over available choices
 Utility maximization
 Choose quantities of goods/services: A, B, …
 By maximizing utility function U(A, B, …)
 Subject to the budget constraint: P(A)*A + P(B)*B + …
= Income (i.e., how much you can afford to spend)
Consumer choice (cont.)
 Optimal: MRSAB = MUA/MUB = P(A)/P(B),
 That is, MUA = P(A) = MUB = P(B) = .. {equal “bang” or
marginal utility per each dollar spent)
 This results in an individual demand function
D(A) = DA(P(A), P(B), … , Income
 Empirical models usually have variables that measure
consumer preferences, demographics, and so on
 Graphical presentation of consumer optimum useful
Consumer choice (cont.)
 Some mathematics:
 Consumer’s optimization problem is given by finding
values for x(1) and x(2) by
Max U(x(1), x(2))
s.t. P(1)x(1) + P(2)x(2) = Income
 The constraint arises from available income to spend
 Two ways to solve this (two-variable problem):
 Substitute for x(2) from the constraint and solve for
x(1)
Consumer choice (cont.)
 Alternatively, use Lagrangian equation given by
L = U(x(1), x(2)) - λ[P(1)x(1) + P(2)x(2) – Income]
 The first-order conditions are given by
dL/dx(1) = 0; dL/dx(2) = 0; and dL/dλ = 0
 Results in MRS1,2 = P(1)/P(2)
 The third f.o.c. means that the budget constraint is met
(it measures the marginal increase/decrease in the
value of L if income rises/prices rise)
Consumer choice (cont.)
 Example: U(x(1), x(2)) = c*lnx(1) + d*lnx(2)
 F.o.c. are given by
c/x(1) = λP(1)
d/x(2) = λP(2)
P(1)x(1) + P(2)x(2) = Income
 Hence, e.g. x(1) = [c/(c+d)][Income/P(1)], which is the
demand curve for x(1)
The law of demand
 The law of demand states that the quantity demanded
is inversely related to the selling price, ceteris paribus
(all other factors being unchanged)
The law of demand (cont.)
 This means that the demand curve is downward sloping and
can be formalized as follows:
QD = f(P, Z ….) where dQD/dP < 0
 There are other factors affecting the demand for goods and
services
 The income effect, which states that the demand rises as the
real purchasing power increases (normal goods) while for
inferior goods the opposite is true
 For instance, consumption of potatoes declines with higher
income (as individuals shift to substitutes such as rice)
 The substitution effect, which means that consumers will shift
to less expensive, though similar products as product prices
rise
 Often income and substitution effects are complementary
Ordinary demand function
 This so-called Marshallian demand function states
that the demand for a good is a function of prices and
income
 For instance, Q(1) = f(P(1), … P(k), Income)
 An important property of ordinary demand functions
is that they are homogeneous of degree zero in
income and prices; i.e., if income and all prices change
by the same proportion, the demand remains
unchanged
Market demand curve
 Market demand curve is the horizontal summation of
the individual demand curves
 The prices of related goods affects the demand (these
can be complements or substitutes)
Market demand curve (cont.)
 Price expectations are also important; if we expect to
see lower prices in the future, the demand for product
will be lower today (as consumption is postponed until
a future date; e.g., sales)
 Market demand is also affected by the number of
people consuming the product; an increase in
population raises the demand for goods and services,
ceteris paribus
 Shifts in tastes would influence the demand for goods,
unrelated to other factors (e.g., because of healthy life
style people are less interested in consuming products
that contain lot of fat, salt, sugar, or calories)
Market demand curve (cont.)
Wester: Managerial Economics
Market demand curve (cont.)
 Using this information, we can write an expression for
market demand curve (linear) as follows:
QD = b(1)*P + Z
where Z = b(0) + b(2)*IN + b(3)*PS + b(4)*PC + b(5)*PE +
b(6)*N
 Changes in P will result in movements along the curve
 Changes in the components of Z will result in shifts in
the entire demand curve
 Example: the demand for good X is given by equation
Q(X) = 10 – 5*P(X) + 0.001*IN + 10*P(Y)
Market demand curve (cont.)
 P(Y) is the price of competing brand to product X (e.g.,
Apply and Samsung smart phones)
 Interpret the parameter estimates
 Examples:
 Calculate the demand for product X given the price of X of
$2, income of $20,000 and price of Y of $2.50
 If income rises to $30,000, how much will this influence
the consumption of product X?
Market demand curve (cont.)
 Normal vs. inferior goods: demand increases
(decreases) with income
 Substitutes vs. complements
 Luxury goods vs. necessary goods – income
elasticity?
 Ordinary goods vs. Giffen goods: demand
decreases (increases) with a higher price
 Are equity shares a Giffen good? We seem to buy
them at high prices and sell them at low prices
(Warren Buffet)!
Market demand vs. firm demand
curve
 Managers are more interested in the demand curve for
the company’s output than that of individuals
 For a monopolist, i.e. a single firm controlling the
whole market, firm’s demand curve is identical to the
market demand curve
 In most cases, a firm supplies only a small portion of
the market and thus its demand curve is not identical
to the market demand curve
 Because of this, pricing decisions of its competitors
affect the demand for its products and pricing (e.g.,
there can be a price leader) decisions – Understand
markets!
Price elasticity of demand
 How to measure the sensitivity of demand to changes
in the price of a product?
 Slope of the demand function
 Let Q(D) = b(0) + b(1)*P where b(1) < 0
 Then the slope is b(1) = ΔQ(D)/ΔP (ΔX = X(2) – X(1))
 Slope is invariant with respect to price if demand curve
is linear
 But the same change in absolute price is different
given the starting price (i.e., in percentage terms)
Price elasticity of demand (cont.)
 Price elasticity of demand overcomes the problem with
the slope measure
 It is defined as E(P) = %ΔQ(D)/%ΔP; it is always negative
 Different price elasticities:
 E(P) > 1, then demand is elastic
 E(P) = infinite, then demand is perfectly elastic
 E(P) < 1, then demand is inelastic
 Alternative measures of price elasticity:
 Mid-point formula, which overcomes the problem with
the starting point (base value) in calculating the
percentages
 It uses the mid point between the start and end price
Price elasticity of demand (cont.)
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Point-price elasticity of demand
It is calculated at a single point along the demand curve
It is the first derivative (slope) of the demand function
Defined as
ε(P) = (dQ(D))/dP)(P/Q(D))
 Example: Q(D) = 50 – 2.25*P and P(1) = 2 and P(2) = 4.
What is E(P) and ε(P) at each point?
 Below we have some data on price (and income)
elasticities for goods categories in the U.S.
 How to interpret these elasticities?
Price elasticity of demand and total
revenue
 Price elasticity of demand is important for predicting
how firm’s revenue performance is influenced by
changes in the price
 Let’s assume that the price of a product falls by 10%
 If the demand remains unchanged, firm’s revenue will
fall by 10%
 But demand will not remain unchanged and hence
some of the price decline is recaptured through the
increase in demand for the firm’s output
 In particular, if demand is elastic (ε(P) > 1), revenues
will rise even if the unit price falls (see pizza example)
Seasonality
 Often time series display regular patterns that repeat
themselves
 These are called seasonal variations, separate from
the underlying trends (e.g., related to income)
 Depending on the item, seasonal variations can be
weekly, monthly, quarterly, and so on:
 Examples:
 Festive seasons give rise to increased food
consumption (e.g., Christmas period)
 Christmas may also increase sales of toys etc.
 Vacation season gives rise to higher gasoline sales
Seasonality (cont.)
 Understanding seasonal variations and estimating
them properly can improve sales/production plans
 The identification of low and high seasons will also
assist in planning production and deliveries
 For instance, winter clothing production takes place
well ahead of their sales in late fall (when they arrive
to stores)
 Example: Seasonality of toy sales
 Other examples: seasonality of alcohol consumption
and demand for gasoline
1995q1
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Seasonality (cont.)
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Toys sales
Trend
Other features of time series
 Deterministic and stochastic trends
 Stochastic trend moves around over time because of
random factors/shocks
 Business cycles – these are different from seasonal
 Structural breaks – significance can be tested
 Stationarity of time series critical
 Requires conversion of the time series (differentiation or
logarithmic transformation)
 Is the variance of the time series constant?
 Cointegration – a linear combination of nonstationary
time series can be stationary if they are cointegrated
Forecasting time series
 Alternative methods:
 Naïve model (random walk) – y(t+1) = y(t), no new info
beyond current period useful
 Linear trend model – y(t+1) = a + b*Trend(y)
 Constant ratio to another variable (often key metric)
E.g., auto sales to nominal GDP (or spending)
 Autoregressive models (e.g., ARIMA) – y(t+1) is based on
its historical time series properties, including seasonals,
trends and other information (no other variables)
 Structural/VAR models – forecast of y(t+1) is based on
models explaining the behavior of y on underlying
variables (for instance, income, prices, etc., to explain
spending) – quarterly data, longer-term forecast
Forecasting time series
 Evaluating the “goodness of fit” of forecasts
 Test the model first using “within sample” data; i.e.,
estimate the model by leaving some data points for
forecasting
 Test statistics to evaluate forecast performance:
 Mean Absolute Error (MAE) of the forecast
 Mean Square Error (MSE) of the forecast
 Root Mean Square Error (RMSE) is the square root of
MSE
 Sometimes it may be helpful to average the results of
alternative forecasting models
Interaction between supply and
demand
Interaction (cont.)
 Market equilibrium is defined as the point where the
supply of and demand for goods equal (earlier chart)
 When the price is below its equilibrium value, P*, there
will be excess demand; the price is bid up as long as the
excess demand situation persists
 The opposite is true for the price that is higher than the
equilibrium price; excess supply leads to unsold goods
in the market and as a result producers will lower
prices in an effort to increase sales
 Example: Q(D) = 25 – 3P and Q(S) = 10 + 2P. Find price
and quantity in the equilibrium?
Interaction (cont.)
 Analyze shifts in demand and/or supply curves
 Special situations:
 Price floors (minimum prices) and price ceilings
(maximum prices); lead to excess supply and
demand
 For instance, gasoline prices, minimum wage
 The impact of taxes on supply and demand
Adjustment
 We can distinguish between short-run and long-run
adjustments
 In the short run, adjustment takes place along given
supply and demand curves (e.g., increase in demand)
Adjustment (cont.)
 In the long-run, existing sellers may adjust fixed inputs
and buyers may change their tastes and preferences
 Long-run adjustments are represented as shifts in
given supply and demand