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.) 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 1995q2 1995q3 1995q4 1996q1 1996q2 1996q3 1996q4 1997q1 1997q2 1997q3 1997q4 1998q1 1998q2 1998q3 1998q4 1999q1 1999q2 1999q3 1999q4 2000q1 2000q2 2000q3 2000q4 2001q1 2001q2 2001q3 2001q4 2002q1 2002q2 2002q3 2002q4 2003q1 2003q2 2003q3 2003q4 2004q1 2004q2 2004q3 2004q4 Seasonality (cont.) 240 220 200 180 160 140 120 100 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