Introduction to Transportation Demand Analysis and Overview of Consumer Theory Moshe Ben-Akiva 1.201 / 11.545 / ESD.210 Transportation Systems Analysis: Demand & Economics Fall 2008Part One: Introduction to Transportation Demand Analysis Outline I. Introduction to Transportation Demand Analysis • Choices • Complexity • Sample statistics • Roles of demand models II. Overview of Consumer Theory 2Choices Impacting Transport Demand ● Decisions made by Organizations – Firm locates in Boston or Waltham – Firm invests in home offices, high speed connections – Developer builds in downtown or suburbs ● Decisions made by Individual/Households – Live in mixed use area in Boston or in residential suburb – Do not work or work (and where to work) – Own a car or a bike – Own an in-vehicle navigation system – Work Monday-Friday 9-5 or work evenings and weekends – Daily activity and travel choices: what, where, when, for how long, in what order, by which mode and route, using what telecommunications 3Complexity of Transport Demand ● Valued as input to other activities (derived demand) ● Encompasses many interrelated decisions – Very long-term to very short-term ● Large number of distinct services differentiated by location and time ● Demographics & socioeconomic matter ● Sensitivity to service quality ● Supply and demand interact via congestion Complexity and Variety �wide assortment of models to analyze transportation users’ behavior. 4Mode Share Statistics Transit Shares for Work Trips in Selected U.S. Cities City Year Transit Mode Share (%) Boston, MA 1990 10.64 2000 9.03 Chicago, IL 1990 13.66 2000 11.49 New York, NY 1990 26.57 2000 24.90 Houston, TX 1990 3.78 2000 3.28 Phoenix, AZ 1990 2.13 2000 2.02 5 Source: US Census, 1990, 2000Travel Expenditures ● The average generalized cost (money and time) per person in developed countries is very stable. % of Income Spent on Travel5% 10% 15% 20% 100 200 300 400 500 600 Time Spent on Travel 14% ~1.1 hrs Motorization Rate (Cars/1000 Capita) 6 Source: Schäfer A., 1998, “The Global Demand for Motorized Mobility”, Transportation Research A, 32(6): 455-477.Transport Demand Elasticities ● Elasticity: % change in demand resulting from 1% change in an attribute ● Derived from demand models: Price In-vehicle time Work Trips (San Francisco) Auto Bus Rail -0.47 -0.58 -0.86 -0.22 -0.60 -0.60 Price Travel time Vacation Trips (U.S.) Auto Bus Rail Air -0.45 -0.69 -1.20 -0.38 -0.39 -2.11 -1.58 -0.43 Source: Schäfer A., 1998, “The Global Demand for Motorized Mobility”, Transportation Research A, 32(6): 455-477. 7Value of Time ● The monetary value of a unit of time for a user. Work Trips (San Francisco) Auto Bus In-vehicle time 140 76 Percentage of Walk access time 273 after tax wage Transfer wait time 195 Vacation Trips (U.S.) Auto Bus Rail Air Percentage of Total travel time 6 79-87 54-69 149 pretax wage Freight Rail Truck Percentage of shipment Total transit time 6-21 8-18 value per day Source: Jose Gómez-Ibañez, William B. Tye, and Clifford Winston, editors, Essays in Transportation Economics and Policy, 8 page 42. Brookings Institution Press, Washington D.C., 1999.Role of Demand Models ● Forecasts, parameter estimates, elasticities, values of time, and consumer surplus measures obtained from demand models are used to improve understanding of the ramifications of alternative investment and policy decisions. ● Many uncertainties affect transport demand and the models are about to do the impossible 9Role of Demand Models: Examples ● From Previous Lecture: – High Speed Rail: Works in Japan/Europe, how about in US? – Traffic Jams: Build more, manage better, or encourage transit use? – Truck Traffic: evaluate tradeoffs of environmental protection. 10Part Two: Overview of Consumer Theory Outline ● Basic concepts – Preferences – Utility – Choice ● Additional details important to transportation ● Relaxation of assumptions ● Appendix: Dual concepts in demand analysis 11Preferences ● The consumer is faced with a set of possible consumption bundles – Consumption bundle: a vector of quantities of different products and services X = {x1,…,xi,…,xm} – A bundle is an array of consumption amounts of different goods ● Preferences: ordering of the bundles – X fY: Bundle X is preferred to Y – Behavior: choose the most preferred consumption bundle – Transitivity, Completeness, and Continuity 12The Utility Function ● A function that represents the consumer’s preferences ordering X fY ⇔ U(X)>U(Y) – Utility function is not unique • U(x1, x2) = ax1 + bx2 • U(x1, x2) = x1ax2b – Unaffected by order-preserving transformation • 10× U(x1, x2) +10 ? • exp(U(x1, x2)) ? • (U(x1, x2))2 ? 13Indifference Curves ● Constant utility curve ● The consumer is indifferent among different bundles on the same curve x2 u1 u2 u3 Indifference curves x1 14Marginal Utility and Trade-offs ● Marginal utility ( ) i i U X MU x ∂= ∂ U (x1, x2) = 4x1 + 2x2 U (x1, x2) = x10.5 x20.5 MU 1 = 4 MU 1 = 0.5 x1 −0.5 x20.5 ● Marginal rate of substitution (MRS) 15 11 2 2 ( ) ( ) U X MU xMRS U X MU x ∂ ∂ = = ∂ ∂ 4 2MRS = 2 1 xMRS x =Consumer Behavior ● Utility (preference) maximization ● Bounded by the available income max U ( X ) m s t . . PX ≤ I ( p x ≤ I )∑ i i i=1 X feasible (e.g. non − negativity) – P - vector of prices P = {p1, …, pi, …, pm} – I – income ● When considering two goods, the constraint would be: p1x1 + p2x2 ≤ I 16Geometry of the Consumer’s Problem I / p2 Income constraint x1 x2 u1 u2 u3 Indifference curves x1 * x2 * Slope I / p1 = -p1 / p2 17Revealed Preferences ● A chosen bundle is revealed preferred to all other feasible bundles: X (P0, I 0) - the demanded bundle at Point 0 X (P0, I 0) f X (P1, I1) if P0 X (P0, I 0) ≥ P0 X (P1, I1) x2 X(P0, I0) X(P1, I1) Income line x1 18Indirect Revealed Preferences ● Transitivity of preferences: – X (P0, I 0) is indirectly revealed preferred to X (P2, I 2) if: X (P0, I 0) f X (P1, I1) and X (P1, I1) f X (P2, I 2) x2 X(P0, I0) X(P1, I1) X(P2, I2) x1 19Optimal Consumption ● The consumer’s problem max U (X ) s.t. PX ≤ I ● Assuming U(X) increases with X PX = I ● The Lagrangean L(X ,λ) = U (X ) +λ(I − PX ) λ: Lagrange multiplier of budget constraint 20Optimal Consumption ●