Alternative several choices bus auto subway attribute

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-Alternative: several choices (bus, auto, subway) -Attribute: characteristics of alternatives (money cost, time cost) -Demand in these cases: demand for one when each consumer chooses b/t auto & bus? Goals -Derive demand function -demand for auto travel = # of auto users =probability of choosing auto * total # in population -Choice probability is important to the derivation of demand function Discrete choice model OR random utility model Consider a representative consumer facing a choice -Choose b/t auto and bus -choice set is {auto, bus} -underlying assumptions about the choice set: 1. Exclusive: one alternative is chosen, other alt. Can’t be chosen 2. Exhaustive: there are no other choices than bus/auto How does the consumer make a decision? -USE THE CONCEPT OF UTILITY! -compare utility attained by choosing auto vs utility attained by choosing bus -let Ua denote utility the consumer receives by choosing a and Ub denote utility consumer receives by choosing b -Auto is chosen when Ua>Ub, (vice versa for bus) Indirect utility function Ub=Ub(Cb,tb), where c denotes monetary cost and t denotes time cost, and b denotes bus (Ua is for auto)
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The Decision rule is: Auto(a) is chosen if Ua(ca, ta)>Ub(cb,tb) and Bus(b) is chosen is Ub(cb,tb)>Ua(ca,ta) Our goals are to understand: 1. Effect of attributes on utility 2. Effect of attributes on choice probability 3. Relative importance of attributes Decomposing utility into systematic and random components Utility itself is not directly observable It’s decomposed into 2 parts: 1. Representative (systematic) utility V, that is a function of attributes and is observable 2. The error term (non-systematic) ε that is random, unobservable Actual Utility and representative utility are NOT the same. U = V + ε Consumers compare U, not V Representative (systematic) Utility -Received by choosing “a”: Va=Va(ca,ta) (for b, replace a with b) -Simple Linear relationship: Vb(cb,tb)= β1cb+β2tb Va(ca,ta)=β1ca+β2ta Interpretation of β1 and β2 β1 is change in systematic utility(v) form a unit change in monetary cost(c) holding time cost (t) constant β1=ΔVa(ca,ta)/Δca | Δta=0 (replace a with b for bus) Β2 is change in systematic utility(v) from a unit change in time cost (t), holding monetary cost (c) constant: β2=ΔVa(ca,ta)/Δta | Δca=0 (replace a with b for bus) Error term (non-systematic) - ε: 1. captures difference b/t U and V 2. Includes factors influencing U but that aren’t included in V 3. Is unobservable and random 4. Unknown value, but we expect that E(εa) = E(εb) = 0 5. Implying E(Va)=Ua and E(Vb)=Ub Choice Probability Utility depends on εa and εb -ε is a stochastic(probabilistic) variable, and has a probabilistic distribution -Assuming distr on ε, we can derive prob that this person chooses a or b -choice prob will give demand func -N*Pa=# of auto users (tot pop x prob for auto)=demand for auto
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  • Spring '07
  • wrigley
  • Economics, probability density function, Maximum likelihood, representative, demand function, relationship b/t

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