di = demand for auto travel (say vehicle trips per day) j = transit mode
A = scale parameter i P = c a r t r a v e l f u e l p r i c e
i T = c a r t r a v e l t i m e j T = t r a n s i t t r a v e l t i εiP = car fuel demand elasticity εiT = car travel time demand elasticity m e T j i , ε = c a r t r a v e l t i m e c r o s s - e l a s t i c i t y w i t h r e s p e c t t o t r a n s i t t r a v e l t i m e
This specific form of the demand function, a constant-elasticity demand function, is chosen because of its wide empirical application in the estimation of travel demand elasticities and for its ease of analytical tractability. 9
The fuel price elasticity of a car measures the percent reduction in car vehicle trips due to a one percent increase in its price. The travel time elasticity of demand measures the percent reduction in car vehicle trips due to a one percent increase in travel time. Finally, the car travel time cross elasticity with respect to transit travel time measures the percent reduction in vehicle trips due to a one percent decrease in transit travel time. This assumes that car and transit are substitutes. 10
Now, for initial values of fuel price, time and trips, denoted by subscript zeros, the equation will be:
j i i i j i i i T T A P P d , 0 T 0 0 0 ε T ε ε =
9 The demand curves usually employed and depicted in graphs are linear demand curves, which have the property that price elasticity declines as we move down the demand curve. Not all demand curves have this property, however; on the contrary, there are demand curves for which price elasticity can remain constant or even rise with movements down the demand curve. The constant elasticity demand curve is the name given to a demand curve for which elasticity does not vary with price and quantity. Whereas the linear
demand curve has the general form: P = a − bQ , the constant elasticity demand curve is instead written as:
k P= 1 η Q Where k and η are positive numbers that determined the shape of the curve.
10 Two goods are considered substitutes if the increase in the price of one determines an increase in the demand for the other. Two goods are considered complements if the increase in the price of one good causes a decrease in the demand for both goods (e.g., coffee and cream). The relationship is further refined by considering perfect versus less-than-perfect substitution and complement.