Question

Luca’s inverse demand for public transportation is given by ?L(?) = 10 − 2?, where ?...

Luca’s inverse demand for public transportation is given by ?L(?) = 10 − 2?, where ? represents the number of trips per week. Julia’s inverse demand is given by ?J(?) = 5 − ?. The price of a one-way ticket is $2.

a) How many trips do Julia and Luca make? How much consumer surplus do they obtain from public transportation?

b) The city decided to offer the public transportation service free of charge. To finance the cost of public transportation, the city will raise the taxes by $7 per person. (If you do the math, that seems to be OK.) Obtain the new pattern of public transportation usage by Luca and Julia. How do you think these two consumers feel about the new financing of public transportation?

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Answer #1

Demand for public transport for Luca: PL(q) = 10 - 2q

Demand for public transport for Julia: PJ(q) = 5 - q

Price of one-way ticket = $2

Equilibrium trips for Luca:

PL(q) = $2

10 - 2q = 2

2q = 8

q = 4

Equilibrium trips for Julia:

PJ(q) = $2

5 - q = 2

q = 3

Consumer surplus for Luca = 1/2 * (10 - 2) * 4 = 16 (Area of triangle formula used)

Consumer surplus for Julia = 1/2 * (5 - 2) * 3 = 4.5

b) Since the public transportation is now free of cost, and the taxes will be deducted per person irrespective of whether the person travels or not, Julia and Luca will now travel freely.

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