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1. (20) Suppose there are two ways for workers to commute downtown to their jobs drive their private vehicle or take the light rail public transit (for now, let both travel modes take about the same time). Demand for driving private vehicles is \( Q_{V}=50-5 Y \) \( 50 \mathrm{P}_{\mathrm{V}}+1000 \mathrm{P}_{\mathrm{T}} \), where \( \mathrm{Q}_{\mathrm{v}} \) is the number of vehicles commuting downtown daily, \( \mathrm{P}_{\mathrm{v}} \) is price to drive (round-trip) downtown (gas, etc.), \( \mathrm{P}_{\mathrm{T}} \) is the transit (round-trip) ticket price, \( \mathrm{Y} \) is of commuters. Initial values of prices and income are \( \mathrm{PV}_{\mathrm{V}}=\$ 15, \mathrm{Y}=\$ 1000 \), and \( \mathrm{P}_{\mathrm{T}}= \) \$20. Explain your work and answers. a. Calculate price elasticity of \( Q_{v} \) with respect to price, \( P_{v} \). How sensitive is commuting downtown in vehicles to a change in \( P_{v} \) ? Explain using your calculated elasticity. b. Calculate the cross-price elasticity of \( Q_{V} \) with respect to a change in \( P_{T} \). How sensitive is commuting downtown in vehicles to a change in the price of public transit? That is, what does this suggest about the relationship between driving and transit? c. Calculate the income elasticity of \( Q_{v} \). d. The Transit Authority proposes making riding transit free \( \left(P_{T}=0\right) \). How much will this change, if at all, the number of vehicles commuting downtown, \( Q_{v} \) ? In other words, compare the new \( Q_{V} \) at \( P_{T}=0 \) to the \( Q_{v} \) at the initial prices and income given in the problem. e. Finally, suppose a road toll is imposed on drivers commuting downtown to fund the free public transit. Given the elasticity you calculated above, do you expect toll revenues to increase or decrease as toll prices rise? Explain.

Given: Demand: Qv = 50 - 5Y - 50Pv + 1000PT Pv = $15,Y = $1000, and PT = $20 Solution: Substitute Pv = $15,Y = $1000, and PT = $20 Qv =50 ? 5Y ? 50Pv