Suppose we have a commuter that has

decided to allocate M dollars to housing, commuting,and dining. Let P be the price of

Housing, h(x) be the amount of housing consumed as a function from the distance to the city,

X be the distance to the city center, and t be the commuting cost per mile. Furthermore, let's

add one more thing to the model: suppose city-level restaurant-quality changes with distance

to the city center - e.g there are better restaurants (or more) at the city center. For simplicity,

assume all restaurants charge the same amount for a meal (regardless of quality). Let

d(x)denote the amount of "restaurants" consumed (using "d" for "dining") and pd be the price of

dining. The commuter can allocate Msuch that:

Ph(x) + tx + pdd(x) =M

A). We have the following choices for d(x): either d(x) = 5 + 3x or d(x) = 53x.

Which one makes more sense to use in the context of this problem, and why?

(b) Now let h(x) = a (where a >0) and t= 6. Use whatever you chose for d(x) in

part a for the rest of the problem. Derive the commuter's bid rent curve.

(c) What restriction do you need to put on the model to ensure the bid rent curve

you derived has a negative slope?

(d) At what distance from the city center x is the commuters' willingness to pay

for housing zero? You can assume the restriction you placed in the part c holds. Do you

need any additional assumptions for the expression you derive here to be positive? If so,

what? If not, explain why it is always positive.