The city is a circle with a radius that extends from the point 0 to the bound- ary of the city x ̄. There is a fixed population N, which we for now consider exogenous or fixed. All workers receive and income y and face a commuting cost t per mile that they drive. Workers have preferences over a compos- ite consumption good c with their utility function given by U(c) = c. All households demand a fixed quantity of land q, which is exogenously deter- mined and carries the rent r(x) per unit of land at location x. The rent at the boundary of the city is equivalent to the agricultural rent ra, that is r(x ̄) = ra All rental income is assumed to paid to absentee landlords who live outside the city. The household budget constraint is then given by y − tx = ri(x)q + c a) Make a list of your exogenous and endogenous variables. b) Solve for the urban bid-rent function. c) Solve for the remaining endogenous variables
Problem 1: Closed City
Assumptions of the model:
The city is a circle with a radius that extends from the point 0 to the bound- ary of the city x ̄. There is a fixed population N, which we for now consider exogenous or fixed. All workers receive and income y and face a commuting cost t per mile that they drive. Workers have preferences over a compos- ite consumption good c with their utility function given by U(c) = c. All households
y − tx = ri(x)q + c
a) Make a list of your exogenous and endogenous variables.
b) Solve for the urban bid-rent function.
c) Solve for the remaining endogenous variables
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