A simple model of the monocentric city can illustrate the trade-off between rent and commuting costs across different locations in a city. Here are the assumptions for this question:
-Every worker in our city is paid the same wage.
-Every worker at every distance from the CBD lives on a piece of land with no housing structures.
-Each worker's piece of land is the same size as every other worker's piece of land. In other words, I do not want you to include the variable H in any part of this model and rent should be in terms of "per unit of land" as opposed to "per square foot of housing".
To save you some time, here are the variables you might use in your answer:
| w = wage | F(L) = distance to the edge of the city | t = commuting cost per mile |
| L = labor | Z = opportunity cost | Ra = agricultural rent |
a) (5 points) Write the equation for the labor supply curve and draw the labor market for our city. You can assume labor demand is given and is a downward sloping curve. Label the y-intercept for the supply curve and the equilibrium values that you get from this market.
b) (4 points) Next, draw the graph that illustrates the rent in this city as a function of the distance from the city center (CBD). Be sure to label all of the endpoints of the graph with the appropriately defined variables.
c) (6 points) Imagine that this city wants to fight urban sprawl so they require that every plot of land is made smaller. Assume this can be done costlessly and after the change, every worker will live on a plot of land that is the same size as every other worker's plot of land. Show what you expect to happen to this city in the graphs you drew in the previous parts of this question (or you can redraw them). Indicate what will happen to wages, the number of workers in the city, city size and rents. Similar to the practice problem, there may be ambiguity in some of the outcomes. You should identify and explain what the different possibilities could be under different circumstances.
