Urban Economics Rent Function Calculations Question

Let’s say there are two sectors of an economy, firms and households. Each household supplies labor to the firms.Households earn $100 per month, they spend $1 per mile to commute to work and they spend $50 on all other goods. Firms produce 1 ton of goods and earn $100 per month net profits on production, but must pay $10 per ton mile to ship its output to the port. All firms, residents use 1 acre of land.

1. Calculate each sector’s bid rent function. That is, what is each sector’s ability to pay for a location as a function of distance to the center? How far from the center will land use change from business use to residential?

2. Draw a graph of sector’s bid rent function as a function of distance from the center. Be sure to label the graph and describe the location of each sector.

3. Briefly explain how the model parameters affect land values (that is, what is the role of income and transportation costs in determining bid rents?)