Reference no: EM133125716

In this problem, you will create a budget constraint diagram to investigate the impact of a transportation cost increase on housing land rents in the city. Consider a 1-class monocentric city on a Von Thunen plane. There are two goods within the city: land q where rent varies over space and a composite good z whose unit price is 1 everywhere. There is a single mode of transportation available to all residents at a cost of k per round-trip mile. Land outside the city rents for a fixed price of RA per acre. Now suppose the city transportation cost increases.

Below, multiple parts of the question ask you to draw a diagram. Prepare a diagram for each part, as specified below. The goal is to show the progression of your work. Your diagrams may be digitally created or drawn by hand. If you draw by hand, I recommend color-coding to enhance legibility and avoiding notebook paper with dark lines (you don't want dark notebook paper lines to obfuscate your work).

1a. Draw and label the axes on the budget constraint diagram (include variable and variable name). Conceptually explain each axis. Also, label two distances (s1 and s2, such that s1 < s2) on the appropriate axis of your diagram.

1b. Consider the initial transportation cost, k. Draw and label the Disposable Income line Y(s) and the Indifference Curve I*. Write the equation for the disposable income line.

1c. Consider the initial cost, k. Draw and label the Budget Constraint line for s1 (label as Line O) and the Budget Constraint for s2 (label as Line H). Why are the budget constraint lines different for distance s1 and distance s2?

1d. Consider the final transportation cost, k'. Draw the new Disposable Income line Y'(s) and write the equation for the line. Draw the Budget Constraint lines O' and H'. How does the steepness of the slopes compare to O and H?

1e. How does the new land rent (called R'(s)) at distance s1 compare to the initial land rent (called R(s)) at distance s1? Explain.

1f. At this stage, you know enough about the change in land rent to create a generic, representative bid-rent diagram of R(s), R'(s), and RA. Draw the bid-rent diagram (the x-axis for a bid-rent diagram is distance and the y-axis is bid-rent). What is the bid-rent at city center before/after the transportation price change? What is bid-rent at some point farther from city center before/after the transportation price change?

1g. From the bid-rent diagram you created in 4f, can you tell whether the city's radius increased, decreased, or stayed the same? Explain.