关键词 > Economics代写

Urban Economics, Problem Set #1

发布时间：2022-09-25

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Urban Economics, Problem Set #1

1) No late problem sets

2) You can only upload one single file. No multiple file submissions.

3) We accept only WORD, EXCEL and PDF formats.

Maximum Points: 50

Question1: 7pts

Question 2: 7pts

Question 3: 8pts

Question 4: 8pts

Question 5: 10 pts

Question 6: 10pts

(1) Von-Th ü nen Model I

A coffee shop is located at M (where x=0) and charges marginal cost prices for its coffee (i.e., c=p). Customers walk to the coffee shop to buy coffee and, aside from the purchase price, incur travel cost of (tx2 ), measured from the shop. The shop’s market reach is 2.3 km and t=2.

If customers’ WTP for the shop’s coffee is $12.83 what is the product’s price in equilibrium?

(2) Von-Th ü nen Model II

Farmers that grow wheat need to sell their product at the market M (where x=0). Marginal cost of growing equals c=$5, marginal travel cost is t=4 (per mile and ton) and the market’s WTP for wheat is $120 per ton.

a) what is the maximum distance x* at which farmers would grow wheat?

b) For each distance point x=10, x=20, and x=30, say whether anybody would grow wheat or not and what the resulting land rent would be. Note, rents cannot be negative.

(3) Von-Th ünen Model III

Refer to the von-Th ünen model where a city’s market reaches to the left and to the right. The firm is competitive and its price equals marginal cost. The firm’s marginal cost is c=1; the market reach is x=14 to the left and x=14 to the right. Marginal transportation cost t equal t=5.

(a) What is customers’ WTP per unit of the good in question? (5 pts)

(b) What is the rent for a person located at x=10? (3 pts)

(4) Von-Th ünen Model with multiple cities

There are two cities, A and B, where B is located 14 miles east of A. Both produce an identical good and consumers’ WTP=16 is the same everywhere. Marginal transportation cost is identical tB=tA=2. Each city prices its good at marginal cost. We know that cB=2; cA is unknown.

(a) What is the maximum market reach of city B to the west? (2 pts)

(b) Now assume there are unserved customers to the west of B (i.e., between A and B). Calculate the minimum cA for this to be true. (6 pts)

(5) Locations of Transfer-Oriented Firms

The distance between the resource (R ) and the market (M) is 10 miles. A firm’s procurement cost is given by PC=2x2, where x is the distance from the resource measured in miles. The firm’s distribution cost is given by DC=6*(10-x). Again, x is the distance from the resource.

(a) What is the Total Freight Cost (TC) at each milestone. This question assumes there are only 11 possible discrete locations, i.e., x=0, 1, 2, 3, …10. Locations between the milestones are not possible. Where should the firm locate? (You can do this “by hand” or in a spreadsheet)

(b) Now assume, the firm can locate between the milestones, for instance at x=5.145. Provide a mathematically exact solution for the optimal location (with 3 decimals). What is the optimal x? At this location, what is PC, DC and TC (three decimals).

(c) How does your answer to all parts under (b) change if the marginal procurement cost PC were equal to zero everywhere?

(6) A pizzeria delivers a pizzas to each customer and incurs a cost of $1 per unit and mile. Each unit needs to be delivered separately (just like we did in class)

Part 1:

(a) Where is the median customer located?

(b) Where is the delivery cost minimizing location and what is its delivery cost?

Location	A	B	C	D	E	F
Distance from A (miles)	0	1	8	2	6	18
Number of customers	3	2	1	2	3	2

Part 2:

Where is the median location if the number of customers at A increased from 3 to 7? What is the delivery cost from this location?