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, no JPEG etc.

Maximum Points: 50

Question1: 7pts

Question 2: 7pts

Question 3: 8pts

Question 4: 8pts

Question 5: 10 pts

Question 6: 10pts

(1) (1) Von-Thünen Model I

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

If customers’ WTP for pizza is $12.99 what is the price of a pizza in equilibrium?

(2) Von-Thünen Model II

Farmers that grow wheat need to sell their product at the market M (where x=0).

Marginal cost of growing equals c=$22, marginal travel cost is t=3 (per mile and ton) and the market’s WTP for wheat is $79 per ton.

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

b) For each distance point x=2, x=6, and x=10, say whether anybody would grow wheat or not and what the resulting land rent would be. Note, rents cannot be negative.

(3) Von-Thünen Model III

Refer to the von-Thünen 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=2; the market reach is x=24 to the left and x=24 to the right. Marginal transportation cost t equal t=6.

(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=12? (3 pts)

(4) Von-Thünen Model with multiple cities

There are two cities, A and B, where B is located 11 miles east of A. Both produce an

identical good and consumers ’ WTP=42 is the same everywhere. Marginal transportation cost are and tA=2 and  tB=4. Each city prices its good at marginal cost (p=c). We know that cB=6; cA  is unknown.

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

(b) Now assume A wants to reach markets (and sell to at least one customer) to the east of B. Calculate the maximum 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=4x2, where x is the distance from the resource measured in miles. The firm’s distribution cost is given by

DC=(10-2x)2. Again, x measures 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 2 decimals) using  calculus. What is the optimal x?  Is it different from your solution from (a) above. At this location, what is PC, DC and TC (two decimals). Show your work!

(c) How does your answer to all parts under (b) change if the distribution cost D where DC= (10-x), i.e., without the squared term. PC remains at PC=4x2.