Assignment 1. Consider a city that must decide how many librar

02 Jun Assignment 1. Consider a city that must decide how many librar

Question
Assignment
1. Consider a city that must decide how many libraries to provide. The city assumes the travel cost is 10 cents per library trip per mile. The table below lists the average production costs (APC) and average distances (AD) to library patrons for different numbers of libraries.

Number of Libraries

APC ($)

AD (mile)

Travel Cost

Average Total Cost

1

0.30

20

3

0.40

10

5

0.50

7

9

0.90

4

11

1.20

2

(a) If the city’s objective is to minimize the average total cost of a library trip, and the city must choose from the options listed in the table, how many libraries should it provide? (complete the table)

(b) If the unit travel cost doubles, how many libraries should the city provide?

1. The table below summarizes the productivity of workers in wheat and cloth production in two parts of a region.

Output

per Hour

Opportunity

Cost

East

West

East

West

Wheat (bushel)

1

4

Cloth

4

6

(c) Complete the table by providing the opportunity costs of producing wheat and cloth in the East and the West. For which good does the East have a comparative advantage and absolute advantage? What about the West?

(d) Assume that transport costs are zero and that the exchange rate is six clothes for three bushels of wheat. Assume that:

• a western household switches one hour from cloth production to wheat production;

• a eastern household switches three hours from wheat production to cloth production and exchanges half of its cloth production;

will the households be better off?

(e) Suppose that the time required to execute the trade in (b) is thirty minutes. Is trade still beneficial? At what transaction cost (time per trade) would the net gain from trade be zero for the western household?

2. We consider a Shopping model. Consumers pay store price plus all transportation costs (Free On Board Pricing). One way to determine the distance that consumers are prepared to travel to shop is to examine transportation costs in light of the demand curve. The equation for the demand function in Q= 10 ? 2P, where Qis the quantity demanded and P the price.

(a) Calculate the equation of the inverse demand function (the Price is function of the Quantity) and evaluate the limit price (maximum price that consumers are willing and able to pay).

(b) If the store price is $4 and transport costs are $1 per mile, what is the equation for the Price-Distance function? Find the radius of the market area. (Hint: Set the price-distance function equal the limit price of the demand function and solve for D.)

(c) Calculate the market area radius if one constructs a more efficient road system that cut downs the time needed to drive to the store and the transportation per mile is now equal to $0.5.

3. Consider a region where two firms are producing the same good at a different price. The first firm is located on the coastline whereas the second firm is located five miles inland. Using the information provided by the excel file (HW1.xls) complete the table on the Excel spreadsheet. Graph the 3 cost curves associated to: (1) the production of the good at home, (2) the purchase of this good from Firm1 and (3) the purchase of this good from Firm2 (X-axis is the distance from the coastline and Y-axis the Cost). What are the market areas for both firms?