# economics homework

1. We

focus again on the firm that produces baseball bats, using 10 tons of wood to

produce 3 tons of bats. Regarding the transport rate, the cost per ton per mile

was $1 for the wood and $2 for the bats. The forest is still located 10 miles

from the market.

(a) Illustrate

with a graph where should be the optimum location. What is the equation for the

Total Transport Cost?

(b) Now

we assume that the cost of shipping woods decreases from $1 per ton to $0.5 per

ton, while the cost of shipping bats remains $2 per ton. Illustrate with a

graph where should be the optimum location. What is the equation for the Total

Transport Cost?

(c) The

forest burns down, forcing the firm to use wood from an another forest which is

now 15 miles from the market. The cost of shipping bats increases from $2 per

ton to $3 per ton, while the cost of shipping woods is now $2 per ton.

(d) The

firms stars producing bats with wood and cork, using 3 tons of wood and 2 tons

of cork to produce 3 tons of bats. Cork is ubiquitous. The cost of shipping

bast remains $3 per ton, while the cost of shipping woods remains $2 per ton.

The distance between the market and the forest is still 15 miles.

2. Why

do breweries typically locate near their markets (far from their input

sources), while wineries typically locate near their input sources (far from

their markets)?

3. Consider

a firm that uses one transferable input to produce one output. The monetary

weight of the output is $5, and the monetary weight of the input is $3. The

distance between M (the market) and F (the input source) is 10 miles.

(a) Suppose

that production costs are the same at all locations. Using a diagram, explain

where the firm will locate.

(b) Suppose

that the cost of land (a local input) increases as one approaches the market.

Specifically, suppose that the cost of land is zero at F but increases at a

rate of $3 per mile as the firm approaches M. Depict the location choice of the

firm graphically.

4. There

is a firm called HiTech which sells its product in city A. HiTech uses two

inputs, which it buys from firms located in city B and C. Both cities are 200

kilometers apart, and the distance between cities A and B, respectively, and

city C is 500 kilometers. HiTech sells its product on the local market in city

A for $500. In order to manufacture its product, HiTech needs three units of

inputs from city B, which are $1 per unit, and one unit from city C, which is

sold for $2. The final product can be transported to city A without any cost.

Transport of one unit from B requires $1 per 100 kilometers , and from C $2 per

100 kilometers.

(a) Provide

a graph representing the above situation. A situation in which variable

transport costs of the output are zero (or negligible) is rather uncommon.

Mention and discuss one example.

(b) Give

a mathematical expression for the production function in this example. What is

the characteristic property of this production function, and what is the

marginal productivity of the production factors?

(c) Determine

the optimal location for HiTech as well as its transport costs and profits per

unit at this location. Provide a graph as well.