economics homework

| August 14, 2017

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.

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