02 Jun Question 1. We focus again on the firm that produces baseball bats,
Question
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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