This homework has two questions.

Question 1: Short Run Your task in this question is to construct

the market supply curve for primary aluminum smelting in 1993. The supply curve

that you will construct pertains to supply decisions in the short run (you can

think of this as roughly equal to a horizon of time of six months or less). In

the short run, aluminum smelters can adjust the volume of aluminum ingot

produced, but they may not be able to adjust the quantities of all categories

of inputs up or down.2 Part of the challenge of this exercise is to identify

which categories of cost would vary as a smelter adjusts its output and which

do not, i.e., which categories of costs constitute marginal costs. Be

forewarned, as would be the case in practice (e.g., if you were doing this as a

consultant), you are going to need to make decisions about which categories of

cost are marginal costs.

If firms are price-takers, each firm should produce at every

plant for which the market price exceeds the marginal cost of producing output

in the plant. Any margin of price over marginal cost makes a contribution

toward covering a plant's fixed costs. To construct a market supply curve,

then, you need information on plant capacities and plant marginal costs. From

this data, you can calculate how much capacity has marginal cost

less than any particular market price. This is the amount of

output one expects from price-taking firms. Plotting this information on a

graph yields a market supply curve.

Detailed Instructions for Building the Industry Supply Curve for

Primary Aluminum

1. Download the smelter cost data provided in

AluminumSmelterData.xls and open it in Excel.

2. Calculate the marginal cost for each smelter. For this, construct a new row at the bottom of the

spreadsheet and enter a formula that sums the relevant cost categories. For

example, if you conclude that the correct definition of marginal cost is the

sum of electricity costs, alumina costs, and other raw materials costs, you

would click on cell C30 and enter "=C13+C17+C19". Then, copy this formula

into all columns C through FC, which will give you a marginal cost number for

each of the 157 plants. Think hard about which categories of costs

constitute marginal costs, i.e., which categories of costs will vary as a

smelter varies its output up or down.

3. Sort the smelters according to their marginal costs.

Highlight the entire data region, excluding the labels in columns A and B.

Don't forget to include your new row added in step 2. This should be the area

C5 through FC30. Click on the "Data" menu in Excel and choose

"Sort". To sort data that is arrayed in rows, you must choose

"options" and then click next to "sort left to right". Then

click "OK". Now choose to sort by the row you just created, row 30

(if you followed the above directions exactly), and click next to

"Ascending." Then click OK.

4. Construct a measure of total, cumulative

capacity in each column. This will tell you how much capacity is more efficient

than any particular plant. For subsequent graphing, it is best to put this in

the row just above the row you created in step 2. Enter

"=sum($C9:C9)" in cell C29. Then copy this formula into cells D29

through FC29. Note: The information in rows 29 and 30 is the supply curve. To

see this, find the "marginal plant" at 1994 market prices; that is,

the plant whose marginal cost is just lower than the market price of $1,110. We

expect that plant and all the more efficient plants to its left to produce at

that price. Their total capacity is given in row 29. This calculation can be

done for any market price.

5. Construct a graph of the supply curve. For this,

highlight cells C29 through FC30. Click on the "insert" menu, and

then on the "chart" item on that menu. Choose the "XY

chart" chart category and choose

the lower-right "chart sub-type" before clicking "Next".

Click "Next" twice more and then "Finish". The resulting

chart is the shortrun industry supply curve.

The remaining part of Question 1 In addition to preparing a

graph of the short-run supply curve for aluminum, answer the following

questions:

a. What categories of cost did you include in your determination

of marginal cost? Why did you include these cost categories and exclude the

other categories?

b. According to the supply curve you constructed, how much

output would be supplied by the aluminum industry at a price of $1,100 per ton?

How does this compare to actual production of primary aluminum in 1993?

c. According to the supply curve you constructed, how much

output would be supplied at a price of $1,500 per ton?

d. The supply curve is constructed under the assumption that

each smelter is operated to maximize its profits. Is this, in your view, a

plausible assumption?

Question 2: Long Run Construct a long run supply curve for

Aluminum using the same data as in Question 1. (You may assume the scrap value

of a plant is zero when you construct

this and take the discount rate to be 8%.) Remember the exit price

of existing smelters is given by Average Total Cost (ATC). You should be able

to work these out for each smelter from the data in the spreadsheet. Also, the

entry price of a new smelter is given by Full Reinvestment Average Total Cost

(FR-ATC). You can use the data from the case and from my teaching in class to

work this out for a generic entrant. Take this to be the entry price. Finally,

you can combine the exit prices of the existing smelters and the entry price

for a generic entrant to construct a long run supply curve.