# Department of Managerial Economics and Decision Sciences

## HOMEWORK: SHORT RUN AND LONG RUN

### SUPPLY CURVES FOR ALUMINUM1 Introduction and Overview

A market supply curve (or industry supply curve) is a schedule that tells us the quantity
of output that sellers are willing to supply at various market prices. The market supply
curve is more than just a theoretical construct. In industries such as copper, chemicals,
and aluminum smelting, it can be constructed from plant-level cost data. Indeed, for these
and many other industries, consultants are paid large fees to construct market supply
curves based on plant-level data for their clients. In this homework, you will construct
short and long run market supply curves that will resemble, to a large extent, the supply
curves that consultants construct for their clients.
NOTE: 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
1Sandeep Baliga, Peter Klibanoff and Nicola Persico. This exercise was prepared for use in class discussion in MECN
courses at Kellogg. Do not copy this document for any other use without explicit permission. Version of
June 27,
2014
.
2 “Input” is a generic term used to refer to the resources that a firm employs to produce its output and includes such
things as raw materials, power, labor, capital, and land.

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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.
To construct the supply curve:
1. Use the information in the case to determine which cost items are relevant to the
supply decisions of an aluminum smelter.
2. Use the data in the spreadsheet on the cost of aluminum smelters,
AluminumSmelterData.xls (available on the course website).
3. Follow the step-by-step instructions (an abbreviated and a detailed version are
provided below).
Abbreviated Instructions for Building the Industry Supply Curve for Primary
Aluminum
Using the smelter cost data provided in AluminumSmelterData.xls, you can
construct an industry supply curve in Excel in the following five steps:
2. Calculate the marginal cost for each smelter by adding a new row that sums the
appropriate cost items.
3. Sort the smelters according to the measure of marginal costs you created in step 2.
4. Create a measure of total cumulative capacity in each column. This will tell you
how much capacity is more efficient than any particular plant.
5. Create a graph of the supply curve by making an “XY” scatter plot of the
marginal cost and cumulative capacity measures you created above.
Detailed Instructions for Building the Industry Supply Curve for Primary
Aluminum
open it in Excel.
2. Calculate the marginal cost for each smelter. To do this, create 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
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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. Create 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. Create a graph of the supply curve. To do 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 type 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?

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## 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 do 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