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how to get this figure). If the average smelter is rational then, noting it’s capacity is 133.02 tpy, it produces according to:
{ The “rational” average smelter’s supply curve is graphed below: Rational average smelter Firm’s Supply On the other hand, if the average smelter is irrational, then irrespective of the price – and noting that it’s capacity is
133.02 tpy – it will always supply output less than or equal to capacity: 25
ECO 204 Chapter 15: Competitive Firms and Markets (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Irrational average smelter Firm’s Supply The possibility of rational and irrational “competitive” firms raises a natural question: “how do we model the industry
supply curve when some firms are rational while others are irrational, and how do we know supply model is right:
rational or rational cum irrational?”. Let’s examine this issue by discussing the HBS case The Aluminum Industry in 1994.
7. “Rational” and “Irrational” Supply Models
In this section we are going to build two models of competitive market supply curves: when all firms are rational, and
when some firms are rational and the remainder irrational. We have seen that, irrespective of the market price and
“returns”, an irrational firm will produce an output less than or equal to capacity (i.e.
). For
convenience, we assume that an irrational firm always produces at capacity (i.e.
).
We have also shown that a rational competitive firm with constant returns will supply output according to:
{ For convenience, we assume that when
that: a rational firm with constant returns will produce at full capacity so { We have shown that a rational competitive firm with decreasing returns will supply output according to: { Armed with these assumptions, let us use the HBS case The Aluminum Industry in 1994 to see how to build supply
models with: (a) rational firms (b) rational and irrational firms.
26
ECO 204 Chapter 15: Competitive Firms and Markets (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Aluminum is one of many commodities traded on the London Metals Exchange (LME) and major newspapers regularly
publish bid/ask prices:
London Metals Exchange Prices, Tuesday, March 2013.
Quotations in U.S. Dollars per metric ton at close of first ring trading in the morning; prices shown are
official closing prices for prior day's trading.
Bid Change Asked Change Aluminum  LME High Grade Spot 1898.00 7.00 1898.50 7.50 Aluminum  LME High grade 3 month future 1931.50 6.50 1932.00 6.50 Copper  LME Cath. Hi Spot 7601.50 14.50 7602.00 16.00 Copper  LME Grade A 3 month future 7639.00 16.00 7640.00 16.00 Lead  LME Spot 2168.00 5.00 2169.00 5.50 Lead  LME 3 month future 2190.00 5.00 2191.00 5.50 Nickel  LME Spot 16925.00 105.00 16930.00 100.00 Nickel  LME 3 month future 17000.00 75.00 17010.00 80.00 Tin  LME Spot 22990.00 290.00 22995.00 245.00 Tin  LME 3 month future 23050.00 350.00 23100.00 390.00 Zinc  LME Special High Grade Spot 1909.00 3.50 1909.50 3.50 Zinc  LME Special High Grade 3 month future 1939.00 5.00 1940.00 5.00 Source: Wall Street Journal Market Data Center London Metals Exchange Prices Commodities traders build and use supply models to forecast future price movements. For example, if demand for
aluminum (AL) is expected to grow at 3% CAGR (Compound Annual Growth Rate) for the next 5 years, we can use supply
models to forecast the trajectory of AL spot prices over the next 5 years6.
We have seen that the aggregate supply curve is the sum of individual supply curves. In turn, for any price between
and
an individual firm’s supply curve is its marginal cost curve, which can be upward sloping (if the firm
has decreasing returns) or flat (if the firm has constant returns). To derive the aggregate supply curve as the sum of
individual firms’ marginal cost curves, one would have to (ala PTC) derive each firm’s cost function by guessing the
functional form of the cost function (is it linear, convex?) and estimating its parameters by regression analysis (exactly as
you did in PTC). Clearly, this is would be cumbersome and time consuming.
In practice, rather than trying to estimate each firm’s cost function from scratch, for a hefty fee we can procure average
variable cost and capacity figures for each AL producer from data providers like CRU and GFMS. See this example for the
average primary AL smelter in 1993: 6 This is one method of forecasting commoditient of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. $/mt Supply
As long as demand
crosses in vertical
portion, we can expect
“large” positive price
movements As long as demand
crosses in flat portion,
we can expect “small”
positive price
movements Industry
Capacity
20.885m
mt However, before commodities traders can use such a supply model to place bets of AL prices they have to be sure that is
the correct model. Perhaps the “correct” model consists of rational and irrational producers. Here’s how one can build a
rationalirrational producer model. From the case one can argue that CIS and state owned smelters are irrational (why?)
while all...
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 Fall '14
 Supply And Demand, Competitive Firm, S. Ajaz Hussain, Sayed Ajaz Hussain

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