Input-Output Analysis, Linear Programming and Modified Multipliers

Suppose that the US government imposes production limit on power generation
and supply sector in order to reduce the greenhouse gas emissions. For more discussions
about reduction in greenhouse gas emissions, see McKinsey & Company (2007). For
illustration purpose we assume that power generation sector should reduce its production
by 20%2 to meet an international requirement. This requirement is evidently burden to
the US economy. Economic loss to U.S. is calculated using the output multiplier for
power generation sector, which is 1.26 (Table 2). 20% reduction in power generation
causes direct loss which is $51.7 billion, and additional indirect loss which is $13.5
billion. In total US economy would be suffering from the loss of $65.2 billion.

Suppose that US government has a plan to recover this loss by increasing
government expenditure. Under the conventional IO approach, we may use the original
multiplier, 1.86 (Table 2), and thus government expenditure would be expanded by $35.1
billion. However, the modified multiplier for government sector with production
restriction is given by 1.84 (Table 2) and thus expenditure should be expanded by $35.4
billion to recover the loss not $35.1 billion. Even if government succeeds to promote the
economy using the government expenditure by $35.1 billion with original multiplier, the
U.S. still loses $616 million because the output multiplier is overestimated. This implies
that US economy may not be recovered fully. The modified multiplier tells us that US
government invests $300 million more to recover the economic loss from the production
restriction on power generation sector. The net gain to use the modified multiplier might
be $316 million (= $616 million - $300 million).

2 US should reduce its greenhouse gas emission to 7% below 1990 emission level under the Kyoto
Protocol, which is equivalent to 2.5 gigatons per year or approximately 30% of current emissions
(McKinsey & Company, 2007; Kim and McCarl, 2008).

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