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The Economic Stimulus Package economic stimulus example.pdf
We have decided to spend 1 billion (1000 million) dollars on a stimulus package. There is a debate, though, about whether to spend it on tax cuts or infrastructure. Research suggests that the multiplier effect for tax cuts is a and for infrastructure it is b. We also know that congressional republicans will not sign on to a package that has less than 100 million in tax cuts and democrats won't sign on for a bill that has less than 300 in infrastructure spending. What's the best mix, in terms of A and B?
X1 = tax reduction
X2 = infrastructure spending
X1+X2=1000 (millions)
X1>=100
X2>=300
S=aX1+bX2
X2=S/b – a/b X1
Slope is –a/b
The maximum stimulus will come at either point A or point B – either the minimum required by the democrats or the minimum required by the republicans.
Since we know that infrastructure spending (tax cuts multipliers range from 0.3 to 1.3 vs. infrastructure spending at about 1.61) It looks like we end up with as much tax cuts as republicans demand as price for passing the bill but no more.
Question: how could we make this a more interesting LP problem?