US GDP vs sub-$50/bbl oil How would we expect US GDP to be affected by oil prices dipping into the 30-50 USD/bbl range?  If you need to make additional assumptions to answer this question, please note these, but still answer the question.

I would expect that this would lower the cost of a major fundamental input and therefore increase the US GDP dramatically.  The US is both the largest producer and consumer of oil.  However, the US produces more oil these days from more expensive sources (shale) -- so perhaps this is a naive assumption?

This article suggests a slight increase -- but perhaps a drop larger than $10 would change this analysis?
Consider a basic case of linear supply and demand functions for oil.

Demand: $q_d = \alpha + \beta P + \gamma X + \epsilon$ Think of X as a demand shifter, so Z could move around if the Chinese economy goes into recession or changes growth speed, someone invents a cheap hybrid car, or Americans wake up one day and decide to drive less. 

Supply: $q_s = \eta + \zeta P + \psi Z + \phi$ Think of Z as a supply shifter, so if Z could move around if we have a shock to oil production like an expansion of fracking, a return of Libyan oil production to market, or the Saudis decide to reduce production for strategic reasons. 

Now in equilibrium supply equals demand ($q_d = q_s$):

$\alpha + \beta P + \gamma X + \epsilon = q_d = q_s = \eta + \zeta P + \psi Z + \phi$ 

Which we can solve for P:

$\Rightarrow P = \frac{(\alpha - \eta) \gamma X - \psi Z  + \epsilon - \phi}{\zeta - \beta}$ 

We can also solve for $\Delta P$:
$\Rightarrow \Delta P = \frac{ \gamma \Delta X - \psi \Delta Z  + \Delta (\epsilon - \phi)}{\zeta - \beta}$ 

When we observe that P has fallen, that may be because $\Delta Z&gt;0$ or because $\Delta X&lt;0$ 

But for the economy, we'd expect quite different results from $\Delta Z&gt;0$ and $\Delta X &lt;0$. A negative demand shock ($\Delta X &lt;0$) for oil probably reflects people being poorer and the economy heading into recession. A positive supply shock ($\Delta Z&gt;0$) probably reflects technological improvements that make oil extraction more cost effective. The former bodes poorly for the economy, the latter bodes well. 

So it isn't enough to say that it is an exogenous change in oil prices, we have to know more about why oil prices are changing. Economics blogger Scott Sumner warns about this particular issue, advising his students and readers to never reason from a price change. However, if we can take a stand on where the shock is coming from we can get some place. For example, if we assume it is entirely a oil supply shock then because we have estimates of the price elasticity of demand for oil, we can ask how much the supply curve would have had to move to drop prices as observed. From a supply curve shift and a sense of the demand function we could then calculate the increase in social surplus(measured in dollars) from the movement in the supply curve. Or you could treat it as a pure positive income shock to american consumers, negative to American oil producers, and use estimates of fiscal multipliers and marginal propensity to consume to estimate the effects.  I suspect you could do something similar with demand shocks.

As a thought experiment, I tried to think of this as a global supply shock. In my scenario oil prices are lower because production is up but there are no additional knock on effects on demand for exports or the US dollar. We also have to take a stand on if this is temporary or permanent. In general you'll get much bigger effects from permenant shocks. I'm going to assume the price shock lasts a single year. I'm not positive that's a coherent scenario but it gives me something to plug into my calculator. 

According to the US Energy Information Administration the US is a net importer of about 5,700,000 barrels of oil and oil products a day. If the price of oil falls from $\approx$\$102 to  $\approx$\$40 a barrel that's about \$127 billion in savings by the American public. That works out to about \$410 a person a year or 0.75 percent of GDP. What about the fiscal multiplier you ask? The marginal propensity to consume numbers are like 4% in representative agent models, which means that if everyone were the same and we have a multiplier of 2 we'd get something like 0.81 percent of GDP. Which suggests that the direct effect of oil price changes can't be very important. That is, if the distributional consequences are not important. 

The aggregate net export numbers obscure that some people are huge net exporters (the people in oil business) but the vast majority of us are modest net importers. Aggregate production was something like 3.4 billion barrels produced by about 600,000 workers call it an even two million to include support staff and that's a massive \$100,000 less per worker (noting that capital will bear much of the adjustment here, but still, that's huge). With 9.1B barrels (5.7B imports  + 3.4B domestic production) in domestic consumption , that works out to more generous /$1,800 a year in savings for the 308 million or so of us who don't work in the oil business. But if everyone is the same, none of that really matters, income losses buy the oil guys are offset but income gains by consumers except to the extent that we are net importers. Do we think that's true here?      

In general, we think that poorer people have a higher marginal propensity to consume than richer people, which generally means that shocks that affect poor people have stronger short-run economic effects than shocks of the same size affecting rich people. The people who work in the petroleum business are much higher paid than the average American (about 91k a year compared with say 43k for the typical worker and of course not everyone works). 

Imagine America had one guy (some trillionare) who owned all domestic oil production and consumed so little of his money that oil price shocks didn't influence his consumption (MPC = 0). Everyone else was a consumer of oil. In that world the short run aggregate effects would be more like that of giving everyone the \$1,800 wealth effect from cheaper oil. So something like 3-4% of income is a non-trivial shocks, and by some accounts lower income people have MPC as high as 0.5, so that could be say 1.5 - 2 percent of GDP directly.  You'd also get a knock on effect of whatever you think the fiscal multiplier is. Some people would say about 2. So that tells you 3-4 percent of GDP stimulus effect should be the upper bound. 

So in my thought experiment I'd say something between 0.75 - 4% of GDP effect from the oil price drop of \$62 a barrel from a pure supply effect.