What happens to price if both demand and supply increase at the same time?

This is a favorite question of teachers because the answer is "it depends".  How can an answer depend?  We have been taught all our lives that in school (not necessarily life) there is an answer to every question.  However in economics the answer often depends on the context of the question, and when both supply and demand shift right, or increase, then the answer of what happens to price is unknown without more information.  To begin this discussion lets look at the market for hamburgers.  We will then shift both supply and demand to the right (increase them) for arbitrary reasons (maybe an increase in preference for hamburger, or it cures cancer or something, for the demand side and a decrease in input costs for the supply side).

However, before you look at the graph, you must consider how far we are going to shift each of the curves.  To give you an example, in the graph below I have shifted the demand curve right (once), but I have shifted the supply curve right three different times.  The reason I have done this is to show you that depending on the size (magnitude) of the shift, the resulting equilibrium price can be at three different levels.
First consider S1 (the smallest shift), this results in an equilibrium price that is greater then the original equilibrium price (Pu>P*).  If we shift out supply a little more to S2, then our equilibrium price will not change, it will still be P* (this happens if both supply and demand shift out the same amount).  Finally, the S3 curve shows us the largest shift, which results in an equilibrium price lower than the original (Pd<P*).  So the answer is "it depends" when both supply and demand increase and you want to know what happens to price.  In order to know for sure, we would need to know the magnitudes of both shifts.

What we do know is that quantity demanded will go up, and you can confirm this by looking at the three red equilibrium points, each of them are located to the right of the original equilibrium point, and quantity.

Why would curves shift out different amounts?  One example would be a $1 decrease in the price of inputs vs. a $10 decrease in the price of inputs.  You can conclude immediately that the $10 decrease would result in a much larger shift for the supply curve.  But keep in mind that this phenomena is not restricted to the supply curve, the demand curve could also shift by different amounts to come up with this ambiguous result.

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