Suppose, as in this question, the market we are interested in can be expressed by the demand equation QD = 40 - 2P and the supply equation QS = 5 + 3P? The question asks "what will happen if the market price is initially $5?"
As we know, market forces move markets toward equilibrium price and quantity; meaning, if we can determine what the eventual equilibrium for this market will be, we will know in which direction it will move from an initial price of $5.
In order to determine the equilibrium price and quantity, we simply set supply and demand equal and find the price, P, that solves that equation.
40 - 2P = 5 + 3P
35 = 5P
P* = 7
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35 = 5P
P* = 7Therefore, the equilibrium price will eventually be $7. This means that the price will rise from $5. As the price rises, the quantity demanded must be falling.