A market equilibrium is the price and the quantity, denoted as the pair (Q*, P*), of a commodity bought or sold at price P*. The following mathematical note provides an introduction of how a market equilibrium (Q*, P*) is derived.
The market equilibrium is found by using the market demand (buyers' behaviour), the market supply (sellers' behaviour), and the negotiating process (to find the agreed upon price and quantity, namely P* and Q*, on which to transact). The market equilibrium is identified by the condition reached at the end of the negotiating process that at the price they negotiated, P*, the quantity of the commodity that buyers are willing to buy, denoted as QD, and the quantity sellers are willing to sell, denoted as Qs, matches exactly.
The equation describing the downward sloping demand, in which Qd represents the quantity demanded by buyers and P the price, is
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