In case of market surplus, some producers won't be able to sell all their goods. This will induce them to lower their price to make their product more appealing. In order to stay competitive many firms will lower their prices thus lowering the market price for the product. In response to the lower price, consumers will increase their quantity demanded, moving the market toward an equilibrium price and quantity. In this situation, excess supply has exerted downward pressure on the price of the product.
In case of market shortage, consumers won't be able to buy as much of a good as they would like. In response to the demand of the consumers, producers will raise both the price of their product and the quantity they are willing to supply. The increase in price will be too much for some consumers and they will no longer demand the product. Meanwhile the increased quantity of available product will satisfy other consumers. Eventually equilibrium will be reached.
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