Whenever there is a change in one of the factors of either supply or demand, market equilibrium will be affected.
Shift in Demand
When there is a change of one of the factors of demand- like the price of the product and related goods, consumer preferences, or income- there is a corresponding change in the demand curve. For instance, if someone's income grows, then his demand for goods will increase, shifting his demand curve to the right. This will lead to a higher quantity being consumed at a higher price, ceteris paribus. Conversely, there can be a negative effect that shifts the supply curve to the left where a lower quantity is consumed at a lower price, ceteris paribus. This can occur when the price of substitutes falls or consumers begin to lose their taste for the product.
Shift in Supply
When there is a change of one of the factors of supply- like changes in the prices of production inputs like labor or capital; a change in production technology and its associated productivity change; or the amount of competition in a specific product market- there is a corresponding change in the supply curve. For example, if worker productivity improves due to some human capital or technology investment, then the costs of production decrease. This exerts a positive effect on the supply curve shifting it right, where the new market equilibrium is at a higher quantity and a lower price, holding everything else constant. There can also be a negative shift that moves the supply curve to the left, with the resulting market clearing price being higher and quantity lower, ceteris paribus. This type of change can occur when the price of an input like labor or raw material jumps.
Shifts in Demand and Supply
Realistically speaking, ceteris paribus doesn't hold in the real world marketplace as many things are happening at once that either have complimentary or contrary influences upon the market equilibrium. You can't gauge what the new market equilibrium might be as you are not holding everything constant, but two things are being changed simultaneously. To find out what the new market equilibrium is you need detailed information on the magnitude of the supply and demand factor changes and the corresponding shifts in the graph, along with knowledge of the shapes of the curves.
Take the market for apples for instance. If both supply and demand increase (on the graph this would be represented by the supply and demand curves both shifting to the right)- if orchard productivity rises while a new medical reports touts the discovery of the newly added health benefits of apples- then the quantity will definitely go up but the new price is indefinite. It could go up if the increase in demand is significant enough, or it could go down if it's not. Similarly, a certain quantity reduction but an uncertain price will pertain when the both demand and supply curves shift to the left. This could happen if the price of apple substitutes like plums drops dramatically, while farm labor becomes much more expensive.
There will be certainty about the price, but not the quantity when the supply and demand curves move in opposite directions. For instance, another medical report could come out detailing the unsanitary apple harvesting conditions, shifting demand curve to the left. Simultaneously, genetic engineers have produced an apple that doesn't require as much costly care as before, shifting the supply curve to the right. Price will certainly go down, but the quantity consumed will demand on how relatively large the shifts of each curve are. Similarly, it could be certain that price would go up, but whether quantity consumed would go up or down is uncertain. This could happen if the demand curve shifts to the right while the supply curve shifts to the left- say if everyone's income increases, thereby increasing their consumption of apples and new government regulations curtail farmer's dependence on cheap illegal alien labor. The price of apples would rise, but it would depend on magnitude of the changes in both the supply and demand curves.
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