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increase in demand and an increase in quantity demanded

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Can you please explain fully the difference between an increase in demand and an increase in quantity demanded, by giving an example of what would cause an increase in quantity demanded and please illustrate the effect of such an increase with a model of supply and demand?

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An increase in demand and an increase in quantity demanded is differentiated.

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First just remember the language "a change in demand" means the curve shifts and "a change in the quantity demanded" means movement along the curve. Our demand function basically an input output model. You plug in a Price and get out a Qty. If you plug in P=5 you get out Q=5 right. So, when we talk about a change in qty demanded we are talking about the effect from a change in price. If price changes from 6 to 2 then "quantity demanded" changes from 2 to 6. Given our demand function below which is
P = 10 - Q
A change in price ...

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