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When plotting a demand curve for a good, lets say carrots with price on the y-axis and quantity demanded on the x-axis. A shift any determinant of demand other than price of carrots results in a shift of the curve. Let us say that determinant in question is income. National income increases and as a result demand for carrots increases (as carrots are a normal good). The shift for an increased demand is referred to as a 'shift to right'. However is this not a vertical shift up. A vertical shift up of the demand curve means that for the same price people will demand more and for the same quantity people will pay a higher price. Is 'a vertical shift up' and 'a shift to the right' just different ways of describing the same movement or does a 'a shift to the right' achieve something different that I have not understood.

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Consider a curve with a negative slope (such as the demand function for a normal good). If you draw a second curve with a negative slope that does not intersect this one then it can either be in the "right-up" or the "left-down" direction from the first. When they talk about shifts they sometimes just mean this general direction where the new curve will be. Sometimes (as with taxes) there really is a shift. Let quantity be the vertical axis. If $D(p) = m - \frac{1}{p}$ then an increase in income will shift the demand curve up. But if $D(p) = \frac{m}{p}$ then an increase in income causes something that is not really a shift but a rescaling of the curve. You might still call this a shift up, as by moving up from the original demand curve you will reach the new one.

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