Question: would a change in price shift the demand curve

Answer: No, There is movement along a demand curve when a change in price causes the quantity demanded to change. It is important to distinguish between movement along a demand curve, and a shift in a demand curve. Movements along a demand curve happen only when the price of the good changes. When a non-price determinant of demand changes the curve shifts. These ``other variables'' are part of the demand function. They are ``merely lumped into intercept term of a simple linear demand function.'' Thus a change in a non-price determinant of demand is reflected in a change in the x-intercept causing the curve to shift along the x axis.