Lecture 2
GRAPHS: A REVIEW

  1. Slope of a line

    • What does the sign (positive or negative) mean?
    • What does the magnitude mean?

  2. Slope of a curve

    • Slope of a curve changes from point to point
    • Slope of a curve at a point is given by the slope of the tangent at that point
    • The steeper the curve, greater is the magnitude of the slope

  3. Intercepts

    • Horizontal and vertical intercepts
    • What do the intercepts represent?

  4. Parameter

    • Variable that is kept fixed when drawing a graph with two other variables
    • When the parameter value changes, the entire curve (or line) shifts

  5. Shift of the curve vs Movement along a curve

    • Shift caused by a change in parameter value
    • Movement caused by a change in one of the variables on the axes of the graph

Example

Consider the equation, P + 2Q = 30, where P is the price of a gallon of milk, in $, and Q is the quantity demanded of milk, in gallons.

  1. Sketch the relationship between P and Q, with price on the vertical axis.

  2. Obtain the intercepts.

    Horizontal intercept = ______
    Vertical intercept = ______

  3. What is the slope of the curve?

    Slope = ______

    Note: Slope = -1(Vert. intercept / Horiz. intercept)

  4. What does the slope tell us?

    As P increases by 2, Q will fall by 1, ceteris paribus.

  5. If price decreases by $3, by how much does quantity demanded change?

    Quantity demanded will rise by 1.5 gallons.

    Note: This is a movement along the curve.

  6. At a price of $5/gallon, what is the quantity demanded?

    12.5 gallons.
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