Question

Draw a downward sloping straight line demand curve touching both the axes. Mark the price elasticity at different points on this demand curve.

Draw a downward sloping straight line demand curve touching both the axes. Mark the price elasticity of demand at different points.

Answer 1

1. Elasticity on a Straight Line Demand Curve: Let's say we wish to assess the price elasticity of demand at point R on a demand curve AB that is either linear or straight. The figure makes it clear that the demand curve's lower line segment, or the part that lies below point R, is denoted by RB, while its upper line segment, or the part that lies above point R, is denoted by RA.
   
   

   ∴ e_P at point R = `"Lower line segment"/"Upper line segment"`

   = `"RB"/"RA"`

   Here, e_P > 1 because RB > RA.

   Similarly, if we want to measure elasticity at any other point on the demand curve, say at K,

   e_P at K = `"KB"/"KA"`

    Here, e_P < 1 (since KB < KA.)

2. Price elasticity of demand at different points on a straight line demand curve: We can measure elasticity at various locations on a straight line demand curve, beginning at the Y-axis and ending at the X-axis, using the point elasticity method (or formula) described above. The price elasticity of demand at various locations on the straight line demand curve can be readily explained. Fig. provides an illustration of this.
   
   

   The demand curve in Figure AB is a straight line, with A representing its Y intercept, B its X intercept, and D its midpoint. Elasticity can be represented at different locations on the linear demand curve using the point method, which measures elasticity as the ratio of line segments above and below the point..

   (1) At point A (where the demand curve touches the vertical axis)

   e_p at A = `"Line segment below A"/"Line segment above A"`

   = `"AB"/"O"`

   = infinity (∞)

   (2) At any point above the mid-point but below A, say at E

   e_p at E = `"BE"/"EA">1`

   because the lower segment is greater than the upper segment, i.e., BE > EA

   (3) At the mid-point D

   e_p at D = `"BD"/"DA"=1`

   because the lower segment equals the upper segment, i.e., BD = DA

   (4) At any point below the mid-point but above B, say at C

   e_p at C = `"BC"/"CA"<1`

   because the lower segment is smaller than the upper segment, i.e., BC < CA.

   (5) At point B (where the demand curve touches the horizontal axis)

   e_p at B = `0/"AB"` = 0

Price elasticity of demand, then, steadily changes from infinity at the Y-intercept to zero at the X-intercept as we move downward from left to right on a straight line demand curve. It is greater than unity (elastic demand) at any point above the mid-point, equal to unitary at the mid-midpointd less than unity (inelastic demand) at any point below the mid-point. This leads us to the general conclusion that a demand curve with a straight line is less elastic near its right end and more elastic toward its left.