Answer :
Final answer:
The elasticity of demand measures the responsiveness of quantity demanded to price changes. For the demand curve P=2/Q, the elasticity is elastic (1.25) as the price falls from $5 to $4, and inelastic (0.89) as it falls from $9 to $8, which illustrates that elasticity varies at different points along the demand curve.
Explanation:
The elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. With the given demand curve equation P = 2/Q, we can calculate the elasticity as the price changes.
Firstly, the elasticity of demand as the price falls from $5 to $4 can be calculated using the midpoint formula for elasticity. We know the corresponding quantities at these prices by rearranging the demand equation to Q = 2/P. At P=$5, Q=0.4 and at P=$4, Q=0.5. The formula for elasticity (E) is:
E = ( (Q2 - Q1) / ((Q2 + Q1) / 2) ) / ( (P2 - P1) / ((P2 + P1) / 2) )
Plugging in the values, we find the elasticity from $5 to $4 is 1.25, which is considered elastic since it's greater than 1, indicating that the demand is sensitive to price changes in this range.
Similarly, to calculate the elasticity of demand as the price falls from $9 to $8, we find Q=0.222 and Q=0.25, respectively, and using the midpoint formula, the elasticity is 0.89, which is inelastic as it's less than 1.
Would we expect these answers to be the same? No. The elasticity of demand changes at different points on the demand curve because it depends on the starting and ending price and quantity. Therefore, even with a linear demand curve like the one given by the equation P = 2/Q, the elasticity of demand typically varies at different price levels.
