Question

11. Review the algebra of demand elasticities on p. 69.
Then assume that the demand curve takes the following form: Q=100 - 2P.
a. Calculate the elasticities at P=1, 25, and 49.
b. Explain why elasticity is different from slope using the formula.

Answer 1

$Q = 100 - 2P$

$a) Elasticity \space of\space demand = (\frac{dQ }{ dP}) \times (\frac{P }{ Q})\\ (\frac{dQ }{ dP}) = -2\\ At P = 1, Qd = 98\\ Thus, \\Elasticity \space of\space demand = (-2) \times (\frac{1 }{ 98}) = -0.02\\ At P = 25, Qd = 50\\ Thus,\\ Elasticity \space of\space demand = (-2) \times (\frac{25 }{ 50}) = -1\\ At P = 49, Qd = 2\\ Thus, Elasticity \space of\space demand= (-2) \times ( \frac{49 }{ 2}) = -49$

b) In the above example, (dQ / dP) is the slope of the demand curve which remains constant for all points along the demand curve while elasticitu keeps on changing at all points or we can say that elasticity is calculated as (%change in quantity demanded / %change in price).