Question

For the demand curve Q=50−P, what is the own-price elasticity of demand when P=16 2/3 (that...

For the demand curve Q=50−P, what is the own-price elasticity of demand when P=16 2/3 (that is, 50/3)? Is demand elastic, inelastic, or unit elastic at that point?

a) -0.5, inelastic

b) -1, unit elastic

c) -0.5, elastic

d) 33.3, inelastic

e) 33.3, elastic

Q = 50 - P

P = 50 / 3

Elasticity of demand = % change in quantity demanded / % change in price

= (dQ / dP) x (P / Q)

dQ/dP is the differentiation of the quantity demanded function with respect to price. So, dQ/dP = -1

P = 50 / 3

Q = 50 - P = 50 - 50/3 = (150 - 50) / 3 = 100/3

Elasticity of demand = (dQ / dP) x (P / Q)

= -1 x [(50 / 3) (100 / 3)]

= -1 x 50/3 x 3/100

= -1/2 = -0.5 is the answer.

Since. the value of elasticity of demand in absolute terms is less than 1, the demand for the product is inelastic which means that for a given change in price, quantity demanded changes by a less amount.

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