Question

FOR EACH OF THE FOLLOWING CASES, CALCUALTE THE POINT PRICE ELASTICITY OF DEMAND, AND STATE WHETHER DEMAND IS ELASTIC, INELASTIC, OR UNIT ELASTIC. THE DEMAND CURVE IS GIVEN BY

QD=5,000-40PX

A. THE PRICE OF THE PRODUCT IS $40

B. THE PRICE OF THE PRODUCT IS $ 80.

C. THE PRICE OF THE PRODUCT IS $20.

Answer 1

In order to calculate point elasticity of demand, first find the derivative of the demand function QD=5,000-40PX with respect to PX. The derivative is denoted by

Therefore,

Now, use the following formula for calculating elasticity (e):

a. When PX = $40,

QX= 5000 - 40*40 = 5000 - 1600 = 3400 and,

Therefore, demand is relatively inelastic because e= -0.47 [0 > |e| > 1].

b. When PX = $80,

QX= 5000 - 40*80 = 5000 - 3200 = 1800 and,

Therefore, demand is relatively elastic because e= -1.77 [1 > |e| > infinity].

c. When PX = $20,

QX= 5000 - 40*20 = 5000 - 800 = 4200 and,

Therefore, demand is relatively inelastic because e= -0.2 [0 > |e| > 1].