Question

1) Given the following demand function Q=8.5-p+0.1y

a) Derive a formular for the price elasticity of demand and income elasticity of demand.

b) find the elasticity if p=6 and y=1000

c) what will happen to price elasticity of demand if income varies.

d) what will happen to income elasticity of demand if income varies.

e) derive the total revenue function. show that the relationship    between price and revenue depends on elasticity (Assume y = 0).

Answer 1

Q = 8.5 - p + 0.1y

a) Price elasticity of demand = (dQ / dp) x (p / Q)

= -1 x [p / (8.5 - p + 0.1y)]

= -p / (8.5 - p + 0.1y) is the answer.

Income elasticity of demand = (dQ / dy) x (y / Q)

= 0.1 x [y / (8.5 - p + 0.1y)]

= 0.1y /  (8.5 - p + 0.1y) is the answer.

b) Price elasticity of demand = -p / (8.5 - p + 0.1y)

= -6 / [8.5 - 6 + 0.1(1000)]

= -6 / 102.5 = -0.0585 is the answer.

Income elasticity of demand = 0.1y /  (8.5 - p + 0.1y)

= 0.1(1000) / [8.5 - 6 + 0.1(1000)]

= 100 / 102.5 = 0.975 is the answer.

c) As it can be seen from the formula from price elasticity of demand, if income increases, the absolute value of price elasticity of demand will decrease and if income decreases, the absolute value of price elasticity of demand will increase. But if seen with a negative sign then, if income increases, the value of price elasticity of demand will also increase and if income decreases the value of price elasticity of demand will also decrease.

d) From the formula for income elasticity of demand, it is seen that if income increases, the value of income elasticity of demand will decrease and if income decreases, the value of income elasticity of demand will increase.