Question

Suppose that demand for a good depends on its price (P), the price of alternative good (PA), and the income of consumers (Y). Given the demand function Q = 100-2P +PA+0.1 Y

Find the price elasticity of demand where P=10, PA= 12 and Y=1000
b. Find the income elasticity of demand where P=10, PA= 12 and Y=1000

Answer 1

Answer: a)
`e_D=-0.104167`

b) income elasticity = 0.521

Explanation:

Since we have given that

Demand function is stated as

`Q=100-2P+P_A+0.1Y`

Here, P stands for price.

`P_A` stands for price of alternative good

Y stands for income of consumers

1) we have given that

P=10, PA= 12 and Y=1000

So, Q becomes

`Q=100-2* 10+12+0.1* 1000\\\\Q=100-20+12+100\\\\Q=200-8\\\\Q=192`

Price elasticity of demand would be

`(dQ)/(dP)* (P)/(Q)\\\\=-2* (10)/(192)\\\\=-0.104167`

Hence,
`e_D=-0.104167`

2) P=10, PA= 12 and Y=1000

So, Income elasticity of demand would be

`(dQ)/(dY)* (Y)/(Q)\\\\=0.1* (1000)/(1)\92\\\=0.521`

Hence, income elasticity = 0.521