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

Step-by-step 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

$Q=100-2\times 10+12+0.1\times 1000\\\\Q=100-20+12+100\\\\Q=200-8\\\\Q=192$

Price elasticity of demand would be

$\dfrac{dQ}{dP}\times \dfrac{P}{Q}\\\\=-2\times \dfrac{10}{192}\\\\=-0.104167$

Hence, $e_D=-0.104167$

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

So, Income elasticity of demand would be

$\dfrac{dQ}{dY}\times \dfrac{Y}{Q}\\\\=0.1\times \dfrac{1000}{1}\92\\\=0.521$

Hence, income elasticity = 0.521