Answer to Question #228590 in Microeconomics for Yyyy

Question

a demand function for a good is q=56.6-0.25p-0.4sp+0.6n
Where q is quantity demand per week, p is the price per unit m is the average weekly income, ps is the price of a competing good and n is the population in millions. Given values are p=65, m=350, ps=60 and n= 24
1. Calculate the price elasticity of demand
2. Find out what would happen to(a) if n rose to 26
3.explain why this is inferior good
4.

Answer 1

The demand function for a good:

q=56.6−0.25p−0.4sp+0.6n

q=56.6-0.25p-0.4sp+0.6n

p=65,

m=350,

ps=60

and n= 24.

1. Substituting values in demand function, we get:

q = 56.6−0.25p−0.4ps+0.6n  

$q= 56.6−0.25\times65− 0.4\times60+0.6\times24$

q=30.75

The price elasticity of demand:

$E=\frac{dQ}{dP}×\frac{P}{Q}\\=−0.25×\frac{65}{30.75}\\=−0.528$

Hence, The elasticity is -0.528 which depicts that the demand is inelastic as the absolute elasticity value is below 1.

2. If n rose to 26,

q = 56.6−0.25p−0.4ps+0.6n  

$q= 56.6−0.25\times65− 0.4\times60+0.6\times26$

q=72.2−16.25−24

q=31.95

The price elasticity of demand:

$E=\frac{dQ}{dP}×\frac{P}{Q}\\=−0.25×\frac{65}{31.95}\\=−0.509$

Hence, The elasticity is -0.509 which depicts that the demand is inelastic as the absolute elasticity value is below 1. The demand in turn becomes more inelastic.

3. In the demand function, the coefficient of income is negative which indicates that an increase in income would lead to a decrease in the demand for the good. Thus, the good is considered to be inferior good, and the demand for normal good increases with an increase in income.