Answer:
The price elasticity of demand for good X is 0.47 which is inelastic.
Explanation:
The demand function for good X is given by
Qdx = 15 - 0.5Px - 0.8Py
where Qdx is the quantity demanded of good X,
Px is the price of good X,
and Py is the price of good Y, which is related to good X
The price of good X is constant at $10.
The price of good Y decreases from $5 to $3.
When price of good Y is $5, the quantity demanded is
[tex]Qdx = 15 - 0.5\ \times\ 10\ -\ 0.8\ \times\ 5[/tex]
[tex]Qdx = 15 - 5 - 4[/tex]
Qdx = 6
When price of good Y is $3, the quantity demanded is
[tex]Qdx = 15 - 0.5\ \times\ 10\ -\ 0.8\ \times\ 3[/tex]
[tex]Qdx = 15 - 5 - 2.4[/tex]
Qdx = 7.6
Midpoint elasticity of demand
= [tex]\frac{\frac{Q2 - Q1}{\frac{Q2 + Q1}{2} } }{\frac{P2 - P1}{\frac{P2 + P1}{2} } }[/tex]
= [tex]\frac{\frac{7.6 - 6}{\frac{7.6 + 6}{2} } }{\frac{3 - 5}{\frac{3 + 5}{2} } }[/tex]
= [tex]\frac{0.235}{-0.5}[/tex]
= -0.47
Since the price elasticity of demand is less than 1 we can say that the demand is inelastic.
