.The demand for roses is explained using the following model: E(Demand for roses)= 0+ 1 logPrice of roses+ 2log(Price of roses)2+ 3 logPrice of carnations+

.The demand for roses is explained using the following model:

E(Demand for roses)= β0+ β1 logPrice of roses+ β2log⁡(Price of roses)2+ β3 logPrice of carnations+ β4 log(Family income)

1. What could be the purpose of including a quadratic term for price of roses in the above model?
2. What are the expected signs of β1 and β2 if you expect the demand for roses to decline with an increase in their price at an increasing rate?

Show that β3 and β4measure the cross price elasticity of demand and income elasticity of demand respectively.