Q $=2002$P $$ PA $+0\mathrm{.}1$Y$2$

where P $=10,$ PA $=15,$ and Y $=100,$ find

a$)$ The Price Elasticity of Demand

$(4$ marks$)$

b$)$ The Cross$-$Price Elasticity of Demand

$(4$ marks$)$

c$)$ The Income Elasticity of Demand

$(4$ marks$)$

d$)$ Estimate the percentage change in demand if PA rises by $3\%.$

Is the alternative good substitutable or complementary?