the demand function Q $=400-2$P $-3$PA $+0\mathrm{.}02$Y where P $=20,$ Pa $=30$ and Y $=4000,$a$)$ Find the price elasticity of demand $(4$ pts$.)$b$)$ Is the demand elastic or inelastic? Why? $(2$ pts$.)$c$)$ Find the cross$-$price elasticity of demand $(4$ pts$.)$d$)$ Is it a substitute good or complement good? Why? $(2$ pts$.)$e$)$ Find the income elasticity of demand $(4$ pts$.))$ Is the good inferior or superior? Why? $(2$ pts$.)8)$ If income rises by $5\%,$ calculate the corresponding percentage change in demand. $(2$ pts$.)$