NOTE: This is a return question. The previous given was vague. I need working examples for parts $($ii$),($iii$)$ and $($iv$)$ of Question $($a$)$ only.

Consider the following demand system for the meat sector.

Table $1.$ Elasticities and budget shares for the meat demand system

where the index meats, $d=$ dairy, $c=$ cereal$\}$; In Qi and In Pi are natural logs of

quantity per capita and price of commodity $i,$ respectively; In $Y$ is natural log of per capita

income; and wi is budget share for commodity $i.$

a$.$ Give the formula for each of the following properties and show whether or

not it holds for the above system

i$.$ Engel aggregation

ii$.$ Cournot aggregation

iii. Symmetry for meats and cereal

iv$.$ Homogeneity

b$.$ Specify the number of equations that you need to write in order to check

each of the properties in a$.$