An equilibrium supply and demand question via implicit differentiation
I don't entirely remember how these concepts go; the information is muddled by a few other topics. The question is listed below, word for word.
The demand and supply for a good are given by the linear functions
where is the quantity demanded, is the quantity supplied, is the price, and is the aggregate consumers' income, which is exogenous. Denote the equilibrium quantity by and the equilibrium price by .
(i) Find the effect of a change in income on equilibrium price and quantity, that is, and , by the method of implicit differentiation.
(ii) Check the result by first solving for the equilibrium price and quantity explicitly and then finding and .
(iii) Repeat (i) and (ii) for the following demand and supply functions
I'm doing my best to try and remember how this all works, but some help on the subject would be appreciated.