Consider the following supply and demand functions of a certain product,

Qd=1000-P

Qs=-1000+2p

where price (P) is in dollars and quantity (Q) is in units.

(i) Find the inverse demand and supply functions.

(ii) Algebraically, find the equilibrium price and quantity.

(iii) Now, suppose an indirect sales tax of $50 per item is imposed on the product by the government. Algebraically, find the new equilibrium price and quantity

(iv) Calculate the total sales tax revenue

(v) Sketch "pre-tax" and "post-tax" (inverse) demand and supply functions

on the same graph. Show the equilibrium point with and without tax. (a clear sketch with all labels shown)