Consider the following supply and demand functions of a certain product, where price (P) is in dollars and quantity (Q) is in units.

Q(d)=1000-P Q(s)=-1000+2P

 (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)