The demand and supply curves for titanium are given by
P = 100 - Q/2
and
P = 2Q
respectively.
The government, fearful that a titanium shortage could jeopardize national security, imposes a tax of $20/oz. on the retail price of this rare metal. It collects the tax from titanium sellers. What is the equilibrium quantity in the market? What is the price paid by the buyer? The price received by the seller net of the tax?
I do not understand the equations, how to manipulate then, and how I end with the tax. Can someone please show the work?
The equilibrium quantity in the market is determined by the intersection of the demand and supply curves. The demand curve is given by P = 100 - Q/2 and the supply curve is given by P = 2Q. Setting the two equations equal to each other and solving for Q yields an equilibrium quantity of Q = 80 oz.
The price paid by the buyer is the equilibrium price, which is determined by the demand curve. Plugging the equilibrium quantity of 80 oz. into the demand curve yields a price of P = 100 - 80/2 = $60/oz.
The price received by the seller net of the tax is the equilibrium price minus the tax. The tax is $20/oz., so the price received by the seller net of the tax is $60/oz. - $20/oz. = $40/oz.
I got Q = 40. Where did you get Q = 80?
100 - Q/2 = 2Q
200 - Q = 4Q
200 = 5Q
Q = 40