Suppose the demand function is p $=1000\mathrm{.}01$x and the supply function is p $=10+0\mathrm{.}02$x$.$

$4\mathrm{.}1.$ Find the equilibrium price and quantity. Plot the supply and demand function.

$4\mathrm{.}2.$ Find consumer surplus, producer surplus and total welfare.

$4\mathrm{.}3.$ Suppose the government imposes a tax of $30$ per unit sold on the seller. Find again the equilibrium

price and quantity, consumer surplus, producer surplus, Total welfare and the tax income of the

government. Explain who is paying the burden of the tax