4*A)In a competitive market for a perfectly private good, Q, withno external effectsthe demand is represented by P^D= 520 - 0.3Q^D, and supply represented by P^S= 40 + 0.3Q^S.Determine the competitive market equilibrium price and quantity.

B)Suppose the government imposes a 20 percent tax on the producers of the product. Determine the new equilibrium price and quantity for consumers and determine how the tax is shared between the producer and consumer.

C)Explain how social welfare in the market is affected and calculate thedead weight lossand thenewconsumer surplus.

D)Now, there is another product, X, with the same demand P^D= 520 - 0.3X^Dand supply P^S= 40 + 0.3X^S,but this product causes an external cost(marginal external cost) MEC = 0.05Q.Determine the socially optimal quantity, X*, and optimal per unit tax, t, to achieve the socially optimal quantity.

(must show calculations)