Consider a market with the following supply and demand functions:

Demand: = 100 2

Supply: = 2 - 20

a) Determine the equilibrium quantity and price in this market.

b) Calculate the consumer surplus by integrating the demand function from the equilibrium quantity to the quantity demanded at a price of zero.

c) Calculate the producer surplus by integrating the supply function from the equilibrium quantity to the quantity supplied at a price of zero.

Show all the necessary steps in your calculations and provide the final values for consumer surplus, producer surplus and total surplus.