US President Joseph R. Biden issued an executive order in August 2021 aimed at making 50 percent of all new vehicles sold in the US by 2030 electric. You have been asked to work on a project analyzing the growing electric vehicle market. It is assumed that this is a market that is characterized by a relatively large number of buyers and sellers, each of whom is considered small enough that their actions alone could not influence the market price (i.e., all buyers and sellers are "price takers"). As part of your analysis, you conducted some surveys among potential electric vehicle consumers as well as representatives from the US automobile industry who may be expanding their production of electric vehicles in response to this executive order. In so doing, you arrive at the following equations characterizing the supply and demand schedules:

Q_S = 20 + 1/2P

Q_D = 130 - 4/3P

Where price is in thousands of USD, and quantity is in tens of thousands of vehicles.

1.Based on this information:

a.(10 pts) What is the competitive market equilibrium price and quantity in this market?

b.(10 pts) At this competitive market equilibrium, what is the consumer surplus?

c.(10 pts) At this competitive market equilibrium, what is the producer surplus?