What happens to consumer and producer surplus after a rent control is established? Do they increase or decrease? What happens to total welfare? Be sure to include the concept of deadweight loss in your explanation.

To answer this question, we must start by defining the key concepts:
Consumer surplus exists when there is a difference between the highest price someone is willing to pay and the market equilibrium price for that item.
Producer surplus is the same concept, but for producers. It is the gap between what a producer wants to sell an item for and the market equilibrium price for that item.
Market equilibrium is the price that finds the balance between supply and demand. At the market equilibrium price, the price point consumers are willing to spend and the quantity of items they want to buy equals out to the amount that has been produced and the price at which producers are willing to sell that item.
Total welfare is found by adding the consumer surplus and producer surplus to determine the general benefit to society.
Deadweight loss describes the surplus that exists when supply does not meet demand.
In the case of rent control, when supply meets demand, there will be an equilibrium price in the rental market. In some cases, governments may opt to enforce rent control to allow lower-income renters to continue to afford to live in their neighborhoods. The lowered rent increases consumer demand for rental property, as renting becomes a more economical choice than buying a home. Conversely, renting out units becomes less attractive to landlords, who may opt to live in the units themselves or pull the units off the market. The supply of rental units decreases while the demand has increased.
Producer surplus decreases when rent control is at play. Landlords are still paying the same costs for mortgages and other services but are not making as much money as they could be without rent control.
The consumer surplus increases in an instance of rent control. That does not mean, however, that renters are better off. Since the housing supply often decreases while demand increases, landlords are able to be picky about the tenants they allow to live in their units. Lower-income tenants are often less desirable to landlords and therefore may be unable to acquire housing.
The total welfare at play is decreased in a case of rent control due to the deadweight loss of the increase in consumer surplus, which is not balanced by the decrease in producer surplus. The longer this disparity continues, the greater the deadweight loss, ultimately resulting in a greater decrease in total welfare.