Final answer:
The initial equilibrium price and quantity are $600 and 600 units, respectively. The imposition of rent control at $300 increases excess demand, and if demand grows further, the government would need to adjust the rent control level to maintain the same shortage level.
Step-by-step explanation:
When assessing how government-imposed rent controls impact the housing market, several economic concepts come into play. Initially, we need to find the equilibrium price and quantity for the market without rent control. Using the demand equation P = 1200 - Q and the supply equation P = Q, we can set them equal to each other to find the equilibrium: 1200 - Q = Q. Solving for Q gives us 600 units, and by plugging this back into either equation, we find the equilibrium price is $600.
With the introduction of a new demand curve, P = 1400 - Q, and the imposition of rent control at $300, the excess demand is affected. Rent control creates a maximum price that is lower than the equilibrium price, resulting in a higher quantity demanded than supplied. This exacerbates the shortage.
If the demand grows and the government wishes to maintain the same level of excess demand as before the increase, they would need to adjust the rent control price accordingly. We would have to calculate the new excess demand at the original control price and determine the new price control that would equate to this level of excess demand.