Question

The supply and demand functions are given as follows:

                               Qx = 2/3P + 150   and Qx= -1/3P + 450

If the government imposes a price ceiling of $120, the resulting excess demand(or shortage) will be_____________?

Answer 1

If the market is unregulated, the market equilibrium will emerge at the intersection of demand and supply curves, that is , where the quantity demanded of the good equals quantity supplied.

But with the price ceiling, there is a maximum limit that has been set for the price above which the goods cannot be traded.

If the goods are traded at ceiling price, P= 120

Then quantity demanded of the good will be:

Qx= -1/3P+450 ( We have chosen this function as the demand function because the slope of the function/equation is negative with respect to Price and we know that price and quantity demanded have inverse relationship according to law of demand).

Thus, Quantity demanded= 450- 1/3*120=450-40= 410 units

Similarly, the quantity supplied at the ceiling price can be calculated as -

Qx= 150+ 2/3P ( According to law of supply, price and quantity supplied have positive relationship. As price rises, quantity supplied rises. The positive slope indicate this)

Thus, quantity supplied= 150+2/3*120=150+80=230 units.

Hence, we have found that at ceiling price P=120, quantity demanded is 410 units whereas quantity supplied is only 230 units. Thus, there is an excess demand (because demand for the good is more than supply, the situation is that of excess demand) for the good in market equal to (410-230) 180 units.