Question

In a small town in France, the demand curve for wine is given by P_D = 124 - 2Q_D and the supply curve for wine is given by P_S = 4 + 2Q_S. Suppose a price ceiling is imposed on wine at a price of $50. This will cause a _____________(shortage/surplus) of ______________ bottles of wine.

Answer 1

We know that in a demand and supply model, the equilibrium price and quantity are established at the point where the demand curve intersects the supply curve. At this intersection, we get the equilibrium price and quantity.

We can find the equilibrium price and quantity by equating the demand and supply equations:

P = 124-2Q = P = 4+2Q

124-2Q = 4+ 2Q

where P is the equilibrium price and Q is the equilibrium quantity.

124-4 = 2Q+2Q

120 = 4Q

Q = 30

We will put this value in any of the equation:

P = 4 + 2 (30)

P = 4 + 60 = $64

We can see that at the equilibrium pirce of $64, the quantity demanded = quanitty supplied = 30 units.

Now, when the price ceiling is imposed, the price decrease and becomes less than the equilibrium price of $64.

At the new price of $50, the quantity supplied is:

P = 4+2Q (supply curve)

50 = 4 + 2Q

Q = 23 units

At the new price of $50, the quantity demanded is:

P = 124 - 2Q (demand curve)

50 = 124 - 2Q

2Q = 124-50

Q = 37 units

Here we can see that, at the new price of $50, the quantity demanded is 37 units and the quantity supplied is 23 units. Which shows that there is excess demand or shortage of wine. There is a shortage of (37-23 = 14), 14 units.