Question

Suppose the demand curve for beer is given by QD = 50 − 10P and the supply curve for beer is given by QS= −10 +20P. Now, the government imposes a price ceiling of $1 in the market for beer. As a result, the producer surplus decreases. Now, a part of the initial producer surplus is part of the deadweight loss and a part of it is transferred to consumers.

a) What is the amount of producer surplus that is transferred to consumer surplus after the price ceiling is imposed?

b) After the price ceiling is imposed, the consumer surplus increases or decreases by how much?

c)What is the deadweight loss (or decrease in the total surplus) after the price ceiling is imposed?

Answer 1

Calculation of equilibrium price and quantity:

Equating demand and supply functions:

50 - 10P = -10 + 20P

50 + 10 = 20P + 10P

60 = 30P So, P = 2 Plugging in the value of P in demand (or supply) function to find Q:

Q = 50 - 10*2 = 30 Q = 30

a) producer surplus that is transferred to consumer surplus after the price ceiling is imposed = $10

calculation: We must find the reservation price of producer (the value of P when Q = 0) in order to find the proucer surplus:

0 = -10 + 20*P So, P = 10/ 20 = 0.50

(i) At equilibrium, producer surplus = ½*(equilibrium price - reservation price) * quantity

PS = ½*1.5*30 = 22.5

(ii) after price ceiling, quantity changes according to supply function with P=1.

Q = -10+20*1 = 10

PS1 = ½*(1 - 0.50) * 10 = 2.5

So, producer surplus that is transferred to consumer surplus = (new quantity * change in price) = 10 * 1 = 10

b) Consumer surplus (CS) decreases by $10

(i)Before price ceiling,

CS = ½*(highest willingness to pay - equilibrium price) * quantity -highest willingness to pay is when Q = 0 in demand function.

CS = ½*(5-2)*30 = 45

(ii) CS after price ceiling:

It will be like the area of a trapezium. When price = 1, the quantity supplied = 10. So. Q=10 vertical line will touch the demand curve corresponding to 4 on y-axis.

CS1 = (½*(highest willingnes to pay - 4) * new quantity) + (4 - new price ) * new quantity

= (½*1*10) + ( 3*10) =5+30 =35

Consumer surplus changes by 35 - 45 =-10 (decreases)

c) Deadweight loss = $30

DWL = ½*(Y-intercept of demand curve - neww price) * change in quantity

= ½*3*20 = 30

The graph with actual dimensions of demand and supply: