Question

1. Suppose that the market supply and demand in a given industry are given by the expressions QS = 20P - 200 and QD = 1,000 - 40P.

a) The government decides to impose a price control defined by P* = 22.5. Should this be understood as a price floor or a price ceiling? Explain.

b) Determine the quantity transacted in the market under the policy described in the previous question. What happens to the consumer surplus, producer surplus and total surplus as a result of this policy? Represent their changes on a graph.

c) Determine the price elasticity of demand as the economy moves from its original equilibrium to the new regulated outcome. What is the economic meaning of the value you obtained?

d) Suppose now that a group of consumers lobbies the government to impose a price ceiling. The government agrees on the condition that total surplus does not change relative to the initial outcome described in parts a and b. Determine the price the government will adopt and represent the total surplus on a graph.

Answer 1

A)The equilibrium is at where Qd=Qs

20p-200=1000-40p

60p=1200

P=1200/60=20

So restricted price above equilibrium price ,so p*=22.5 is price floor.

B) At price floor ,the quantity sold is equal the quantity demanded at that price floor.

Qd=1000-40*22.5=1000-900=1000

So price floor=22.5 ,100 units will be traded in the market .

The EQUILIBRIUM CONSUMER surplus was =area (A+B+C)

And price floor consumer surplus=A

So CONSUMER surplus Decreases.

The EQUILIBRIUM producer surplus=E+D

And price floor producer surplus=E+B

AnD B>D

So producer surplus Increases.

Total surplus ( equilibrium)=A+B+C+D+E

Price floor total surplus=A+B+E

So total surplus Decreases.

C)Price elasticity of demand=(∆Qd/∆p)*p/Q

Elasticity of demand=(-100/2.2)*20/200

Elasticity of demand=-10/2.2=-4.54

It tells that demand is more elastic .it means small Increase in price will leads large Decrease in quantity demanded and vice versa.

D) In price ceiling ,the quantity sold in market is equal to QUANTITY supplied at that price.

So to maintain the same total surplus as part a) , government need to restrict price so that quantity supplied at that price is equal to 100( as part b).

Q=20p-200

100=20p-200

20p=300

P=300/20=150

The total surplus again equal to A+B+E.