Question

Suppose the industry demand curve of bananas in the banana industry is given by equation

p=10−qd .....(1)

And the supply curve is given by

2

p = qs .............(2)

There is an equilibrium price p* for which qd = qs = q*

The equilibrium price in this market is $5 and quantity is 5. Suppose a price ceiling of $2 is imposed on this market

The area of a right triangle is 12 Base Height ; The area of a rectangle isLength Width

1. The new equilibrium quantity is smaller than the old equilibrium quantity by _____

2. The amount of shortage in the new equilibrium will be ________

3. At the old equilibrium, the consumer surplus is _________

10.At the new equilibrium the producer surplus is _________ 11.The deadweight loss is ___________

12.Draw a graph, call it GRAPH 3 to represent questions 7 - 11

Answer 1

The industry demand curve of bananas: p=10−qd

The industry supply curve of bananas: p = qs

The equilibrium price p* for which qd = qs = q* is: equilibrium price = $5 and equilibrium quantity = 5

When a price ceiling of $2 is imposed on this market,

1. The new equilibrium quantity is smaller than the old equilibrium quantity by 3 units.

Putting the value of the price ceiling $2 in the industry supply curve of bananas we get, p = qs which is equal to qs = 2 i.e. The new equilibrium quantity = 2.

The old equilibrium quantity = 5, so the The new equilibrium quantity is smaller than the old equilibrium quantity by 5 - 2 = 3 units.

2. The amount of shortage in the new equilibrium will be 6 units.

The quantity supplied when price ceiling = $2, p = qs so qs = $2

The quantity demanded when price ceiling = $2, p=10−qd, which is qd = 10 - p which is qd = 10 - 2 = 8

So, the amount of shortage in the new equilibrium = Quantity Demanded in the new equilibrium - Quantity Supplied in the new equilibrium

= 8 - 2 = 6 units

3. At the old equilibrium, the consumer surplus is 12.5

From the diagram above the old Consumer Surplus is shaded in red and marked as cs old. The old consumer surplus is before the price ceiling is imposed. I have drawn the supply curve from S because p = qs and there is no intercept so it starts from 0 and I have drawn the demand curve from 10 because p=10−qd, so when qd = 0, p = 10.

The consumer surplus is = 1/2 * base * height = 1/2 * 5* 5 = 12.5

10. At the new equilibrium the producer surplus is 2 units.

In the diagram, the new Producer Surplus is also marked in red and named as ps new. The new producer surplus is after the price ceiling is imposed.

The producer surplus = 1/2 * base * height = 1/2 * 2 * 2 = 2

11. The deadweight loss is 18.

The deadweight loss is the area of the triangle marked in blue. The formula for deadweight loss = 1/2 * (P2 - P1) * (Q2 - Q1) = 1/2* (8 -2) * (8-2) = 1/2 * 6 * 6 = 18.