Question

The demand function for a good is Q=1200-P while the supply functions is Q=-200+P. World price is $300 and the nation is is imposing a quota of 200 units.

a. Graph the demand and supply function to scale and label axis and intercepts.

b. Determine the quantity demanded before and after the quota.

c. Determine the quantity supplied before and after the quota.

d. Determine the quantity imported before and after the quota.

e. Determine the consumer surplus before and after the quota.

f. Determine the producer surplus before and after the quota.

g. Determine government cost of the quota.

h. Determine the dead weight loss.

i. Identify on the graph in part (a) the dead weight loss.

Answer 1

a) The given demand function

Q= 1200-P

Quantity demanded when price is zeo = 1200. This is the x axis intercept

Price when quantity demanded is zero = 1200. This is the y axis intercept.

(0 = 1200-P

P = 1200 )

The given supply function is

Q = -200+P

Quantity supplied when price is zero= -200

Price when quantity supplied is zero= 200

The given supply and demand function can be drawn as follows

In the diagram x and y axis represents quantity and price respectively. S is the supply curve and D is the demand curve. Initially the world price is 300.

b) Quantity demanded before quota(world price 300) = 900

Q = 1200-300= 900

Import demand = domestic demand-domestic supply

Import demand = (1200-P) - (-200+P, )

Import demand = 1400+2P

Import quota of 200 means import demand is 200.

When import demand is 200

200 = 1400+2P

2P = 1400-200=1200

P = 1200/2 = 600

New Price with import quota of 200 = 600

When price is 600, domestic demand is

Q = 1200-600= 600

Quantity demanded before quota = 900

Quantity demanded after quota= 600

This has represented in the above graph

c) Quantity supplied before quota

Q = -200+300 =100

With quota of 200, price increase to 600(calculated in part b)

Quantity supplied after quota

Q= -200+600 =400

Quantity supplied before quota= 100

Quantity supplied after quota= 400

d) import = Domestic demand -domestic supply

Before quota, demand = 900, supply= 100

Import= 900-100 =800

After quota, demand = 600, supply= 400

Import = 600-400 =200

Import before quota= 800

Import after quota =200