Question

Consider the market for oil in Staubovia. Domestic demand for oil can be represented by P=100-2QDanddomestic supply of oil can be represented by P=25+3QS, where Q is measured in millions of barrels. (2 graphs)

a .Calculate the equilibrium price and quantity, showing all necessary work. Graph the market for oil on graph 1, being sure to properly label axes, curves, intercepts, and equilibrium.

Suppose that Staubovia imports oil, and that the world price for oil is $40 per barrel

b. Calculate how many barrels of oil are imported, and label these imports Itrade this on graph 1.

c. Suppose now that President Staub decides to impose an import quota. After the import quota, the price of a barrel of oil is now $58 Calculate how many barrels of oil are imported with the import quota, and label these imports Iquota on graph 1.

d. Calculate and label the quota rent, QR, that results from this policy. Who does the quota rent go to?

e. Show graphically how producer, consumer, and total surplus would change in Staubovia as a result of imposing the quota. You do not need to calculate the changes in surplus. Who in Staubovia is better off and who is worse off after this policy?

f. On Graph 2, show how this policy would affect Staubovia's output and price level in the short-run.

Answer 1

a) A market is in equilibrium when quantity demanded and quantity supplied become equal.

The given demand function is

QD = 100 - 2QD

The given supply function is

QS = 25 + 3QS

When market is in equilibrium, QD = QS

100 - 2QD = 25 + 3QS

100 - 25 = 3QS + 2QD

75 = 5Q ( Q = quantity)

Q = 75/5 = 15

When Q = 15

Price is

P = 100 - 2QD

= 100 - 2*15 = 70

The equilibrium quantity = 15

Equilibrium price = 70

The given demand function is

P = 100 - 2QD

Where 100 = price when quantity demanded is 0( y axis intercept)

Quantity demanded when price is 0 =

0 = 100- 2QD

2QD = 100

QD = 100/2 = 50

Therefore 50 is the x axis intercept

-2 = Slope of the demand curve

The supply fuction is

P = 25 + 3QS

Where 25 = price when quantity supplied is 0 ( y axis intercept)

3 = the slope of the supply curve

The market for oil and equilibrium in the market can be drawn as follows.

In the diagram x and y axis represents quantity and price respectively. D is the demand curve and S is the supply curve. Equilibrium price is 70 and equilibrium quantity is 15.

b) The world price of oil = $40

Import = Domestic demand - domestic supply

When price is 40, domestic demand is

40 = 100-2QD

2QD = 100-40 = 60

QD = 60/2 = 30

Demand = 30

When price is 40, quantity supplied is

40 = 25 + 3QS

40 - 25 = 3QS

15 = 3QS

QS = 15/3 = 5

Quantity supplied = 5

Import = 30 - 5 = 25

In the diagram Pw is the world price and import of quantity 25 has metioned.

c) The world price after import quota = 58

Quantity demanded when price is 58

58 = 100- 2QD

2QD = 100 - 58 = 42

QD = 42/2 = 21

Demand = 21

Quantity supplied when price is 58

58 = 25 + 3QS

58 - 25 = 3QS

33 = 3QS

QS = 33/3 = 11

Supply = 11

Import after quota = 21 - 11 =10

In the diagram with new world price 58, import is 10.

d) Quota rent = (Worldprice with quota-free trade price) * import

Quota rent = (58 - 40) * 10 = 180

quota rent = 180

quota rent has shaded in the below diagram

Who receives the quota rent depends on the quota administration.

The government receives the quota rent if the government auctions the quota right.

If the government gives away the quota right, then quota rent will go to the receivers of quota right. Usually quota rights are given to someone in the importing country.