Question

Suppose there are only two oil producing countries in the world and who compete

with one another: Canada and Norway. The world inverse demand for oil is given by P(Q) =

180 ? qC ? qN where qC and qN are the quantities of oil brought to market by Canada and Norway,

respectively. The cost function for extracting oil is identical across both countries and equal to

C(q) = 60q. The two countries engage in Cournot competition by choosing how much oil to

extract.

Suppose Norway were to invade Canada

and take control of their oil production.

(a) Assuming Norwegian oil producers are just as efficient at extracting oil, calculate how

much total oil will be extracted by the Norwegian Empire. What happens to the world

price of oil?

(b) Because of concerns about how the invasion would affect the world price of oil, the U.S.

tells Norway that it would intervene in any attempted invasion of Canada. Suppose King

Harald of Norway tells the U.S. that if Norway were to control the world supply of oil that

it could reduce its costs to C(q) = 10q and the world price of oil would actually fall. If you

believe Harald, is his claim about how the world price would change accurate?

(c) Convinced by Harald’s claims, the U.S. allows the invasion to proceed (because Canada

has not fulfilled its obligations to NATO). Graph the inverse demand function for oil, show

the old world price, the new world price, and highlight graphically the change in consumer

surplus and producer surplus. There is no need to calculate the actual values of CS and PS.

(You can assume Harald’s claims about the new cost function are correct.)

Answer 1

Let's first of all see that how much Norway and Canada would produce on their own under a cournot equilibrium.

In Canada:

P(Q) = 180 ? qC ? qN so Total revenue (TR) = qC* P(Q)

We get TR = (180-qC ? qN )*qC

=180qC- qC² - qN qC

Derivating TR with respect to qC gives us marginal revenue (MR) in canada

So, MR = 180-2qC-qN

We have total cost (TC) = 60qC

Derivating TC with respect to  qC gives us marginal cost (MC) in canada

So, MC = 60

Equilibrium is achieved when MC=MR. So, equating the two we get,

180-2qC-qN = 60

Solving it, -2qC = 60+qN-180 = -120+qN

qC = 60-1/2qN Lets call it equation-1 (actually it is Canada's best response function)

Doing an exactly similar calculation for Norway gives us Norway's best response function which will be:

qN = 60-1/2qC we will call it equation-2  (actually it is Norway's best response function)

Putting the value of qN from equation-2 to equation-1 we get,

  qC = 60-1/2*(60-1/2qC )

solving the equation we get,

qC = 60-30-1/4qC

qC = 40

Putting the value in equation-2 = qN = 60-40/2 =40

So, in equilibrium both qC = qN = 40

Equilibrium Price = 180-40-40 = 100

(a.) Assuming Norwegian oil producers are just as efficient at extracting oil. we will have new demand function as

P(Q) = 180- qc -qN =180-Q we say that Norway has control over total output Q (Q = qC+qN)

TR = 180Q-Q²

MR = 180-2Q

TC= 60Q

MC= 60

At equiibrium. MC = MR

180-2Q=60

Solving, we get Q = 60

Putting this in price equation we get P = 180-60 = 120

So, when Norway controls the total quantity the equilibrium price rises from100 to 120 and quantity falls from 80 to 60.

(b.)

Suppose King Harald of Norway tells the U.S. that if Norway were to control the world supply of oil that

it could reduce its costs to C(q) = 10q then everything else remaining the same we get a new TC = 10q

So, new MC = 10

MR = 180-2Q (same as in part a)

New equilibrium, MR =MC

180-2Q = 10

Q = 85

P = 180-85 =95

So, his claim about how the world price would change is indeed accurate. The world price can now be reduced to 95.

(c.) Consumer surplus is defined as the area under the demand curve and above the equilibrium price and Producer surplus is defined as the area above the supply curve and below the equilibrium price and is shown as