Economics

1. The GWEE natural resources research and consulting firm is bespoke to
Cartel Oil Co. has two major plays or fields. The firm must produce a report telling Cartel
how maximize profits from developing the two fields. They conduct analysis on
exploration to date and estimate that marginal cost of production is different in each and
given by
MC1 = 30 + 3Q1
MC2 = 9 + 6Q2
a. Invert the MCs to express them in terms of output from the two fields as a function of
cost.
b. Solve for joint output from the fields in terms of the two respective marginal costs.
This is Cartel Oil’s supply or marginal cost curve
c. The economic analysts have estimated the demand curve for oil as
QD = 300 – 2P
d. Derive Cartel Oil’s profit maximizing level of output assuming it has monopoly
power.
e. Given your answer in d. solve for the price they will charge. What is Cartel Oil’s
profit?
f. What is their price elasticity of demand? What is their supply elasticity of demand?
g. What are the production levels at for the two fields?
2. After successfully completing the first study Cartel Oil Co. hires GWEE to consult with
them on dealing with pesky producers on the competitive fringe. GWEE decides to use a
dominant firm approach to find Cartel Oil’s profit maximizing level of output and price
to charge.
GWEE preliminary research comes up with an estimated total demand for oil, marginal cost for
the firms on the competitive fringe, and Cartel’s marginal cost. The specifications for each are
given below.
2
w
W
NON NON
O O
a Q Q a b P with the World Inverse Demand P b
MC c d Q
MC e f Q
− = − =
= +
= +
Where a=120, b=10, c=35, d=17, e=12, and f=7.
a. GWEE calculates the demand for oil for Cartel Oil as the difference between Total
Demand and non-Cartel Supply. Explain the steps and perform the calculations.
b. What is the maximum price Cartel Oil could charge? What price would they have to
charge to drive non-Cartel out of the market?
c. Derive Cartel Oil’s total revenue and marginal revenue functions.
d. Find the profit maximizing quantity and price for Cartel Oil? What are the profits?
e. Calculate the level of output and profit for the non-cartel firms. What is their market
share of production? What are their profits?
f. Calculate the price elasticity for total oil demand, cartel oil, and non-cartel firms.
g. What are the four factors which determine Cartel Oil to have market power?
h. Suppose Cartel Oil was actually a group of firms working together. What are four basic
problems for Cartel Oil continuing to operate?
3. GWEE is hired by Cartel Oil to conduct a dynamic analysis for profit maximizing in the
short-run and the long-run (you can treat this as effectively two periods). Your research
estimates total oil demand for the two periods and total income/GDP. Cartel Oil provides
you with their level of reserves, marginal cost, and their cost of capital (interest rate)
Qd = 200 – 1/3 P + Y,
R = 250,
GDP or Income (Y) = 70 and does not grow,
Interest rate (r) = 10%,
and TC = 60Q.
a. Estimate the level of production and price in each period if Cartel Oil produced in a
competitive environment. What is the optimal price, level of output, and profit? Show
the situation graphically.
b. Estimate the level of production and price in each period if Cartel Oil behaved as a
monopolist. What is the optimal price, level of output, and profit? Show the situation
graphically.
c. Explain intuitively the differences in a. and b. with an emphasis on the dynamic
behavior.
d. Suppose that income/ GDP increase by 10% in the 2nd period. Redo your calculations
in a. and b. Show the two situations graphically. Explain intuitively.

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