Natural gas characteristics

Question 1
Suppose we have a market for natural gas characterized by the chart above. Assume the following
functional forms for the supply and demand curves:
: = 100 −
: = 25 + 0.5
1. What is the equilibrium price and quantity under a competitive model (round to the nearest
integer)?
2. Now suppose that there is only one provider of natural gas in this market. What is the functional
form for the Monopolist’s Marginal Revenue curve (HINT: The slope is twice as negative)? Draw
this curve on the chart above.
3. Calculate the quantity and price charged by this Monopoly.
4. Calculate the deadweight loss, producer surplus, and consumer surplus in both the competitive
and Monopoly case.
5. Now suppose the government implements a price control, setting the maximum price charged
to be $55. Calculate the new quantity produced by the monopolist.
6. At the price control, calculate the deadweight loss, producer surplus, and consumer surplus.
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Question 2
Suppose we have an electricity market where there are two potential suppliers of electricity. The market
is characterized by the following demand curve:
: = 60 − 2
= 1 + 2
The firms both have the same zero marginal costs:
1 = 2 = 0
1. Using the Cournot Duopoly model, calculate the reaction curves for the two firms. Graph the
curves.
2. Using the reaction curves, calculate the profit maximizing output for each firm. What is the total
output in the market under a duopoly?
3. What is the equilibrium price that will be set in this market?
Question 3
Suppose the market for oil consists of two players: OPEC countries and non-OPEC countries. The market
is characterized by the following demand curves. NOTE: The demand curves are expressed with
quantity as a function of price in this case:
: = 400 − 2
− : = −20 +
1. What is OPEC’s demand curve expressed with as a function of ? (HINT: Subtract the
quantity equation for non-OPEC countries from the total demand equation).
2. What is OPEC’s marginal revenue curve? (HINT: Solve the demand curve in Part 1 above for P
and then solve for Marginal Revenue as you would for a Monopoly).
3. What is the profit maximizing quantity for OPEC, assuming it has a constant marginal cost of 20?
4. What is the equilibrium price in this market?
5. What is the quantity produced by Non-OPEC countries? What is the total production from both
OPEC and non-OPEC countries?

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