Questions:
Q1. An island country has a large reserve of oil, all owned by a single firm. The demand and marginal cost curves for oil are as follows:
|
Price ($)
|
Quantity demanded
|
Marginal cost
|
Total revenue
|
Marginal revenue
|
|
90
|
0
|
|
|
|
|
|
|
30
|
|
|
|
80
|
20
|
|
|
|
|
|
|
30
|
|
|
|
70
|
40
|
|
|
|
|
|
|
30
|
|
|
|
60
|
60
|
|
|
|
|
|
|
30
|
|
|
|
50
|
80
|
|
|
|
|
|
|
30
|
|
|
|
40
|
100
|
|
|
|
|
|
|
30
|
|
|
|
30
|
120
|
|
|
|
|
|
|
30
|
|
|
|
20
|
140
|
|
|
|
|
|
|
30
|
|
|
|
10
|
160
|
|
|
|
|
|
|
30
|
|
|
|
0
|
180
|
|
|
|
Assume that, by law, oil cannot be imported to, nor exported from, the island.
a. Add total revenue and marginal revenue to the table, and draw a graph showing all three curves (demand, marginal revenue, and marginal cost). (Note: Remember that marginal revenue should be plotted at the midpoint; for example, the marginal revenue as output rises from 0 to 20 units should be plotted at Q = 10 units.)
b. From your graph, determine the profit-maximizing quantity of oil produced by the firm, and the price that the firm will charge. Explain briefly.
c. Is the allocation of resources under this arrangement efficient or inefficient? Explain briefly.
d. Calculate consumer surplus and producer surplus for this monopoly outcome.
Now suppose that a central planner for the government is given the task of finding what price and quantity would emerge if the firm were somehow made to behave as a perfectly competitive firm.
e. What quantity of oil does the central planner have the firm produce, and what price is charged? Explain briefly.
f. Calculate consumer surplus and producer surplus for this perfectly competitive outcome. Is there an increase or decrease in the total surplus to the firm and the consumers combined, compared to part (d)? Explain briefly.
Q2. Suppose your economics class is graded on a curve, such that your grade on a quiz depends not only on your performance, but also on the performance of others in the class. You and your classmates have two choices, to study for a quiz or not. If you and your classmates study for a quiz, you all will receive 80. If you study and they do not, you will receive 90 and they will fail the quiz and receive 49. If you choose not to study and neither do your classmates, everybody will receive 49. But if your classmates study and you do not, they receive 90 and you will fail i.e. you receive 49. Assume that all of your classmates make the same choice.
a. Construct the payoff matrix
You
|
Classmates
|
|
Study
|
Not study
|
|
Study
|
|
|
|
Not study
|
|
|
b. Which strategy will you follow? Will you decide to study, or not study? Is this a dominant strategy? Explain briefly.
c.Which strategy will others in the class follow? Will they decide to study, or not study? Is this a dominant strategy? Explain briefly.
d.Find the Nash equilibrium? Is this a prisoner's dilemma? Explain briefly.