6. Suppose that there are two identical firms in the silver mining industry. The cost curve of each firm is C(Q) = 0.25Q². Quantity (Q) is measured in troy ounces per day. Demand per day for silver is QD = 408 – 8P where price (P) is measured in dollars per troy ounce. a) If the two firms are price takers, then what are the supply curves of each firm? What is the industry supply curve? b) If the two firms behave as price takers, then what will be the price and quantity that clear the market? c) If the firms formed a cartel, then what would be the marginal cost of the cartel? d) If the cartel is a monopolist, then what price will the cartel charge for silver? What quantity will it sell? Illustrate the demand, marginal revenue and marginal cost curves in a diagram. Assume that the firms in the cartel divide the production and the profits equally. e) What are the profits of an individual firm in the cartel? f) Suppose that firm 1 "cheats" on the cartel by producing 2 more ounces than its allotted equal share. If firm 2 does not cheat (so firm 2 produces the same number of ounces as they did in part (e)) and firm 1 produces 2 more ounces, then what will be the new price in the market? Show that firm 1 will earn more by cheating than it did in part (e). g) Briefly explain why it is that firm 1 could increase its individual profits by increasing production from the cartel solution but that cartel itself could not increase profits by increasing production.
6. Suppose that there are two identical firms in the silver mining industry. The cost curve of each firm is C(Q) = 0.25Q². Quantity (Q) is measured in troy ounces per day. Demand per day for silver is QD = 408 – 8P where price (P) is measured in dollars per troy ounce. a) If the two firms are price takers, then what are the supply curves of each firm? What is the industry supply curve? b) If the two firms behave as price takers, then what will be the price and quantity that clear the market? c) If the firms formed a cartel, then what would be the marginal cost of the cartel? d) If the cartel is a monopolist, then what price will the cartel charge for silver? What quantity will it sell? Illustrate the demand, marginal revenue and marginal cost curves in a diagram. Assume that the firms in the cartel divide the production and the profits equally. e) What are the profits of an individual firm in the cartel? f) Suppose that firm 1 "cheats" on the cartel by producing 2 more ounces than its allotted equal share. If firm 2 does not cheat (so firm 2 produces the same number of ounces as they did in part (e)) and firm 1 produces 2 more ounces, then what will be the new price in the market? Show that firm 1 will earn more by cheating than it did in part (e). g) Briefly explain why it is that firm 1 could increase its individual profits by increasing production from the cartel solution but that cartel itself could not increase profits by increasing production.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please solve parts d, e, and f only. thank you
Transcribed Image Text:6. Suppose that there are two identical firms in the silver mining industry. The cost curve of
each firm is C(Q) = 0.25Q². Quantity (Q) is measured in troy ounces per day. Demand per
day for silver is QD = 408 - 8P where price (P) is measured in dollars per troy ounce.
a)
If the two firms are price takers, then what are the supply curves of each firm?
What is the industry supply curve?
b)
If the two firms behave as price takers, then what will be the price and quantity that
clear the market?
d)
c) If the firms formed a cartel, then what would be the marginal cost of the cartel?
If the cartel is a monopolist, then what price will the cartel charge for silver? What
quantity will it sell? Illustrate the demand, marginal revenue and marginal cost
curves in a diagram.
Assume that the firms in the cartel divide the production and the profits equally.
e)
What are the profits of an individual firm in the cartel?
f)
Suppose that firm 1 “cheats" on the cartel by producing 2 more ounces than its
allotted equal share. If firm 2 does not cheat (so firm 2 produces the same number
of ounces as they did in part (e)) and firm 1 produces 2 more ounces, then what will
be the new price in the market? Show that firm 1 will earn more by cheating than it
did in part (e).
g) Briefly explain why it is that firm 1 could increase its individual profits by
increasing production from the cartel solution but that cartel itself could not
increase profits by increasing production.
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