Suppose that diamonds can be extracted for the cost of $100 per diamond. Consumers value diamonds according
Question:
Suppose that diamonds can be extracted for the cost of $100 per diamond. Consumers value diamonds according to the following formula, expressed in dollar equivalent units:
where x is the number of diamonds extracted.
(a) Plot the total cost and value of extracting diamonds on a graph, with x, the quantity of diamonds, on one axis and total costs and values on the other.
(b) What is the socially optimal extraction level of diamonds, assuming that consumer valuations and extraction costs are given exactly the same weight? Calculate this amount and indicate the economic reasoning that leads you to this conclusion. Also show the socially optimal extraction level on the same graph that you used for part (a).
(c) Show that a monopolist producer of diamonds would produce exactly the socially optimal level of diamonds provided that he had the power to charge different prices for each diamond sold. How is the total surplus divided among the consumers and the producer?
(d) Now assume that diamonds are produced by many small producers who take the price of diamonds as given in making their extraction decisions. Assume that each producer has a very small production capacity (up to which he can extract at $100 per diamond), but that an unlimited number of producers can enter. Show that the socially optimal level will be produced once again. How is the total surplus divided among the consumers and the producers?
(e) Now return to part (c) and assume that the monopolists is not permitted to charge different prices for each diamond he sells but must charge the same price for all diamonds. Now show that production will fall below the socially optimal level. This discrepancy can be understood by observing that the producer fails to fully internalize the marginal social gain from an additional diamond produced. Carefully verify that you indeed understand this.
(f) Show that these ideas can be used to extend and understand the discussion in the text regarding externalities and international trade.
Step by Step Answer:
Answer a here is the graph c A monopolist producer of diamonds if allowed to charge different prices ...View the full answer
