Question
The marginal cost of catching a ton of shrimp is $1,500. After Hurricane Carmen destroyed most shrimping boats, Bubba Gump Shrimp Co., run by Forrest
The marginal cost of catching a ton of shrimp is $1,500. After Hurricane Carmen destroyed most shrimping boats, Bubba Gump Shrimp Co., run by Forrest Gump and Lt. Dan Taylor, obtained a monopoly in this market. They plan to sell the shrimp at a price of $2,000 per ton; they are certain that the price elasticity of demand at this price is -2. Would you advise Forrest and Dan to increase or decrease the price of shrimp, or have they chosen the optimal price? Explain.
2.In the summer of 2019, the Royal Mint minted a million 50 pence coins commemorating Brexit, which was supposed to happen on October 31. After that deadline for Brexit was missed, the initial plan was to melt all the million coins carrying the wrong date. The final decision was to melt all but 10,000 coins, which would be sold to collectors at 10 each.
The Chancellor of the Exchequer Sajid Javid suggests that melting the coins is costly, and taxpayers will foot the bill. However, the marginal cost of melting 10,000 coins is negligible, as is the value of the metal used to produce it.
a.Suppose that the Bank of England's goal was to maximize profit, and it did so optimally. Given the zero marginal cost of melting an additional coin, what can be said about the elasticity of demand for October 31 Brexit memorial coins at the current (optimal) price?
b.Assuming the demand is linear, derive the demand curve. In other words, find and in the equation .
c.Suppose that the Bank of England decided that it would melt all but one coin. Using the demand curve you derived in (b), find the price at which Bank of England would be able to sell this coin.
Comment: You may find the answer to (c) unrealistic. This is likely because the collector's willingness to pay for a coin is higher if it is the only such coin in the world, rather than one of 10,000. This is an example of a negative externality, akin to congestion, where additional users diminish the value of a product. We will cover this in Weeks 8-9.
d.How would your answer to (a) change if melting each coin produces precious metals in non-negligible amounts?
Hint: How does this change the marginal cost of selling (rather than melting) a coin?
3.Rogue Creamery, located in Southern Oregon, has capacity to produce 12,000 pounds of Rogue River Blue cheese annually. In reality, it produces 10,000 pounds, which sells at $30 a pound. The marginal cost of producing a pound is $10.
a.Assuming that Rogue Creamery prices optimally, what is the elasticity of demand for this cheese at the current price?
b.Assuming that the demand curve is linear, derive the demand equation.
c.Write down the inverse demand curve (P as a function of Q) and the marginal revenue curve. Verify that you would get the same optimal price and quantity using the "MR=MC" principle.
Rogue River Blue won the top prize at World Cheese Awards, the first cheese from the United States to do so. This brought considerable interest to the products of the Creamery. Specifically, demand for Rogue River Blue cheese doubled: for any given price, twice as many people are willing to buy the cheese. To make optimal pricing decisions after this demand shock, they have retained you as a consultant. They promised to pay you $1,000 for your services.
d.Find the optimal price in the short run, i.e., before the Creamery has a chance to adjust its capacity.
e.The CEO of Rogue Creamery proposes a plan, where some facilities that currently produce other cheeses would be repurposed for production of Rogue River Blue. It would increase the capacity by 8,000 pounds per year, to 20,000. This would result in $80,000 of foregone profits from the other cheeses per year. Would you approve this idea?
f.Before you have a chance to present your advice, the CEO comes back with a different plan. The plan is essentially half of the previous one: it would expand the capacity to produce Rogue River Blue by 4,000 pounds per year, and cost half as much, i.e. $40,000. What would your recommendation be now? Would you advocate for the previous plan, the new one, or would you advise against any expansion?
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