To protect, the wild populations of cockatoos, the Australian authorities have o

Question

To protect, the wild populations of cockatoos, the Australian authorities have outlawed the export of these large parrots. An illegal market in cockatoos has developed. The cost of capturing an Australian cockatoo and shipping him to the United States is about $40 per bird. Smuggled parrots are drugged and shipped in suitcases. This is extremely traumatic for the birds and about 50% of the cockatoos shipped die in transit. Each smuggled cockatoo has a 10% chance of being discovered, in which case the bird is confiscated and a fine of $500 is charged. Confiscated cockatoos that are alive are returned to the wild. Confiscated cockatoos that are found dead are donated to university cafeterias. What is the reliability that a smuggled parrot will reach the buyer alive and un confiscated? If p is the market price of a smuggled parrot, what is the expected revenue to a parrot-smuggler from shipping one parrot? What is the expected cost, including expected fines and the cost of capturing and shipping, per parrot? Suppose there is an unlimited number of potential smugglers so that the market supply schedule is perfectly elastic. At what price will cockatoo's be supplied? The demand function for smuggled cockatoos in the United States is D(p) = 7200 - 20p per year. How many smuggled cockatoos will be sold in the United States per year at the equilibrium price? How many cockatoos must be caught in Australia in order to satisfy the equilibrium demand in the U.S.? Suppose that instead of returning live confiscated cockatoos to the wild, the customs authorities sold them in the American market at the equilibrium price of smuggled parrots. How many cockatoos will be sold in the United States? How many cockatoos will be permanently removed from the Australian wild? Suppose that the trade in cockatoos is legalized, in which case it costs about $40 to capture and ship a cockatoo to the United States in a comfortable cage with a negligible number of deaths in transit. What would be the equilibrium price of cockatoos in the United States? How many cockatoos would be sold in the United States? How many cockatoos would be caught in Australia for the U.S. market?

Explanation / Answer

a) The chances of remaining alive of a smuggled parrot is 50% and out of that 10% have a chance of being confiscated. The probability of a smuggled parrot being alive and unconfiscated therefore can be calculated as (1 – 0.5) * (1 – 0.1). Hence, the probability that a smuggled parrot will reach the buyer alive and unconfiscated is 45% or 0.45.

b) The probability that a smuggled parrot will reach the buyer alive and unconfiscated is 45% or 0.45. Therefore when the price of smuggled parrots is p, the expected gross revenue to a parrot-smuggler from shipping a parrot is 0.45p.

c) The cost of capturing and shipping per parrot is $40 per bird whereas the expected cost of a smuggled bird being alive and captured is 0.10 * $500 = $50. Hence, the total cost is $40 + $50 = $90 per bird.

d) If smugglers are risk-neutral, expected economic profits are zero. So in such scenario expected cost will be equal to expected benefits i.e. 0.45p = $90. Hence, p = $200.

e - i) D(p) = 7200 - 20p

D(200) = 7200 - 20 * 200

D(200) = 7200 - 4000

D(200) = 3200

3200 smuggled cockatoos will be sold in the United States per year at the equilibrium price.

e - ii) As 50% die in the transit and 10% of the remaining are discovered and confiscated, hence, 45% of captured birds are sold in the market. At equilibrium, 3200 birds are required to be sold. To sell 3200, number of birds should be captured are:

Birds Captured = Birds Sold / 0.45 = 3200 / 0.45 = 7,111 birds.

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