Please explain and show work! thank you!

1. Market for Cockatoos In order to protect the wild populations of cockatoos, the Australian authorities have outlawed the export of these 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 them die in transit. Each smuggled (dead or alive) 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 Australian wild. Confiscated cockatoos that are found dead are donated to university cafeterias (suppose they taste ok). Smugglers are price takers. a. What is the probability that a smuggled parrot will reach the buyer alive and not confiscated? b. Denote the price for a cockatoo as P. What are the expected marginal revenue and expected marginal cost of selling a cockatoo? c. The demand function for smuggled cockatoos in the United States is Q = 7200 20F. If the cockatoos market is in the long run equilibrium, what is the price and the number of cockatoos caught in Australia? d. Suppose instead of returning live confiscated cockatoos to the wild, the customs authorities sell them in the American market. What would be the long run equilibrium price for each cockatoo? How many cockatoos will be caught from the Australian wild? e. Suppose that the trade in cockatoos is legalized. Suppose that it costs $40 to capture and ship a cockatoo to the United States in a comfortable cage and that the number of deaths in transit by this method is negligible. In the long run equilibrium, what would be the price and number of cockatoos caught in Australia