Elizabeth, the manager of the medical test firm Theranos, worries aboutthe firm being sued for botched results from blood tests. If it isn’t sued, thefirm expects to earn profit of $120, but if it is successfully sued, its profit will beonly $10. Elizabeth believes that the probability of a successful lawsuit is 20%.If fair insurance is available and Elizabeth is risk averse, how much insurancewill she buy? (Hint: Assume that Elizabeth starts with a wealth ofwand shebuys insurance coveringx≤(120−10) = 110 of her loss. Write down herexpected utility as a function ofxand then take a derivative with respect toxto find the optimal insurance. If you want more hints, have a look at the secondinsurance problem solved in the lecture notes.)

2standard deviation a particular telephone number is used to receive both voice calls and fax messages. suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (a) what is the expected number of calls among the 25 that involve a fax message?

Bear, inc. estimates its sales at 200,000 units in the first quarter and that sales will increase by 20,000 units each quarter over the year. they have, and desire, a 25% ending inventory of finished goods. each unit sells for $35. 40% of the sales are for cash. 70% of the credit customers pay within the quarter. the remainder is received in the quarter following sale. cash collections for the third quarter are budgeted at

The market for corn in country a is highly competitive. at the current market price of $5/bushel there is a shortage of 100,000 bushels of corn in this country. media reports claim that the price of corn will rise drastically in the near future. according to these reports, the neighboring country b had witnessed a similar situation recently. at the same price, the shortage in country b was also 100,000 bushels and eventually the equilibrium price in b went up to $10/bushel. both countries are known to have equal number of corn producers and the market supply of corn is identical at all prices. this, combined with the fact that consumers in the two countries also have similar tastes and preferences, led the media to conclude that the price of corn in country a would soon be as high as $10/bushel. the new equilibrium price turns out to be below $10/bushel, what inferences can be drawn?