The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. here is a possible model: c(x, y) = 7,000 + 500x2 + 50y2 where x is the reduction in sulfur emissions, y is the reduction in lead emissions (in pounds of pollutant per day), and c is the daily cost to the firm (in dollars) of this reduction. government clean-air subsidies amount to $500 per pound of sulfur and $100 per pound of lead removed. how many pounds of pollutant should the firm remove each day in order to minimize net cost (cost minus subsidy)?

German brothels recently began offering a monthly subscription service for multiple purchasers. if you thought that the brothels' encouragement of prostitution was immoral to begin with, would you consider this pricing plan to be even more immoral? suppose a particular patron at a german brothel has the following willingness-to-pay schedule for services at the brothel, per session. session willingness to pay 1st $84 2nd $72 3rd $60 4th $48 5th $36 6th $24 suppose this consumer would not demand any more sessions, even for free. also assume that the marginal cost to the brothel, per session, is constant at $12. at a price of $78.00 per session, the number of sessions demanded by this consumer would be . at this price and quantity, consumer surplus is $ and producer surplus is $ . suppose the brothel has devised a new pricing scheme for consumers who demand more than 1 session. this pricing scheme is a subscription service, whereby consumers can pay a flat fee of $259.20 and can have up to 6 sessions total. using this subscription pricing model, this consumer would demand sessions. under this scenario, consumer surplus is $ and producer surplus is $ . (hint: for consumer surplus, consider how much total value the consumer places on all sessions, versus the total price paid.)