(e) (6%) Find the inverse demand function p =D (q), and write down both the domain and range for D (q). 1 (f) (10%) Given the inverse demand function obtained above, and note that the sales revenue of the firm is given by s = p(q) x q. Find both the first- and second-derivatives of s with respect to p, i.e., s' (q) and s" (q).
3.13. A detective has evidence that 2 persons were involved in the crime he is investigating. Three suspects with very similar criminal records were seen close to the crime scene. Two of them are believed to be guilty. What is the probability that the first suspect being interviewed is guilty? Considering that the detective has managed to confirm one interviewee as having been involved in committing the crime, what is the probability that the next person to be interviewed is innocent?
1. Solve the Conscription game when bonus b=$500 and the cost of serving c-$400. How does this solution differ from that when b=$300? Interpret your answer in terms of an all-volunteer army. 2. Suppose in MAD that at endgame, if both players back down, the payoffs are -1.5 each. How does thi affect the solution?
24. lim x-0 √√2+x-√2 x
(1 point) Consider the demand for tickets to see a specific hockey team play. The price of the ticket can be related to the quantity demanded (q) by the function: p=114 0.01q. When the arena is not close to full capacity the total cost can be expressed by the function: Cost = 63q + 50,000. Find marginal revenue (MR) as a function of quantity demanded. MR = Let p* and q* be the price and quantity demanded where profit is maximized. * q* = || The hockey players union has negotiated a deal requiring the team owner to pay an extra $10,000 a year in salaries to the players. What should the new ticket price ( P₁) be to ensure that profit is maximized. P1 =
(1 point) The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 300 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. What rent should the manager charge to maximize revenue?