Imagine that you are holding 5,000 shares of stock, currently selling at $40 per share. you are ready to sell the shares but would prefer to put off the sale until next year for tax reasons. if you continue to hold the shares until january, however, you face the risk that the stock will drop in value before year end. you decide to use a collar to limit downside risk without laying out a good deal of additional funds. january call options with a strike of $45 are selling at $2, and january puts with a strike price of $35 are selling at $3. assume that you hedge the entire 5,000 shares of stock.(a) what will be the value of your portfolio in january (net of the proceeds from the options) if the stock price ends up at $30. (omit the "$" sign in your response.)

Suppose there are three types of consumers who attend concerts at your university’s performing arts center: students, staff, and faculty. each of these groups has a different willingness to pay for tickets; within each group, willingness to pay is identical. there is a fixed cost of $1,000 to put on a concert, but there are essentially no variable costs. for each concert: i. there are 140 students willing to pay $20. (ii) there are 200 staff members willing to pay $35. (iii) there are 100 faculty members willing to pay $50. a) if the performing arts center can charge only one price, what price should it charge? what are profits at this price? b) if the performing arts center can price discriminate and charge two prices, one for students and another for faculty/staff, what are its profits? c) if the performing arts center can perfectly price discriminate and charge students, staff, and faculty three separate prices, what are its profits?