Plaintiffs purchased state lottery tickets and were winners along with 76 others. The state had advertised that $1,750,000 would be the prize, but it distributed only $744,471. Plaintiff sued the lottery director, alleging fraud in the conduct of the lottery. The state lottery law provides for administrative hearings upon complaints charging violations of the lottery law or of regulations thereunder. It also allows any party adversely affected by a final order of the administrative agency to seek judicial review. Must the plaintiffs exhaust their administrative remedies? Why or why not?

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

To : of $25 up to 35 2 35 up to 45 5 45 up to 55 7 55 up to 65 20 65 up to 75 16 is$25 up to $35 ?

Your subscription to investing wisely weekly is about to expire. you plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $620, also payable immediately. assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?