Consider a game of mutually assured destruction played by two superpowers, country 1 and country 2. country 2 has precipitated an international incident. country 1 can either ignore the incident or escalate the crisis. if it ignores the incident the game ends and both countries receive a payoff of 0. it if escalates, then country 2 can either escalate further or back down. if it backs down, then the game ends, country 1 receives a payoff of 2, and country 2 receives a payoff of 2. if country 2 escalates further then 1 and 2 play a game where they move simultaneously. each has two strategies in this subgame: back down or doomsday. the payoffs in the subgame are as follows: find all subgame perfect nash equilibria of this game.

Quantitative problem: you need $20,000 to purchase a used car. your wealthy uncle is willing to lend you the money as an amortized loan. he would like you to make annual payments for 4 years, with the first payment to be made one year from today. he requires a 8% annual return. what will be your annual loan payments? round your answer to the nearest cent. do not round intermediate calculations. $ how much of your first payment will be applied to interest and to principal repayment? round your answer to the nearest cent. do not round intermediate calculations. interest: $ principal repayment

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.

On the first day of the fiscal year, a company issues an $7,500,000, 8%, five-year bond that pays semiannual interest of $300,000 ($7,500,000 × 8% × ½), receiving cash of $7,740,000. journalize the first interest payment and the amortization of the related bond premium. round to the nearest dollar. if an amount box does not require an entry, leave it blank.