In a scene at the end of The Princess Bride, the hero, Wesley, confronts the evil Prince Humperdinck. This interaction can be modeled as the following game.

Wesley can either be strong or weak, as randomly picked by nature with equal probability. Wesley,knowing if he is strong or weak, can then choose to stand or continue lying on the bed.The prince observes this decision but does not know Wesley's type and chooses to fight or surrender. The prince can beat a weak Wesley (Wesley was "mostly" dead only a few hours earlier) and can really beat up a weakWesley who stays in bed. If a weak Wesley stands and the prince fights, then the base payoffs are 1 for the prince and -1 for Wesley. If Wesley stays in bed, then the prince gets 2 and Wesley still gets -1. If Wesley is weak and the prince surrenders, regardless of whether Wesley has stood or not the base payoffs are 1 for Wesley and 0 for the prince. A strong Wesley, however, will destroy the prince and enjoy doing it should the prince try to fight. It is easier for Wesley to beat the Prince if he stands, though, so in that case he gets a payoff of 3 while the prince gets -2. If Wesley stays in bed and the Prince chooses to fight, the payoffs are 1 for Wesley and -1 for the prince. In the event that the prince chooses not to fight, Wesley gets 2 if he stands and 1 if he stays in bed while in either case the prince gets 0. The final complication to the payoffs is that if Wesley is weak, standing costs him some extra amount c, while it costs a strong Wesley nothing.

a) (5 points) derive the extensive form of the game

b) (10 points) derive a pooling BNE where q= 0.5 represents the prince's initial belief that Wesley is weak. Be sure to include what are the prince's beliefs about Wesley's type if he observes Wesley in bed or observes him standing. Find the range of values for c that makes the belief valid.

c) (10 points) derive a separating BNE for this game as well as the range of c over which it is valid.

5.1 Price Elasticity of Demand and Price Elasticity of Supply Calculate the price elasticity of demand Question The table shows the price and quantity demanded for floor mats, Using the Midpoint Method, what is the price elasticity of demand between points B and C? Note: Remember to take the absolute value of the result and round to the nearest hundredth. Rounding should be done at the end of your calculation. Point Price Quantity A $10 500 B $13 480 C $16 460 D $19 440 $22 420Question 10 2 pts Refer to Figure 2.2.1 above. At a price of $ 1.50, there is: OFan alternative equilibrium between supply and demand. O a surplus of coffee in the market. an excess of quantity demanded over quantity supplied. an excess of quantity supplied over quantity demanded. Question 11 2 pts Refer to Figure 2.2.1 above. If the price of $1.50 is a price imposed by the government, we can call it: a socially optimal equilibrium price. O a price floor. O a fiscal price. a price ceiling.Question 1 Not yet answered Points out of 1 Flag question (This question refers to the MRU video 'The Demand Curve Shifts'.) If, at a certain price, buyers suddenly demand a greater quantity of a good than they did previously, there has been: Select one: a. movement along a demand curve, from right to left. b. movement along a demand curve, from left to right. c. a decrease in demand d. an increase in demand. Question 2 Not yet answered Points out of 1 Flag question The government plans to increase cigarette taxes in six months. Since consumers should expect the future price of cigarettes to increase, the current demand for cigarettes will increase, and the price of cigarettes will rise even before the tax is implemented. Select one: True False AQUESTION 7 Exhibit 4-5 - 52 50 51 Price Quantity Refer to Exhibit 4-5. A change from Point A to Point B represents a(n): a. decrease in quantity supplied. b. increase in quantity supplied c. increase in supply. d. decrease in supply.4. Draw Figure for Comparative Static Result for a $500.00 increase in I. How would an economist describe the relationship between widgets and income? 5. Calculate the income elasticity of demand for widgets. Interpret your results. 6. Calculate the price elasticity of supply for widgets. Interpret your results