Question 1: The following data represents five points on the supply curve for orange juice and five points on the demand curve for orange juice.
|
Price ($ per gallon)
|
Supply (Millions of Gal.)
|
Demand (Millions of Gal.)
|
|
1
|
100
|
700
|
|
2
|
300
|
600
|
|
3
|
500
|
500
|
|
4
|
700
|
400
|
|
5
|
900
|
300
|
a) Graph the points of these supply and demand curves for orange juice. Be sure to put price on the vertical axis and quantity on the horizontal axis.
b) Do these points seem to lie along two straight lines? If so, figure out the precise algebraic equation of these lines.
c) What is the equilibrium price and quantity for the market of orange juice? Calculate consumer surplus, producer surplus and welfare.
d) Suppose that a freeze in Florida reduces orange juice supply by 300 million gallons at every price. How would this shift affect the equilibrium price and quantity? How would it affect consumer surplus, producer surplus and welfare? Calculate the elasticity of demand using this supply shift. Make sure to include calculations with your explanations.
e) Assume the government applies a tax to consumers that will make them reduce their consumption by 300 million gallons at every price. How much was taxed? What is the new equilibrium? Who will pay more of the tax, producers or consumers? Calculate the elasticity of supply with this shift in demand. Make sure to include calculations with your explanations.
Question 2: Two classmates A and B are assigned an extra credit group project. Each student can choose to Slack or Work. If one or more players choose to Work, the project is completed and provides each with extra credit valued at 4 payoff units each. The cost of completing the project is that 6 total units of effort (measured in payoff units) is divided equally among all players who decide to Work and this is subtracted from their payoff. If they both Shirk, they do not have to expend any effort but the project is not completed, giving each a payoff of 0. The teacher can only tell whether the project was completed and not which student contributed to it.
a) Create a payoff matrix for this game assuming that students choose to Slack or Work simultaneously. Make sure you identify the players, the actions and the payoffs for each player.
b) Find the Nash equilibrium and explain why the result you found is LAW, equilibrium.
Assume there are two countries involved in war. Country A is considering invading Country B through a bridge which is the only access point to country B. If country A invades through the bridge country B has the option to either fight or run away. Once country B chooses either to fight or run away, country A can decide either to retreat through the bridge or continue with the assault.
a) When the two countries fight, the confrontation ends in a stalemate and both armies are vanished. If one country decides to fight while the other runs away, the country fighting keeps its numbers, while the country retreating loses half of its army. If both countries run away they both lose half of their army. Draw a game tree and find the Nash equilibrium for this game. Explain.
b) Can country change the outcome of the game by burning the bridge they are crossing to invade and committing its troops to fight? Expand the game tree to show this option for country A and find the new Nash equilibrium. Explain.