BUEC 232 Lecture Notes - Lecture 7: Conditional Probability, University Of Florida, Random Variable

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azurehyena719

28 Jan 2019

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Simon Fraser University

Department

Business Economics

Course

BUEC 232

Professor

N. Payne

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BUEC 232 Lecture Notes - Lecture 6: Sample Space, Disjoint Sets

BUEC 232 Lecture Notes - Lecture 7: Conditional Probability, University Of Florida, Random Variable

BUEC 232 Lecture Notes - Lecture 8: Random Variable, Normal Distribution

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The outcome of each die is in no way affected by the other, they are completely independent. Unions: two events a and b are given. The union of these two events is written as: A u b: an important formula for unions is: p(a u b)=p(a) + p(b) - p(a and b). This rule is referred to as the addition rule: example of unions: we have a class of 100mba students. Accounting (a), 15 take finance(f) and 10 take both. : in this case, at least on subject refers to. Therefore, it is just p(a) + p(f) - p(a and f) which is 25+15-10=30. Conditional probability: conditional probability that x occurs given that y occurs is p(x|y, we can define conditional probabilities in terms of unconditional probabilities, p(b|a)= p(b and a)/p(a, p(a and b) can also be written as: p(b)*p(a|b)

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1) Suppose that a monopolist has zero marginal cost and faces two consumers. The first is Antonio. Antonio has an inverse demand function given by the following schedule: p(1) = 5 p(2) = 4 p(3) = 3 p(4) = 2 p(5) = 1 p(6) = 0

a) What would Antonio be willing to pay for one unit of the monopolist's good?

b) What would Antonio be willing to pay for a second unit of the monopolist's good?

c) How much would Antonio be willing to pay for 5 units of the monopolist's good?

The second customer is Bianca. Bianca has the following inverse demand function: p(1) = 8 p(2) = 7.5 p(3) = 7 . . . p(15) = 1 p(16) = 0.5 p(17) = 0

d) How much would Bianca be willing to pay for 18 units of the monopolist's good?

e) Suppose the monopolist offered two ways to purchase its good - you can buy 5 units for the amount you answered in part c), or 18 units for the amount you answered in part d). Which offer would Antonio take? Which offer would Bianca take?

f) What is the most Bianca would pay for 18 units of the monopolist's good if she were also able to buy 5 units for the amount you answered in part c)?

g) Suppose the monopolist were to offer 5 units for the amount you answered in part c) and 18 units for the amount you answered in part f). How much profit could the monopolist make? Could the monopolist change the packages she offers and make still more money?

h) What are the packages the monopolist could offer that would earn the most money?

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Two firms set prices in a market with demand curve Q = 6 â p, where p is the lower of the two prices. If firm 1 is the lower priced firm, then it is firm 1 that meets all of the demand; conversely, the same applies to firm 2 if it is the lower priced firm. For example, if firms 1 and 2 post prices equal to 2 and 4 dollars, respectively, then firm 1âas the lower priced firmâmeets all of the market demand and, hence, sells 4 units. If the two firms set the same price p, then they each get half of the market, that is, they each get 6âp . Suppose that prices can only be quoted in dollar units, such as 2 0, 1, 2, 3, 4, 5, or 6 dollars. Suppose, furthermore, that costs of production are zero for both firms. Finally, suppose that firms want to maximize their own profits.

(a) Show that the strategy of posting a price of 5 dollars weakly dominates the strategy of posting a price of 6 dollars. Does it strictly dominate as well?

(b) Are there any other (weakly) dominated strategies for firm 1? Explain.

(d) Suppose for a moment that this market had only one firm. Show that the price at which this monopoly firm maximizes profits is 3 dollars.

(e) Can you give a reason whyâin any price competition modelâa duopoly firm would never want to price above the monopoly price? (Hint: When can a duopoly firm that prices above the monopoly price make positive profits? What would happen to those profits if the firm charged a monopoly price instead?)

(g) Show that when we restrict attention to the prices 1, 2, and 3 dollars, the (monopoly) price of 3 dollars is a strictly dominated strategy. (h) Find the outcome of iterated elimination of (weakly) dominated strategies.

(h) Find the outcome of iterated elimination of (weakly) dominated strategies.

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As we observed in this chapter, central banks, rather than purposefully setting the level of the money supply, usually set a target level for a short-term interest rate by standing ready to lend or borrow whatever money people wish to hold at that interest rate. (When people need more money for a reason other than a change in the interest rate, the money supply therefore expands, and it contracts when they wish to hold less.)

A. Describe the problems that might arise if a central bank sets monetary policy by holding the market interest rate constant. (First, consider the flexible-price case, and ask yourself if you can find a unique equilibrium price level when the central bank simply gives people all the money they wish to hold at the pegged interest rate. Then consider the sticky-price case.)

B. Does the situation change if the central bank raises the interest rate when prices are high, according to a formula such as R - R₀= a(P - P₀), where a is a positive constant and P₀a target price level?

C.Suppose the central bankâs policy rule is R - R₀= a(P - P₀) + u, where u is a random movement in the policy interest rate. In the overshooting model shown in Figure 15-12, describe how the economy would adjust to a permanent one-time unexpected fall in the random factor u, and say why. You can interpret the fall in u as an interest rate cut by the central bank, and therefore as an expansionary monetary action.

BUEC 232 Lecture Notes - Lecture 7: Conditional Probability, University Of Florida, Random Variable

BUEC 232 Lecture Notes - Lecture 6: Sample Space, Disjoint Sets

BUEC 232 Lecture Notes - Lecture 7: Conditional Probability, University Of Florida, Random Variable

BUEC 232 Lecture Notes - Lecture 8: Random Variable, Normal Distribution

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