There are two groups of customers in the market. Demand of group number 1 is Q1(p) = 3−0.5p, and demand of group number 2 is Q2(p) = 5−2p. The market is served by a monopolist with MC = 1. (a) Write down the market demand function (remember that demand function should be welldefined for all possible prices). Plot it. (b) Derive the MR(Q) for the market demand and plot it on the graph from above. (c) What price will the monopolist charge if she cannot price discriminate? Find the corresponding consumer surpluses for both groups. (d) Now suppose that the monopolist can set different prices for different groups. What prices will she choose? Find the corresponding consumer surpluses for both groups. (e) Who wins and who loses when discrimination is allowed? How does total welfare change?
In: Economics
Ann and Bill play the following game in which 4 gold coins are to be won. Ann selects a word from the set {up, out, over} and Bill selects a word from the same set (it could be the same word). If the words selected by the two players differ, then Ann wins one gold coin, and the remainder go to Bill. If the words selected by the two players are the same, then the number of gold coins won by Ann equals the number of letters in the chosen word, and the remainder go to Bill.
(a) Represent this scenario as a zero-sum 3 × 3 game.
(b) Calculate the equilibrium strategies for the game, and explain how the players should play the game using these strategies.
(c) Use the answer you deduced in part (b) to determine the game value v and show explicitly that Ann’s payoff is bounded above by this game value.
In: Statistics and Probability
1.The classical probability concept applies only when all possible outcomes are _________.
2.In general, if r objects are selected from a set of n objects, any particular arrangement (order) of these objects is called.____________ The number of ways in which r objects can be selected from a set of n distinct objects (in other words, that is when the order of objects doesn't matter) is called___________
3.The sum of the probability in the formula for the mathematical expectation is equal to ________
4.A fair game is defined to be in which:
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the probabilities of all events are equal |
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the sum of all probabilities equals to 1 |
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E = 1 |
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E = 0 |
5.The mathematical expectation for a game is determined by multiplying each amount by its ________ and adding the products.
6. In a probability Tree Diagram such as that of Figure 41.1a on page 113 of the textbook, the branches representing the ------------ of a event.
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possibilities |
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number of leaves |
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probability |
7.The number of ways of choosing zero objects from a distinct object is ________
8.The probability of selecting a defective component from 20 components, 3 of which are defective is 3/20. This is an example of:
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the classical probability concept |
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the frequency interpretation of probability |
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the law of large numbers |
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subjective probability |
In: Statistics and Probability
a financial analyst you are trying to put together a report about three different bonds. One portion of the report requires you to estimate the expected return and standard deviation of each bond.
Which bond has the highest expected return?
Which bond has the riskiest? [Hint: You must use the probability model to compute the expected risk]
|
Probability |
Yield for Bond X |
Yield for Bond Y |
Yield for Bond Z |
|
0.10 |
12% |
14% |
7% |
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0.20 |
4% |
3% |
9% |
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0.30 |
23% |
7% |
15% |
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0.05 |
6% |
-20% |
30% |
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0.15 |
8% |
5% |
2% |
|
0.09 |
1% |
-12% |
0.1% |
|
0.11 |
9% |
2% |
10% |
In excel. How do you know which bond is risker than the other?
In: Finance
In: Statistics and Probability
An insulated tank, fitted with a freely moving frictionless piston, has an initial volume of 1 m3 and contains 20 kg of refrigerant 134a at 200 kPa. A stirrer with a rotation rate of 300 rpm and a torque of 15 J/rotation is included in the tank. Find the time required for the refrigerant to evaporate completely.
Ans= [73.36 minutes]
In: Other
An adiabatic piston-cylinder device with no leaks executes expansion work during which 2 kg of saturated liquid water at atmospheric pressure (101.325 kPa) is completely turned into saturated steam. What is the entropy generated for this process? (Use proper units)
*Please write clearly and directly note any references to property tables!*
In: Mechanical Engineering
2- Gases A2 and B2 react according to the equation: A2 + B2 → AxBy . If equimolar ( not necessarily stoichiometrically equivalent) quantities are placed in a reaction vessel with a massless, frictionless piston and allowed to react to completion. The density of the gas mixture after reaction is 1.5X the original density. Find the empirical formula? Is there only one possibility? Explain.
In: Chemistry
Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.006, and 74.000. Calculate the sample mean and sample standard deviation. Round your answers to 3 decimal places. Sample mean = Sample standard deviation =
In: Statistics and Probability
A piston cylinder device with air is going through an isentropic compression. The initial pressure is 0.1 MPa and temperature is 300 K. During the isentropic compression process, the volume is decreased to 1/18 of the initial volume. Using variable specific heats, determine the pressure and temperature at the end of the compression process. What is the amount of work consumed?
In: Mechanical Engineering