Let V (p)=a+bU (p), where p is a lottery, a and b are some constants, and U (p) is a von Neumann-Morgenstern utility function. Suppose U (p) = 2, and U ()=10. Under what conditions (if any) V (p) has an Expected Utility Rep- resentation (EUR) if i) V (p)=0, V (7) = 1. ii) a iii) a == 1 and b = and b = ? ¥?

Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] . Which of them has a µ of zero using the probability model approach.   1. [12.5968, 4, -2 and -12.5968]   2. [12.5968, 2, -2 and -12.5968]

Suppose you sample one value from a uniform distribution with a = 0 and b=20. a. What is the probability that the value will be between 12 and 172 b. What is the probability that the value will be between 4 and 72 c. What is the mean? d. What is the standard deviation? a. The probability that the value will be between 12 and 17 is (Type an integer or a decimal)

The preference of an agents on lotteries can be represented by an expected utility function u such that u(x) = 3y^1/2 -10. Then the agent is A) not risk averse B) risk loving C) risk neutral D) risk averse E) NOPAC

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Given this frequency distribution, what demand values would be associated with the following random numbers? (Do not round intermediate calculations.) Demand Frequency 23 1 16 2 18 43 Random Number Simulated Demand 0.1 0.6 0.4

Maximize z=4x+5y Subject to: x+y<or=4 x-y>or=-2 x<or=3 x>or=0, y>or=0

Given this frequency distribution, what demand values would be associated with the following random numbers? (Do not round intermediate calculations.)  Demand Frequency 0 18 1 15 2 18 3 49 Random Numbers.     Stimulated Demand 0.2 0.5 0.5

Given this frequency distribution, what demand values would be associated with the following random numbers? (Do not round intermediate calculations.) Demand Frequency 17 1 19 21 43 Random Number Simulated Demand 0.0 0.6 0.6

25. Billy’s Bakery bakes fresh bagels each morning. The daily demand for bagels is a random variable with a distribution estimated from prior experience given by # of bagels sold in one day probability 0 .05 5 .10 10 .10 15 .20 20 .25 25 .15 30 .10 35 .05 The bagels cost Billy’s 8 cents to make, and they are sold for 35 cents each. Bagels unsold at the end of the day are purchased by a nearby charity soup kitchen for 3 cents each a) Based on the discrete distribution above, how many bagels should Billy’s bake at the start of each day? b) Determine the optimal number of bagels to bake each day using a normal distribution approximation. (Hint: You must compute the mean and the variance of the demand from the discrete distribution above.)26. Weiss’s paint store uses a reorder point inventory system to control its stock levels. For a particularly popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard…