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Consumer's Opportunity Set

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a) Consumers' opportunity set show the various combination of two good that are available given the amount of income and prices? Do you agree or disagree. Discuss

b) Suppose all prices doubled and at the same time consumers' income also doubled, will this alter the consumer's opportunity set. If yes, explain. If no, explain

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a) This statement is true for a two-good model. In this case the opportunity set shows all possible consumption bundles of the two goods that someone can afford given the prices of the two goods and the person's income level. It is constraint by the budget line as follows;

P1X1 + P2X2 ≤ consumer's income

However, this relationship ...

Solution Summary

Consumers' opportunity set shows all possible consumption bundles of n goods that someone can afford given the prices of the n goods and the person's income level. It is constraint by the budget equation as follows:
P1X1 + P2X2 + P3X3 + ...................... + PnXn ≤ consumer's income. Consumers can consume at the maximum level on his or her budget line. However, he or she can consume anywhere below the budget constraint. In this case he or she doesn't exhaust his or her income.

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Probability and Decision Analysis

1. Use the normal approximation without the correction factor to find the probabilities in the following exercises.

a. In a binomial experiment with n = 300 and p=.5, find the probability that P is greater than 60%.
b. Repeat Part a with p = 55
c. Repeat Part a with p = .6

2. Determine the probability that in a sample of 100 the sample proportion is less than .75 if p=.80.

3. A commercial for a manufacturer of household appliances claims that 3% of all its products require a service call in the first year. A consumer protection association wants to check the claim by surveying 400 households that recently purchased one of the company's appliances. What is the probability that more than 5% require a service call within the first year? What would you say about the commercial's industry honesty if in a random sample of 400 households 5% report at least one service call?

4. The Red Lobster restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. What is the probability that less than 70% rate the food as excellent?

5. A baker must decide how many specialty cakes to bake each morning. From past experience, she knows that the daily demand for cakes ranges from 0 to 3. Each cake costs $3.00 to produce and sells for $ 8.00 and any unsold cakes are thrown into the garbage at the end of the day.
a. Set up a payoff table to help the baker decide how many cakes to bake.
b. Set up the opportunity loss table.
c. Draw the decision tree.

6. Refer to Problem 5. Assume that the probability of each value of demand is the same for all possible demands.
a. Determine the EMV decision
b. Determine the EOL decision

7. The manager of a larger shopping center in Buffalo is in the process of deciding on the type of snow clearing service to hire for his parking lot. The two services are available. The White Christmas Company will clear all snowfalls for a flat fee of$40,000 for entire winter season. The Weplowen Company charges $18,000 for each snowfall it clears. Set up the payoff table to help the manager decide, assuming that the number of snowfalls per winter season ranges from 0 to 4.

8. Refer to Problem 7. Using subjective assessments, the manager has assigned the following probabilities to the number of snowfalls. Determine the optimal decision.

P(0) = .05 P(1) = .15 P(2) = .30 P(3)=.40 P(4)=.10

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