In a small town there are two places to eat: 1) a Chinese restaurant and 2) a pizza place. Everyone in town eats dinner at one of the these two places or eats dinner at home.

Assume the 20% of those who eat in the Chinese restaurant go to the pizza place the next time and 40% eat at home. From those who eat at the pizza place, 50% go to the Chinese restaurant and 30% eat at home the next time.  From those who eat at home, 20% go to the Chinese restaurant and 40% to the pizza place next time. We call this situation a system. This system can be modeled as a discrete-time Markov chainwith three states.

1. Define the three states and write down the one-step transition probability matrix.
2. If a family has decided to eat dinner in the Chinese restaurant with the probability of 0.05 or in the pizza place with the probability of 0.15 today, what is the probability that this family will eat dinner at home in two days
3. If a lady is having pizza today, how long will it take for her to have pizza again
4. Given that a man has been eating at the Chinese restaurant today and yesterday, on average, how long will it take for him to eat at the pizza place for the first time?
5. If a family plans to eat at home on Sunday, what is the probability that they will eat Chinese on Tuesday (same week) for the first timethen they will eat Pizza on Friday (same week) for the first time?

(Tragedy of the Commons) Canterbury is a small pastoral town with a grassy area known as the “commons.” The town’s two farmers may freely graze their cattle on the commons. In the spring each farmer simultaneously and independently buy (identical) cattle for $10 a head. The farmers must send their cattle to the commons during the spring and summer to feed and fatten them up. At the end of summer the cattle are sold at the market price of $1 per hundred pounds. (The farmers are price-takers in the larger cattle market.) The problem is that the commons is a small area that can only feed so many cattle before the grazing becomes poor. To capture this idea, let Q be the total number of cattle sent to the commons. The total weight (in hundreds of pounds) of all the cattle at the end of the season is given by W(Q) = 100Q − 10Q^2 , so that weight of a single cow is W(Q)/Q = 100 − 10Q. Let qi be the number of cattle farmer i buys in the spring and sends to the commons. Assume that a farmer can send a “fractional” cow so that qi can be any number greater than or equal to zero. (You can think of this as the farmer sending the cow to the commons for only a fraction of the season.) Naturally, Q = q1 + q2. Thus, the payoff functions are u1(q1, q2) = (100 − 10q1 − 10q2) q1 − 10q1 and u2(q1, q2) = (100 − 10q1 − 10q2) q2 − 10q2.

(a) Write the game in normal form.

(b) Find farmer 1 and 2’s best response function. It’ll help to notice that the game is symmetric.

(c) Find the Nash equilibrium number of cattle each farmer sends to the commons (i.e., head of cattle purchased): (q*1 , q^2 ).

(d) Show that the equilibrium is inefficient because too many cattle are sent to the commons in equilibrium. That is, show that q*1 + q*2 exceeds the quantity that would maximize the joint payoff. (The joint payoff is (100Q − 10Q^2)− 10Q = 90Q − 10Q^2 .)

(e) What is the intution behind part (d)? Can you think of other contexts, possibly including ones we covered in class, to which the same type of analysis applies? That is, where there is "too much" of an activity in equilibrium

A town official claims that the average vehicle in their area sells for more than the 40th percentile of your data set. Using the data, you obtained in week 1, as well as the summary statistics you found for the original data set (excluding the super car outlier), run a hypothesis test to determine if the claim can be supported. Make sure you state all the important values, so your fellow classmates can use them to run a hypothesis test as well. Use alpha = .05 to test your claim. (Note: You will want to use the function =PERCENTILE.INC in Excel to find the 40th percentile of your data set) First determine if you are using a z or t-test and explain why. Then conduct a four-step hypothesis test including a sentence at the end justifying the support or lack of support for the claim and why you made that choice

The Town of Weston has a Water Utility Fund with the following trial balance as of July 1, 2019, the first day of the fiscal year:

During the year ended June 30, 2020, the following transactions and events occurred in the Town of Weston Water Utility Fund:

1. Accrued expenses at July 1 were paid in cash.
2. Billings to nongovernmental customers for water usage for the year amounted to $1,381,000; billings to the General Fund amounted to $109,000.
3. Liabilities for the following were recorded during the year:

4. Materials and supplies were used in the amount of $276,000, all for costs of sales and services.
5. After collection efforts were unsuccessful, $14,100 of old accounts receivable were written off.
6. Accounts receivable collections totaled $1,472,400 from nongovernmental customers and $48,700 from the General Fund.
7. $1,041,400 of accounts payable were paid in cash.
8. One year’s interest in the amount of $176,100 was paid.
9. Construction was completed on plant assets costing $252,000; that amount was transferred to Utility Plant in Service.
10. Depreciation was recorded in the amount of $262,100.
11. The Allowance for Uncollectible Accounts was increased by $10,000.
12. As required by the loan agreement, cash in the amount of $102,000 was transferred to Restricted Assets for eventual redemption of the bonds.
13. Accrued expenses, all related to costs of sales and services, amounted to $90,000.
14. Nominal accounts for the year were closed.

Required:
a. Record the transactions for the year in general journal form.
b. Prepare a Statement of Revenues, Expenses, and Changes in Fund Net Position.
c. Prepare a Statement of Net Position as of June 30, 2020.
d. Prepare a Statement of Cash Flows for the year ended June 30, 2020. Assume all debt and interest are related to capital outlay. Assume the entire construction work in progress liability (see item 3) was paid in entry 7. Include restricted assets as cash and cash equivalents.

Sabrina, Kris, and Kelly are the only three residents of the small town of Charleston. They are considering whether to hire a police officer to patrol the town. Sabrina values the police officer at $610 per week, Kris values the police officer at $230 per week, and Kelly values the police officer at $150 per week. The competitive wage for a police officer is $900 per week.

a. If the protection provided by the police officer to one resident does not diminish the protection provided to the other residents, then the police officer is   (Click to select)  a commons  an excludable  a rival  a nonrival  a nonexcludable  good.

b. Suppose Sabrina proposes a tax whereby all three residents split the cost of the police officer equally.

Will the majority of them support this tax?

• No, they will not support the tax.

• Yes, they will support the tax.

Is this outcome socially efficient?

• This outcome is not socially efficent.

• This outcome is socially efficient.

c. Suppose Kris suggests a proportional tax on income to pay for the police officer. If Sabrina earns $4,000 per week, Kris earns $1,500 per week, and Kelly earns $500 per week, what proportional tax on income would just cover the cost of the police officer?

Instructions: Enter your response as a percent.

A proportional tax rate:  %

Will the majority of them support the tax?

• Yes, all three would support the tax.

• No, all three would not support the tax.

• No, two of them would not support the tax.

• Yes, two of them would support the tax.

d. Is a regressive tax system likely to lead to the socially optimal outcome in this case?

• No

• Yes

a) Bargain Town is a large discount chain. The management wishes to compare the performance of its credit managers in Ohio and Illinois, by comparing the mean dollar amount owed by customers with charge accounts in both two states. A small mean is desirable.

Suppose that Bargain Town randomly selected the following small samples.

Sample of Ohio accounts Sample of Illinois accounts

n_o=10 n_o= 6

yo = $124 y₁ = $68

s²_o= 1681 s²_o= = 484

Assuming that equal variances, independent samples, and normality assumptions hold, compute a 95% confidence interval for μo-μ1.

b) Assuming that only the independent samples and normality assumptions hold, test H_o: μ_o-μ₁=0 versus H₁: μ_o-μ₁≠0 by setting α=0.05. Based on the test we cannot reject the Null Hypothesis.

True or False?

c) To carry our the F-test for equality of population variances, you need to first calculate the values of F, r₁, r₂,F_α^(r₁,r₂)

Compute the following: F, r₁, r₂,F_α^(r₁,r₂)

Carry out the F -test for equality of variances, H_o: σ²_o=σ²₁versus H₁: σ²_o≠σ²₁ Do we reject the null hypothesis?

Select one:

a. [F, r₁, r₂, F_α^(r₁,r₂) , reject H_o versus H₁ ] = [2.565, 6, 9, 6, reject]

b. [F, r₁, r₂, F_α^(r₁,r₂) , reject H_o versus H₁ ] = [2.565, 9, 4, 6, reject]  

c. [F, r₁, r₂, F_α^(r₁,r₂) , reject H_o versus H₁ ] = [3.473, 9, 4, 6, reject]

d. [F, r₁, r₂, F_α^(r₁,r₂) , reject H_o versus H₁ ] = [2.565, 8, 5, 5, we cannot reject]

e. [F, r₁, r₂, F_α^(r₁,r₂) , reject H_o versus H₁ ] = [3.473, 9, 4, 6, we cannot reject]

You are on the police force in a small town. During an election year, a candidate for mayor claims that fewer police are needed because the average police officer makes only four arrests per year. You think the population mean is much higher than that, so you conduct a small research project. You ask 12 other officers how many arrests they made in the past year. The average for this sample of 12 is 6.3, with a standard deviation of 1.5. With your sample evidence, test the null hypothesis that the population mean is four arrests against the alternative that it is greater than four. Set your alpha level at .01.

In the town of Maplewood a certain type of DVD player is sold at just two stores. 38% of the sales are from store A and the rest of the sales are from store B. 7% of the DVD players sold at store A are defective while 3% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? Express your answer as a percentage rounded to the nearest hundredth.

Suppose that the short-run supply and demand for pineapples in a certain town are described by the following two equations:

Q^S= 1,000,

Q^D= 2,000−200p.

Pineapples are an imported produce in this market, so the government imposes a tax of $1 per pineapple. Which of the following statements is true?

1. The after-tax equilibrium is given by p^S=5, p^B=6 and Q^T= 1,000.
2. The after-tax equilibrium is given by p^S=4, p^B=5 and Q^T= 1,000.
3. The deadweight loss of this tax is zero.
4. Only (a) and (c).
5. Only (b) and (c)

1. Suppose you and a rival are the only producers of oysters in a town. Each morning you harvest

   oysters to sell in the afternoon. You both have the choice to collect 10 or 20 dozen oysters. Each dozen has a marginal cost of $10 (so the cost of 10 dozen oysters is $100). If 20 dozen oysters in total are brought to the market, they will sell for $35 each. If 30 dozen oysters in total are brought to the market, they will sell for $25 each. If 40 dozen oysters in total are brought to the market they will sell for $20 each. You and your rival must simultaneously decide how many oysters to collect in the morning.

   A.Write out the payoff matrix for this game. B.Find the pure strategy Nash equilibrium for this game. C.Suppose, instead, you could discuss with your rival how many oysters to collect in the morning. D. What outcome would you agree to? Is this different from the Nash equilibrium?