Consider a principal-agent problem with three exogenous states of nature, θ_1,,θ_2,θ_3, two effort levels, e_L and e_H and two output levels, distributed as follows as a function of the state of nature and the effort level:
State of Nature   θ_1   θ_2   θ_3
Probability   1/4   1/2   1/4
Output under e_H   18   18   1
Output under e_L   18   1   1
The principal is risk neutral, while the agent has utility function u(w)=w^(1/2). when receiving monetary compensation w, minus the cost of effort, which is normalized to 0 for e_L and to 0.1 for e_H. The agent’s reservation expected utility is 0.1.
   Derive the first-best contract.

   Derive the second-best contract when only output levels are observable.

   Assume the principal can buy for a price 0.1 an information system that allows the parties to verify whether state of nature θ_3 happened or not. Will the principal buy this information system? Discuss.

1. The results of a mathematics placement exam at two different campuses of Mercy College follow:

What is the computed value of the test statistic?

3.0

4.0

2.0

11.9

2.

The results of a mathematics placement exam at two different campuses of Mercy College follow:

Is there a difference in the mean score of Campus 1 and Campus 2 of Mercy College? Given that the two population standard deviations are known, what is the p-value?

1.0000

0.9651

0.0651

0.0002

3.

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?

What are the degrees of freedom?

12

4

16

17

prepare general journal entries to record the following perpetual system merchandising transactions of Belton Company. use a separate account for each receivable and payable; for example, record the sale on June 1 in Accounts Receivable - Avery & Wiest.

June 1 sold merchandise to Avery & Weist for $9500; terms 2/5, n/15. FOB destination (cost of sales $6,650).

2 purchased $ 4900 of merchandise from Angolac Suppliers; terms 1/10, n/20, FOB shipping point.

4 purchased merchandise inventory from Bastille Sales for $11,400; terms 1/15, n/45, FOB Bastille Sales.

5 sold merchandise to Gelgar for $ 11,000; terms 2/5, n/15, FOB destination (cost of sales $7700)

6 Collected the amount owing from Avery & Weist regarding the June 1 sale.

12 paid Angolac Suppliers for the June 2 purchase.

20 Collected the amount owing from Gelgar regarding the June 5 sale.

30 Paid Bastille Sales for the June 4 purchase.

Part 2

Based on the information provided above, calculate (a) net sales, (cost of goods sold), and (c) gross profit for the month ended June 30, 2020.

1. An investor has the opportunity to buy one of four different stocks.  Each stock is currently selling for $50 per share, and the investor will choose one of the stocks and purchase 20 shares of one of the stocks and sell them one year later.  (Hence, the investor is making an initial investment of 20*$50=$1000.) When buying the stock, the investor doesn’t know whether or not there will be a recession when she goes to sell the 20 shares of stock in one year. If there is a recession (state 1) the selling prices will be $45, $52, $58, and $40. If there is no recession (state 2), the selling prices will be $60, $56, $54, and $53.

a. complete the payoff and opportunity loss tables reflecting profits after selling the 20 shares of stock at the end of the year.

b. are any of the stocks clearly inferior choices?

c. What is the alternative chosen using the optimistic criterion?

d. what is the alternative chosen using the pessimistic criterion?

e. what is the alternative chosen using the minimax regret criterion?

the Critical Path is A-B-F-I-J-K=21    

1-)If all critical path activities were crashed by 25%, calculate the new overall project duration?

Please solve the problem below and include the excel formulas to the answers:

Consider a monopolist with a total cost of TC=9+Q and marginal cost of $1 (MC=1). The monopolist faces a demand curve of P=11-Q.

1. Graph the monopolist

2. Find price and quantity that the monopolist charges.

3. Find the profit and consumer surplus.

4. Find the deadweight loss to welfare.

Many typical household cleaners contain a toxic chemical. Assume the percent of this toxic chemical in one glass cleaner is approximately normal. The mean percent is 3, the standard deviation of the percent is 1.

1.(4 points) Randomly select one bottle of the glass cleaner, find the probability that the percentage of the toxic chemical is more than 3.255.

2.(4 points) Randomly select 10 bottles of this glass cleaner, find the probability exactly 3 bottles which contain the toxic chemical more than 3.255.

3.(4 points) Find the 80th percentile of the distribution of toxic chemical percent (of the glass cleaner), ?80p80.

4.(4 points) Assume random samples with sample size of 16, find the probability that the sample mean percentage (of the toxic chemical) is less than 2.5.