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ATLAS POTS LIMITED COMPANY

Atlas Pots Limited produces stainless steel pots and pans. AtlasPots Limited

can pursue either of two distribution plans for the coming year.The firm can

either produce pots and pans for sale under a discount store labelor

manufacture a higher quality line for specialty stores andexpensive mail order

catalogs. High initial set up costs along with Atlas Pots limitedcapacity make it

impossible for the firm to produce both lines. Profits under eachplan depend

upon the state of the economy. One of three conditions willprevail:

The outcome under each plan for each state of the economy is givenin the table

below. Figures in the table are profits measured in dollars. Theprobabilities for

each economic condition represent crude estimates.

Economic

Conditions

Discount Line

outcomes ($)

Specialty Line

outcomes ($)

Growth 220,100 230,760

Normal 178,988 162,000

Recession 140,000 20,850

Economic Conditions Probability

Growth 0.3

Normal 0.5

Recession 0.2

Read the above case study carefully and write down the correctoption

number (e-g A, B, C, D) in the given Excel file.

1. The expected value for the Atlas Pots Limited in case ofdiscount line will

be:

Marks: 2

A. 172512

B. 183524

C. 189530

D. 199230

2. Using the Specialty Line outcomes, the expected value for theAtlas Pots

Limited will be:

Marks: 2

A. 141343

B. 151245

C. 154398

D. 166658

3. The variance of profits in case of discount line outcome willbe:

Marks: 5

A. 782529468

B. 790496496

C. 801235659

D. 823526908

4. The standard deviation of profits for Specialty line outcomewill be:

Marks: 5

A. 73111.2534

B. 76225.6326

C. 80212.5632

D. 81396.5842

5. The standard deviation of profits for the Discount line outcomewill be:

Marks: 2

A. 24382.51

B. 25121.85

C. 26258.58

D. 28115.77

6. Base on the calculations of standard deviation in both cases,which of

the following statements is TRUE:

Marks: 2

A. Discount line is more risky.

B. Specialty line is more risky.

C. Level of risk is same in both cases.

D. Level of risk can not be determined through thesecalculations.

7. What is the advantage of the standard deviation over theaverage

deviation?

Marks: 2

A. Because the standard deviation requires squaring of deviationsbefore

further computation, positive and negative deviations do not cancelout.

B. Because the standard deviation does not require squaring ofdeviations, it

is easy to tell whether deviations are positive or negative.

C. The standard deviation expresses the average deviation inpercentage

terms, so that different choices can be more easily compared.

D. The standard deviation transforms subjective probabilities intoobjective

ones so that calculations can be performed.

14. Use calculus to find the first order conditions. Use solver then to solve the first order conditions. Show your work for the first order conditions and include the relevant portion of excel f(x.) =-22x2 + 22xy - 1ly2 + 110x -40y - 23A risk neutral principal hires a risk averse agent to work on a project. The agent' 5 utility function is V(w.-i) = WT: - 3(a). where w is wage, 303,-) is the disutility associated with the effort level 3,- exerted on the project. The agent can choose one of two possible effort levels, 814 or 31,, with associated disutility levels 3(EH) = 4, and 3(a) = 2. 0 If the agent chooses effort level 61.1, the project yields 80 with probability 1/ 2, and 0 with probability 1 / 2. e If the agent chooses q, the project yields 80 with probability 1/4 and 0 with probability 3 /4. The reservation utility of the agent is 0. Let {wH,wL} be an outputcontingent wage contract, where am is the wage paid if the project yields 80, and am is the wage if the yield is U. The agent receives a xed wage if :0 H = wL. (a) If effort is observable, which effort level should the principal implement? What is the best wage contract that implements this effort? [5 marks] (b) Suppose effort is not observable. What is the optimal contract that the principal should offer the agent? What effort level does this contract im- plement? [8 marks] (c) Compare the optimal contract in part (a) with that in part (b) and provide intuition for any similarity or difference in the income risk they impose on the agent and in the principal's payoff. ['2' marks]