QUESTION 1 Decision Analysis Show all calculations to support your answers. You

Question

QUESTION 1 Decision Analysis

Show all calculations to support your answers. You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (c) of this question if you wish. Guide to marks: 20 marks - 6 for (a), 4 for (b), 10 for (c)

(a) What is meant by the term “standard reference lottery”? What is it used for? Provide a simple example.

(b) What are the advantages and disadvantages of using marginal analysis to solve decision problems?

(c) Ajax Corporation believes there is a possibility of increased demand in the coming year for one of its products, code named X-120. Actually, there could also be a decrease in demand.

Three responses are envisaged: install new equipment capable of greater throughput, work overtime, or continue production at the current level, The following net profits, over a one year horizon, are estimated for X-120:

1 Which alternative would an optimist choose?

2 Which alternative would a pessimist choose?

3 Which alternative is indicated by the criterion of regret?

4 Assuming probability of an increase in demand = 0.6, using expected monetary values what is the optimum action?

5 What is the expected value of perfect information?

Decrease in Demand Increase in Demand New equipment $60,000 $240,000 Overtime $100,000 $220,000 Current level $100,000 $140,000

Explanation / Answer

(a) Consider a set of consequences for which utilities are to be assessed. Let ci, cj , ck be consequences from that set such that ci cj ck.
The utilities of a decision maker for the possible consequences in a decision problem can be assessed using several certainty equivalents:
A reference gamble is a choice between two lotteries:
1 the certain lottery L = [1.0, cj ]
2 the simple lottery L = [p, ci; (1 p), ck]
L is the reference lottery of the ”gamble” — if u(ci) = 1.0 and u(ck) = 0, then L is called a standard reference lottery

(b) In marginal analysis, the cost of an activity is measured against incremental changes in volume to determine how the overall change in cost will affect the bottom line of a business. Marginal analysis can show the cost of additional production by a business all the way up to the break-even point. This is generally the maximum cost that a business can sustain without losing money.

For example, Assume, for example, that you produce a product that sells for $120 each and costs $100 a piece to produce if you produce 50 of those products. This will result in a total cost of $5,000 and a total revenue of $6,000. Once you produce the 51st unit of this product, your total revenue then goes to $6,120. Assume that your total cost goes to $5,150. In this case, the decision to produce the 51st unit would be a bad one because the cost of production per unit increases to $100.98 per unit. Your net benefit goes up by $120, while the overall cost increases by $150, meaning that the cost outweighs the benefit and that the production of the additional unit is not worth the extra cost.

(c) 1 Optimist follow Maximax approach - Best of the Best.

Best of 3 alternatives are - New Equipment - $240,000, Overtime - $220,000, Current Level - $140,000

Best of these best is New Equipment - $240,000

So the optmist choose New Equipment decision.

2 Pessimist follow Maximin approach - Best of the Worst.

Worst of 3 alternatives are - New Equipment - $60,000, Overtime - $100,000, Current Level - $100,000

Best of these worst is Overtime or Current Level - $100,000

So the optmist choose Overtime or Current Level decision.

3. Regret for Decrease in demand = $40,000, $0, $0

Regret for Increase in demand = $0, $20,000, $100,000

Maximum regret for New equipment = $40,000

Maximum regret for Overtime = $20,000

Maximum regret for Current level = $100,000

The mimimum of these 3 is Overtime = $20,000.

So, criterion of regret alternative is Overtime.

4. probability of an increase in demand = 0.6

probability of an decrease in demand = 1 - 0.6 = 0.4

For new equipment, expected monetary values = 0.4 * $60,000 + 0.6 * $240,000 = $168000

For Overtime, expected monetary values = 0.4 * $100,000 + 0.6 * $220,000 = $172000

For Current level, expected monetary values = 0.4 * $100,000 + 0.6 * $140,000 = $124000

So, the optimum action is Overtime which gives maximum expected monetary values.

5. Expected value without information is the maximun expected value = $172000

Expected value with information = 0.4 * Max payoff of decrease in demand + 0.6 * Max payoff of increase in demand

0.4 * $100,000 + 0.6 * $240,000 = $184000

Expected value of perfect information = Expected value with information - Expected value without information

= $184000 - $172000 = $12000

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