Harry Tomfilger (HT) is a supplier of fashion clothing. It faces a decision on the choice of advertising campaign for a new product that it plans to introduce through major high street retailers. The impact of any advertising campaign is believed to be closely linked to levels of consumer spending over the next year; to simplify matters, the possible alternatives have been characterised as high, medium or low expenditure. The Marketing Director has set out her assessment of the likely "pay-offs" from the three advertising campaigns in the form of the matrix given below (showing net sales revenues in £000s under each scenario). The company does not, initially at least, have reliable estimates of the probability of each level of consumer spending occurring.
(i) From the company\'s point of view, is this as it stands a situation of risk or uncertainty? Distinguish clearly between the two, giving additional examples.
Situation of uncertainty because reliable (objective) probability measures are not available to the company ie three "states of nature" but no indication of their likelihood of occurrence. (2 marks for uncertainty + explanation + 2 marks for suitable examples).
(ii) Showing your workings, what advice would you give under each of the following criteria? (these are worth 2 marks each):
(c) Hurwicz Alpha (assuming a value for a of 0.8).
(a) Campaign C (0) (b) Campaign A (110) (c) Campaign A = 0.8(110) + 0.2(-20) = 84*,
Campaign B = 0.8(90) + 0.2(-30) = 66, Campaign C = 0.8 (100) + 0.2(0) = 80
(iii) Assume, now, that the company\'s Marketing Director, using the latest government predictions, decides that the probability of low consumer spending is 20% and that of high consumer spending, 35%. What is the risk neutral decision for the company? (5 marks)
Campaign A = 0.2(-20) + 0.45(40) + 0.35(110) = 52.5
Campaign B = 0.2(-30) + 0.45(80) + 0.35(90) = 61.5* ( maximum EV)
Campaign C = 0.2(0) + 0.45(40) + 0.35(100) = 53
(iv) What is the maximum that HT should be prepared to pay for information that will tell it with certainty what will happen to consumer spending next year (ie whether it will be low, medium or high)? Show clearly the method used.
Two possible methods (a. EV perfect info-EV imperfect info, or b. Minimum EOL)
HT\'s sister company, Clothesline, produces a trouser press for use by busy executives.
The annual demand function for the product is estimated at:
P = 380 - 0.02Q
MR = 380 - 0.04Q
(where P = price per unit, Q = annual quantity sold)
The firm\'s marginal cost function is given as: MC = 20 + 0.08Q
(v) Advise Clothesline on the output level and price that maximise sales revenue from the trouser press. (4 marks)
MR = 380 - 0.04Q = 0
Q = 380/0.04 = 9500, P = 380 - 0.02(9500) = 190
(vi) Calculate the output and price that maximise profits from the product.
MC = MR
20 + 0.08Q = 380 - 0.04Q
0.12Q = 360
Q = 360/0.12 = 3000, P = 380 - 0.02(3000) = 320
Assume now that the company is re-organised into separate manufacturing and distribution divisions, which both aim is to maximise profits. The total costs of the manufacturing division are estimated to be:
TC = 10,000 +10Q + 0.03Q2.
MCmfg = 10 + 0.06Q
MCdist = 20 + 0.08Q -(10 + 0.06Q) = 10 + 0.02Q
(vii) What is the optimal transfer price between the manufacturing and distribution divisions? (Assume that there is no external market for the product being transferred). (5 marks)
For astute candidates this is a straightforward (and easy question). With no external market, optimal transfer price (Pt) = MCmfg (at Q that maximises profit
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