Advanced: Construction of cost and revenue functions when learning curve effects exist Delroads Electronics Ltd (DEL) produces a variety of products including an electronic navigational unit for use in ships. Construction of the unit is a delicate assembly operation by a team of highly- skilled operatives. Components used in the unit are purchased from outside manufacturers. The unit is sold in relatively small numbers, and a new model is produced each year.
Costs associated with production of the new model of the unit are:
• fixed costs £35 000 • variable costs £20 wages per labour hour worked, plus £20 materials per unit Production of the first unit of the new model will take 60 labour hours, and work of the operatives is known to be subject to an 83% learning curve effect. Learning curve effects are achieved only within a model.
Market research has forecast that annual sales of the new model are associated with unit prices as follows:
1 unit can be sold at unit price £10000 500 units can be sold at unit price £327.80 Requirements:

(a) Explain what a learning curve effect is, and suggest reasons for the effect in this particular case. (6 marks)

(b) Draw a diagram (accurately to scale) on the graph paper supplied, demonstrating the rela¬ tionship between units of output, total costs and total revenues in respect of the new model. Set out sufficient workings to justify your diagram. (12 marks)

(c) Use your diagram and supporting workings to identify the profit-maximising units of output and unit price in respect of the new model.
(7 marks)
Notes: In evaluating learning curve effects you should use the cumulative average time equation

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y= a/x0.269 or y = ax ax-0.269 In evaluating the link between revenue and output you should use the equation y = ax"