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 2     The Energy Buster

(a)   Profit

In order to ascertain the optimum price, you must use the formula P = a – bQ

Where P = price; Q = quantity; a = intersection (price at which quantity demanded will be nil); b = gradient of the demand

curve.

The approach is as follows:

(i)   Establish the demand function

b = change in price/change in quantity = $15/1,000 = 0·015.

We know that if price = $735, quantity = 1,000 units.

Establish ‘a’ by substituting these values for P, Q and b into our demand function:

735 = a – 0·015Q

15 + 735 = a

Therefore a = 750.

Demand function is therefore P = 750 – 0·015Q

(ii)  Establish marginal cost

The labour cost of the 100th unit needs to be calculated as follows:

Formula = y = ax^b .

a = 1·5

Therefore, if x = 100 and b= –·0740005, then y = 1·5 x 100–0·0740005                = 1·0668178

Therefore cost per unit = 1·0668178 x $8 = $8·5345

Total cost for 100 units = $853·45.

–0·0740005

If x = 99, y = 1·5 x 99^–·0740005 = 1·0676115

Therefore cost per unit = $8·5408

Total cost for 99 = $845·55

Therefore cost of 100th unit = $853·45 – $845·55 = $7·90.

Therefore total marginal cost = $42 + $7·90 = $49·90.

Fixed overheads have been ignored as they are not part of the marginal cost.

(iii) Find profit

(1)   Establish the marginal revenue function

MR = a – 2bQ

MR = 750 – 0·03Q

(2)   Equate MC and MR

49·90 = 750 – 0·03Q

0·03Q = 700·1

Q = 23,337

(3)   Find optimum price

P = 750 – (0·015 x 23,337)

= $399·95

(b)   (i)   Penetration pricing

With penetration pricing, a low price would initially be charged for the Energy Buster. The idea behind this is that the price will make the product accessible to a larger number of buyers and therefore the high sales volumes will compensate for the lower prices being charged. A large market share would be gained and possibly, the Energy Buster might become accepted as the only industrial air conditioning unit worth buying.

The circumstances that would favour a penetration pricing policy are:

–    highly   elastic   demand   for   the   Energy   Buster   i.e.   the   lower   the   price,   the   higher   the   demand.   The   preliminary research does suggest that demand is elastic.

–    if significant economies of scale could be achieved by Heat Co, then higher sales volumes would result in sizeable reductions in costs. This is not the case here, since learning ceases at 100 units.

–    if Heat Co was actively trying to discourage new entrants into the market. In this case, new entrants cannot enter the market anyway, because of the patent.

–    if Heat Co wished to shorten the initial period of the Energy Buster’s life cycle so as to enter the growth and maturity

stages quickly. We have no evidence that this is the case for Heat Co, although it could be.From the above, it can be seen that this could be a suitable strategy in some respects but it is not necessarily the best one.

(ii)  Market skimming

With market skimming, high prices would initially be charged for the Energy Buster rather than low prices. This would enable Heat Co to take advantage of the unique nature of the product, thus maximising sales from those customers who like to have the latest technology as early as possible. The most suitable conditions for this strategy are:

–    the product is new and different. This is indeed the case with the Energy Buster.

–    the product has a short life cycle and high development costs that need to be recovered quickly. The life cycle is fairly short and high development costs have been incurred.

–    since high prices attract competitors, there needs to be barriers to entry in order to deter competitors. In Heat Co’s case, there is a barrier, since it has obtained a patent for the Energy Buster.

–    the strength and sensitivity of demand are unknown. Again, this is not the case here. Once again, the Energy Buster meets only some of the conditions which would suggest that although this strategy may be suitable the answer is not clear cut. The fact that high development costs have been incurred and the life cycle is fairly short are fairly good reasons to adopt this strategy. Whilst we have demand curve data, we do not really know just how reliable this data really is, in which case a skimming strategy may be a safer option.