Notes and References

CHAPTER 1

1. In a famous example, Carnegie used to estimate future demand for steel by counting the number of chimneys issuing smoke in Pittsburgh.

CHAPTER 2

I. This reads: 'Total revenue is a function of output.' The letter f is conven­tionally used, but any other letter would suffice.

2. Averages themselves may be difficult to find, even if totals are known, if output is of more than one kind.

3. Strictly speaking, where Ax= I unit. 4. Mathematically

dy

dx

limit Llx~o

5. The proof of all these rules of differentiation is given in Alpha C. Chiang, Fundamental Methods of Mathematical Economics, 2nd ed. (Tokyo: McGraw­Hill, Kogakusha, 1974) chap. 7.

6. Similarly if y = u - v dy du dv

dx dx dx

7. Implicit in the concept of a derivative is the assumption that x is continu­ous, i.e. we can produce 0.5, 0.1, 0.001, etc., units of x.

8. As total revenue equals price times output, this is equivalent to the demand function P = 6 - x. Then total revenue = Px = ( 6 - x )x = 6x - x 2 .

9. Mathematically, x = -2 gives the minimum of this function, as (d2 n)fdx2

is positive at this point. 10. The symbol a is used rather than d to refer to the partial, rather than the

total, derivative. 11. The modern technique of linear programming, however, can deal with in­

equality constraints. See Chap. 12. 12. This is a maximum as d2 Ilfdy2 = -8.

240 Fundamentals of managerial economics

CHAPTER 3

1. J. Wiseman, 'Costs and Decisions'. Paper presented at Association of University Teachers of Economics Conference at York, 1978, (forthcoming).

2. To concentrate attention on essential aspects of decision-making, a number of simplifying assumptions have been made throughout this example, e.g. only three possible levels of sales are considered.

3. This precludes the possibility of stocking bread for more than one day, which we have removed by assumption.

4. With more durable goods the cost of holding stock must be considered. This is another type of decision problem (see Chap. 14).

5. This utility function corresponds to diminishing marginal utility of money. The marginal utility of money = f1U/AM, which is the slope of the utility function.

6. An indifference curve shows combinations of characteristics that yield the same total utility.

See R. G. Lipsey, An Introduction to Positive Economics, 3rd ed. (London: Weidenfeld & Nicolson, 1972) pp. 173-80.

7. This is a decision-theory convention. The economist would regard losses as having negative utility, but this can create problems for the approach adopted here.

8. This section is quite complicated and may be omitted without loss of continuity.

CHAPTER 4

1. Capital gains on sale of assets by a firm give rise to profits which are in a rather different category from those profits arising from the normal activities of the firm in producing goods and services.

2. Throughout this chapter we are concerned only with the accountant in his role of correctly recording monetary items. We are not concerned with how ac­countants may interpret these amounts in practice. However, there is evidence that such interpretations are made on the basis of historic cost.

3. Inflation Accounting: Report of the Inflation Accounting Committee; Chairman, F. E. P. Sandilands (London: H.M.S.O., 1975).

CHAPTER 5

1. We should note that some economists, notably Professor Milton Friedman, would deny the importance of realistic assumptions in formulating theories. In essence he says that a theory is only to be judged by its predictive power, and it is sufficient for the firm to act 'as if' it were maximising profits. Whether it actually wants to maximise profits is irrelevant and hence not worthy of employ­ing economists' time (see M. Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1935) pp. 3-43.

2. The values to be attached to these weights, as well as the whole concept of present value, are discussed in Chapter 13.

3. A. A. Berle and G. C. Means, The Modern Corporation and Private Prop­erty, rev. ed. (New York: Harcourt, Brace & World, 1967).

4. J. K. Galbraith, The Affluent Society, 2nd ed. (Harmondsworth: Penguin Books, 1970); J. K. Galbraith, The New Industrial State, 2nd ed. (Harmonds­worth: Penguin Books, 1975).

Notes and references 241

5. In many cases the main shareholders, directors and managers would be the same individuals. In other cases they would be closely associated.

6. W. J. Baumol, Business Behaviour, Value and Growth (New York: Mac­millan Co., 1959; rev. ed. New York: Harcourt, Brace & World, 1967).

7. This is at the point of unit elasticity on the demand curve- see Chap. 7 (p. 98)- total revenue of or' is generated.

8. 0. E. Williamson, 'A Model of Rational Managerial Behavior', in A Be­havioral Theory of the Firm, ed. R. M. Cyert and J. G. March (Englewood Cliffs, N.J.: Prentice-Hall, 1963).

9. It is formulated in mathematical form and the interested reader is referred to Williamson, op. cit., for greater detail.

10. R. L. Marris, 'A Model of the Managerial Enterprise', Quarterly Journal of Economics, vol. 77 (1963) 185-209.

11. See Marris, op. cit., for further details. 12. H. A. Simon, 'A Behavioural Model of Rational Choice', Quarterly

Journal of Economics (Feb 1955) pp. 99-118. p. R. M. Cyert and J. G. March, A Behavioral Theory of the Firm (Engle­

wood Cliffs, N.J.: Prentice-Hall, 1963). 14. This has links with Williamson's concept of 'managerial slack', discussed

previously.

CHAPTER 6

1. Under certain conditions the firm may be able to influence the external environment by planning, advertising and political activity (see Chap. 10, p. 153).

2. We should also note the possibility of physically identical goods being perceived as different products by the public. For example, a certain physical good may be manufactured under brand label X for the general market, and manufactured under license to a retailer who will sell it under an own brand of Y. It may well be the case that consumers do not see Y as a close substitute for X, especially if they are not competitively displayed in the store.

3. A further complication is that the price charged to the retailer is often arrived at indirectly by a discount from the retail price to the consumer. Hence the demand curve itself is related to final retail prices in a complex way. This is discussed in more detail in Chap. 11 (p. 174 ).

4. There may be further complications in regard to tax- e.g. delay or relief on corporation tax on specific investment expenditure- e.g. setting up new plant and equipment in areas of high unemployment where the Government gives tax incentives.

5. Ownership by a firm of a given area often does not carry the legal right of ownership of minerals under the area, or any right of extraction.

6. See A. Koutsoyiannis, Modern Microeconomics, 2nd ed. (London: Mac-millan, 1979), chap. 6: 'Monopoly', pp. 177-9.

7. This is comprised of the aggregate of firms' marginal cost curves. 8. See Chap. 4, p. 49, for discussion on this point. 9. SA C2 is the short-run average cost curve associated with the optimal plant

size. 10. A similar difficulty in respect of monopoly was discussed earlier in this

chapter (p. 77).

242 Fundamentals of managerial economics

CHAPTER 6 -APPENDIX

1. This is a two-person zero-sum game, since the gains for one are equal the losses for the other. Both cannot gain or both lose.

2. The problem can also be solved by linear programming (see Chap. 12, p. 184).

3. The modulus symbols I xI refer to the absolute value of x. Therefore if x>O, i"xl=x,andifx<O, lxl=-1 times x.

4. The decision theory of Chap. 3 (p. 24) can now be seen as a game against nature, with events interpreted as the moves of nature. However, in this situation the maximin criteria may be inadequate, as it is inappropriate to assume that nature would react in the worst possible way.

CHAPTER 7

1. See, for example, W. Duncan Reekie, Managerial Economics (Oxford: Alan, 1978)p.ll7.

2. It should be obvious that an unconstrained sales-revenue maximiser would operate where Ep = 1.

3. This problem is not specific to price elasticity, but applies to all elasticity measures.

4. This problem is discussed more explicitly in the section on multi-product pricing (see Chap. 11, p. 169).

5. Alternatively the 'raw' data can be adjusted to take account of seasonal or cyclical variations.

6. For example, see Julian Simon, Applied Managerial Economics (Englewood Cliffs, N.J.: Prentice-Hall, 1975) pp. 304-7.

7. The method of least squares is adequate in providing a straight line of best fit through the observations. However, there are circumstances where the linear approach is inadequate and polynomial functions (for example, quadratic or cubic) must be estimated. The procedure is then more difficult and is more fully described in Alpha C. Chiang, Fundamental Methods of Mathematical Economics, 2nd ed. (Tokyo: McGraw-Hill Kogakusha, 1974).

8. Thusi) = ("kD)/n and P = ("kP)/n. 9. We would now have four equations to solve simultaneously for the four

parameters a, {3 1 , {32 and {33 • For a more detailed explanation of multiple regres­sion, see K. A. Yeomans, Statistics for the Social Sciences, vol. 2 (Harmonds­worth: Penguin Books, 1973) pp. 191-234.

10. The conditions for identification are discussed in more detail in Baumol, Economic Theory and Operations Analysis, 3rd ed. (London: Prentice-Hall International, 1972) appendix to Chap. 10.

11. See, for example, M. Dutta, Econometrics (Cincinnati: Southwestern Publishing Co., 1975) chap. 4, on the problems of serial correlation and heteros­cedasticity.

12. There are other supplementary tests of the goodness of fit of a regression equation. These can be found in any intermediate statistical text.

13. The least-squares method of estimates is too complicated to be used for the logistic function. The 'three-points method' is normally used to estimate values of a, k and b (see, for example, Yeomans, op. cit., chap. 5). The function­al forms outlined above are by no means exhaustive.

Notes and references 243

14. One of the problems of market experiments is that unless the experiment is performed for long enough only the first two stages may be reported, resulting in misleading sales projections.

15. For a more comprehensive discussion of estimate appraisal see H. Theil, Applied Economic Forecasting (Chicago: Rand McNally, 1966).

CHAPTER 8

1. The isoquant is convex since a concave isoquant would represent technic­ally inefficient production methods, i.e. production technique involving more of all inputs for a given output level compared to an alternative technique.

2. For example, take output Q1 and techniques T1 and T2 •

K

L

Figure 8.9(a)

A point A (involving OR of capital, and OS of Labour) is possible via factoring OA into its constituent vectors OM and OP using the Parallelogram Law of vector addition. Thus ON of K and OG of Lon T1 , plus OH of K and OF of Lon T2 will give the required output Q, with total input use OR of K and OS of L.

3. Except in the rare case of the relative cost of K and L being equal to the slope of a portion of the isoquant -in which case there are multiple solutions on the 'flat' portion, rather than a unique corner solution.

4. Except in the rare case where the cost of labour and capital is equal to the

244 Fundamentals of managerial economics

slope of the isoquant, and hence all combinations (i.e. any technique) are optimal.

5. This is a multiplicative production function analogous to the exponential function described in Chap. 7 (p. 108).

6. These probabilities are calculated using the binomial distribution introduc­ed in Chap. 3. Denote by p the probability of each man not being absent (p = 0.9). Then q = 1 - p = 0.1 We wish to find the probability of at least 10 men being available if 11 are employed. Then x = 10, n = 11.

P(x ;;;.to)= P(x = lO)+P(x = 11)

CHAPTER 9

=ttCto(0.9)to (O.l)t +11Ctt(0.9)11 (O.l)o

""0.7.

1. From Chap. 2 (p. 10) the slope of the total cost function is equal to marginal cost. Thus if marginal cost is determined, the slope of the cost function is also determined.

2. For a fuller explanation see Chap. 8, p. 124. 3. In fact, for the mathematically initiated, average fixed cost describes a

rectangular hyperbola. 4. This provides us with the justification for 'standby tickets' at greatly

reduced prices. Suppose the aircraft has a capacity for 200 passengers and 170 seats filled at time of take-off. Then as long as the standby ticket price is more than £8.00, selling standby tickets will increase total profit (as long as demand for standard tickets is not affected).

5. A. A. Alchian, 'Costs and Outputs', in The Allocation of Economic Re­sources, ed. M. Abramovitz (California: Stanford University Press, 1959), reprinted in Price Theory, ed. H. Townsend (Harmondsworth: Penguin Books, 1973) pp. 228-49.

6. Ibid. p. 233. 7. Note that because costs are incurred at different time intervals they are

here expressed in present value terms (see Chap. 13 (p. 207) for a discussion of present value).

8. Alchian, op. cit., p. 242. 9. The differences between economists' and accountants' cost concepts are

discussed in Chap. 4. 10. Joel Dean, Managerial Economics (Englewood Cliffs, N.J.: Prentice-Hall,

19 51) p. 260. Others, notably J. Wiseman, have forcefully argued that oppor­tunity cost is a subjective concept, and therefore impossible to record. 'Costs and Decisions'. Paper presented at Association of University Teachers of Econo­mics Conference at York, 1978 (forthcoming).

11. J. Johnston, Statistical Cost Curves (New York: McGraw-Hill, 1960). 12. C. A. Smith, 'Empirical Evidence on Economies of Scale', in The Theory

of the Firm, ed. G. C. Archibald (Harmondsworth: Penguin Books, 1971) p.28.

CHAPTER 10

1. D. Dunbar, Advertising: Facts and Figures. Paper No.8 of series 'The Case for Advertising' (London: J. Walter Thompson, 1976).

2. Factory cost, administration, royalties, etc.

Notes and references 245

3. National Board for Prices and Incomes, Report No. 113, Cmnd 4066 (London: H.M.S.O., 1966).

4. See Table 10.1 for a comparison of the importance of advertising for different products.

5. This is equivalent to assuming that the supply curve for the good is per­fectly inelastic, so that when advertising shifts the demand curve, the same quantity is sold at a higher price.

6. The general Baumol sales-revenue maximisation model is introduced in Chap. 5, p. 66).

7. I.e. total revenue is a positive but decreasing function of advertising.

CHAPTER 11

1. Note that the pricing decision only occurs in markets which are imper­fectly competitive. Under perfect competition price is given, and the only element to be decided by the firm is the quantity to be produced.

2. This data problem also applies to other market structures: oligopoly, monopolistic competition, etc.

3. For an excellent concise discussion see F. M. Scherer, Industrial Pricing: Theory and Evidence (Chicago: Rand McNally, 1970) chap. 4.

4. Probably the most influential of these was the study by R. L. Hall, and C. J. Hitch, 'Price Theory and Business Behaviour', Oxford Economic Papers (1939) pp. 12-45, reprinted in Oxford Studies on the Price Mechanism, ed. P. W. S. Andrews and T. Wilson (Oxford: Oxford University Press, 1951) pp. 107-38.

5. This result is dependent on the assumption of linear costs. If production is on the downward part of a U-shaped average-cost curve, then MC is less than A VC, and the equation will result in a price higher than that which maximises profit.

6. This contrasts with the profit-maximising approach where fixed costs are paid out of the revenue from each product depending on the cost and revenue functions for the product. However, there is no process of 'sharing' the fixed costs. They are determined residually in the process of arriving at the optimal price and output combinations for each product.

7. The calculus of price discrimination is demonstrated in E. F. Brigham and J. L. Pappas, Managerial Economics (New York: Dryden Press, 1972) pp. 297-302.

8. Except for a few exempt goods, e.g. in the United Kingdom, books and certain pharmaceutical goods.

CHAPTER 12

I. I. H. Ansoff, Corporate Strategy: An Analytic Approach to Business Policy for Growth and Expansion (Harmondsworth: Penguin Books, 1968) p. 113.

2. Ibid. p. 116. 3. I.e. firm A taking over firm B considers its acquisition as desirable as a

whole, but does not see each product taken over as desirable in the light of demand and cost conditions, and its own rival products.

4. If competition is imperfect the second term is negative (price falls as out­put expands) and MR < P.

246 Fundamentals of managerial economics

5. The method can also be used for three variables, by drawing in three dimensions, but the necessary geometry becomes complex.

6. In practice this means choosing as Z a common multiple of coefficients in the objective function, so that the objective function is located conveniently on the graph.

7. There are several (equivalent) procedures termed the Simplex method. The one adopted here we find most useful.

8. Note that if units of y 1 and y 2 are measured in kilograms, each unit of y 3

will weigh t'. + f = : : kilograms. Thus each ! : kilograms of y 3 will contain 3 units of starch and 4 units of protein.

9. Note that these shadow prices refer to the problem after the constraints have been simplified by dividing through by the common denominator. Thus the shadow price of A above refers to the effect on profit of changing the first constraint from x + 2y.;;;;; 10 to x + 2y.;;;;; 11 and this refers to 5 units of A in the original problem (see p. 188).

CHAPTER 13

I. See Chap. 5, p. 68, above. 2. See Chap. 12, p. 180, for discussion of diversification. 3. It is conventional to use '0' to denote the present, so that year 1 is one

year into the future, etc. 4. One solution is to combine the expected-value and risk-premium ap­

proaches. If, for example, project A is considered more risky the discount rate could be raised to 12 per cent, and the new expected net present value calculated.

5. H. M. Markowitz, 'Portfolio Selection', Journal of Finance, vol. vii, no. 1 (Mar 1952) 77-91, reprinted in The Theory of Business Finance: A Book of Readings, ed. S. H. Archer and C. A. D'Ambrosio (New York: Macmillan Co., 2nd ed. 1976) pp. 150-63.

6. It is unusual for the sum of required outlays to exactly equal the funds constraint. The constraint can be written in inequality form (where sum of required funds is less than or equal to the constraint), and the problem solved by linear programming, with the maximisation of present value as the objective function.

CHAPTER 14

I. This is assuming holding costs increase at a constant rate from it to it+t over the period. Then the average cost per unit of stock held is Ut + it+t )/2.

2. This point is similar to that made about plant size and flexibility: see p. 139.

3. The loss of sales through lack of stock depends on the reactions of custo­mers which in turn depends on the type of good (is demand postponable?), the availability of alternative supplies and the strength of customer loyalty.

4. F. M. Scherer, Industrial Pricing: Theory and Evidence (Chicago: Rand McNally, 1970) p. 21.

5. This assumes a steep U-shaped average cost curve, so that there are strong incentives for keeping output constant.

6. Scherer, Industrial Pricing, provides general empirical evidence for this pattern of behaviour. The example provided- copper, machinery and fabricated metals -all satisfy the conditions outlined above.

Notes and references 247

7. This coincidental feature of this model (that total order costs equals total holding costs at the optimum) is due to the particular geometrical properties of the rectangular hyperbola. Note that at q * the tangent to total holding cost curve is equal and opposite to the tan~ent to total ordering costs.

8. This is a minimum as (d2 T)f(dq ) = (2Sa)/(q 3 ) > 0. 9. This is a minimum as

6cdq 2Sa - +- >o.

8 q3

In this example optimum order quantity does not occur when total holding cost equals total ordering cost.

Answers to Numerical Questions

CHAPTER 2

1 (i) MPL = 5 - 2L + K. MPK = L + 4 - 6K. (ii) MPL = 10 +2L +9L2 +2K -2LK.

MPK=2L -L2 +8K -6K2 •

2 (i) Q=a/2(3, (ii) Q=.,;;iiC (iii) Q=(a-b)/2((3+c). 3 x 1 =8. x 2 = 14. Z= 128.

CHAPTER 3

(i) Produce 1000 books (expected profit= £1000). (ii) Produce 2000 books (expected opportunity loss= £0).

2 (i) No overhaul (expected cost= £340). (ii) Overhaul (expected cost= £400).

CHAPTER 6

4 (i) A plays III, B plays II, value of game = 2. (ii) A plays II and III in the proportions t, %, while B plays I and II in the

proportions t, %. The value of the game = - t.

CHAPTER 7

5 D= 80- 5P. (i) TR=l6Q-(Q2 )/5. AR=(80-Q)/5. MR=l6-(2Q)/5.

(iii) D =50. Ep =- 0.6 (iv) Ea =- 0.78. (v) P= 8.

Notes and references

CHAPTER 8

3 MPL = 5 -2K +2I(l. MPK=4LK- 2L -10K.

{i) Returns to labour constant. Returns to capital depend on the size of L. If L > 2f then increasing returns to capital If L < 2f, diminishing returns to capital.

(ii) Returns to scale vary with the magnitude of LandK.

CHAPTER 12

3 Z = 2. x1 = 1. x2 = 0, X3 = 0.

4 Profit=42. x 1 =4,x2 =2.

5 Z = 1242 A = 1.47 B = 3.16

6 V1 =0.05, V2 =0.17. Z= 130. X= 50, Y= 10.

CHAPTER 13

5 {i) PVA = - 14. {ii) IRRA = 11.5.

CHAPTER 14

PVB =- 129.2. /RRB =4.8.

2 {i) E.O.Q. = 10 tons. M.A.C. = £60. {ii) Yes. Stock costs increase £5, purchase costs fall £18

249

{iii) If the number of orders stays the same as in (i), E.O.Q. must remain at 10 tons. Then holding costs must fall to 15 per cent.

Index

absolute value 91 n acquisition cost 232 advertising 152-63

as a cost of production 154 distribution of 152 elasticity 152 and market share 153 optimal budget 155-9 and sales revenue maximisation

159-61 and size 154 and time 161-2

Agee, M. H., Taylor, R. E., and Torgerson, P. E. 236

Alchian, A. A. 143-5, 150 Ansoff, I. H. 180, 181 Archer, S. H., and D'Ambrosio, C. A.

223 aspiration levels 71 average profit method 206-7

Baumol, W. J. 3, 20, 44, 66,67, 107n, 111,159,202

Bayes Theorem 40 Beed, C. S. 74 Berle, A. A., and Means, G. C. 64,

64n binomial distribution 39, 128 n break-even analysis 140-2 Brigham, E. F., and Pappas, J. L.

170 n, 178 business decisions 1-3

capital market 214 capital rationing 221 Carsberg, Bryan 3

cartel 85, 166 certainty-equivalent 219 change-of-sign rule 216 Chiang, A. C. 11 n, 102 n Cobb-Douglas production function

124, 127,128 coefficient of determination 103,

147 competition 75-6

perfect 79-82 pure 82 monopolistic 82-4

constrained optimisation 18-20, 184 consumer

demand 94-9 durables 95 goods 96

Cookenboo, L., Jnr 151 cost 130-51

average 5, 6, 133 of capital 209 current 52 empirical analysis 145-50 engineering approach 150 functional form 146-9 historic 48, 50 long-run curve 135-7 marginal 5, 10, 132 and output dimensions 143-5 relationship between short- and

long-run 137 replacement 50 short-run functions 131-5 of stocks 225 survivor technique 150

cost-plus pricing 167-8

covariance approach 220-1 Cyert, R. M., and March, J. G. 68n,

71-3,

Dean,Joel 57,111,145,150,163, 178

decision theory 24-44 an example 42-4

decision-tree analysis 35-7 demand 94-111

elasticity 96-9 estimation 99-111 firm 99 forecast assessment 11 0 functions 94-9 industry 99 and multiple products 182-4 replacement 96 and time 99, 109 and uncertainty 226-7

depreciation 50-2 and investment 208

derivatives 9-17 application of 13-17 concept of 9-10 partial 17-18,95 rules for fmding 11-13

diminishing returns, law of 133 discounting 204,207-9

the discount rate 209-10 discount tables 222 and taxation 221

distributive margins 174 diversification 180-2, 205 Dorfman, R. 202 Dorfman, R., Samuelson, P., and

Solow, R. 202 Doyle, P. 163 duality 195-202 Dunbar,D. 153n Dutta, M. 107 n

economic models 2 economies of scale 138-9 Egerton, A. 44 elasticity 96-9

advertising 104, 152 arc 98

Index

cross 99 income 99, 104 and marginal revenue 98, 167 point 98 price 98, 104 and price discrimination 170 and pricing 98

entry and advertising 153 ease of 164

estimation assessment 11 0 costs 145 -50 demand 99-109

expansion path 130 expected net present value 217-21 expected value 23,217

251

of perfect information 25-6 exponential function 104, 107, 124 n

feasible region 187, 194 basic feasible solution 189

Ford Motor Company 76 Friedman, Milton 60n, 150

Galbraith, J. K. 65 game theory 87-92

dominance 88 example 91 mixed strategies 88-91 value of a game 89

gross present value 208 growth maximisation 69-71

Hall, R. L., and Hitch, C. J. 167n Hawkins, C. J., and Pearce, D. W. 223 Heineke, J. M. 111, 129 Hirshleifer, J. 223 historic-cost convention 48

identification problem 105-7 income effect 95 indifference curves 31, 31 n, 220 inferior goods 9 5 inflation

accounting 52-4 and investment 209 pricing 168, 177 and stocks 225-6

252

input substitution and capacity 118-19 limited substitution 116-17 perfect substitution 116, 122 zero substitution 114, 122

integer programming 202 integration 181 internal rate of return 208

and present value 210-17 inventories 225-36

and demand estimation 226-7 inventory models 229-36 and oligopoly 228-9 speculation in 225-6

isocost 122 isoprofit 118 isoquant 116-19, 121, 127 investment 204-21

capital rationing 221 covariance approach 220 discounting 207-17 discount tables 222 multi-period analysis 215-17 optimal distribution 210-4 and taxation 221 traditional appraisal methods

205-7 types of decision 205 and uncertainty 217-21

joint products 183-4 Johnston, J. 148

Kay,J. A. 57 Kierstead, B. S. 92 kinked-demand model 86-7 Kotler,P. 163 Koutosyiannis, A. 74, 79 n, 92, 111,

129

Lagrange multipliers 19-20,89, 184 lead time 229 least squares 102, 104, 147 limit pricing 165 linear programming 184-202

duality 195-201 general form 185

Index

graphical method 186-8 and investment 221 n minimisation problems 193-5 non-linear programming 202 Simplex method 188-93

Upsey, R. G. 31 n logistic function 108

McGuiness, T., and Cowling, K. Ill Machlup, F. 74 managerial objectives 59-74 managerial utility 68-71, 204 marginal analysis 4-20

and cost-plus pricing 168 marginal cost 5, 10, 132

of advertising 156 relationship to marginal product

133 as transfer price 171

marginal efficiency of capital 209 marginal factor productivity 117,

123,133 marginal rate of substitution 117,

120 marginal revenue 5, 76

ofadvertising 156 and multiple products 182-3

market structure 75-87 and advertising 153 and pricing 164-6 and stocks 226

Markowitz, H. M. 220 n Marris, R. L. 69 maximin criteria 88 maximisation

of the difference between two functions 15-17

of a function 13-15 and linear programming 184-93 of a multivariate function 17-18

mergers 182 Merrett, A. J., and Sykes, A. 223 minimax criteria 88 minimisation 13-15

and linear programming 193-5 oflosses 26-7

mongrel curve I 06 monopolistic competition 82-4

Index 253

monopoly 76-9 and advertising 153 pricing 164-5

multiple products definition 179-82 and linear programming 184-6 pricing 169-70 production of 182-4

multi-product firms 179-202

Needham, D. 92 net present value 208 non-linear programming 202 Nordquist, G. L. 74 normal goods 95 normal regression equations

103

objective function 185 oddments, method of 91 oligopoly 84

and advertising 153,155 collusive 85-6 and game theory 87-92 non-collusive 86-7 pricing 165-6 and stocks 228-9

opportunity cost 48, 50, 145 of capital 208-10, 225

opportunity loss 26, 40-1 an example 42-4

optimisation 1-2 constrained 18-20, 184 and linear programming 184, 191,

201 organisational slack 73 output, dimensions of 143-5

Parker Pen Company 76 Parry Lewis, J. 20 partial differentiation 17-18 payback method 206 peak profit method 206 penetration price policy 165 perfect competition 79-82, 153 pivoting 190-3 plant size 135

and flexibility 139

posterior probability analysis 37-41 power structures 64-6 prediction errors 110 present value 62,204-19 Price Commission 61 price leadership 86, 166 pricing 164-78

and advertising 155 cost-plus pricing 167-8 and government regulation 177 and investment 204 limit pricing 165 monopoly pricing 7 6-9, 164-5 of multiple products 169-70 oligopoly pricing 85-7,165-6 penetration policy 165 price discrimination 170 retail pricing 174-7 skimming policy 165 spare part or component pricing

173-4 transfer pricing 171-3

primal 195 probability 23 Procter & Gamble 7 6 producer goods 96 product Jefinition 76-8, 84

multiple products 179-82 production 113-29

Cobb-Douglas production function 124, 127

efficiency 119-20 long-run 126-8 of multiple products 182-4 optimal input combinations 120-3,

130-1, 184 functions 113 short-run 123-6 and stocks 226

profit 46-57 accountant v. economist 46-54 contribution analysis 142 definition 4 7-8 and depreciation 50-2 and inflation 50-4 managerial earnings and manage­

ment capital 49-50 measurement period 46-7

254

and performance 55-6 sources of 56-7

profit margins and cost-plus pricing 167-8 and retailing 17 4-7

profit maximisation and advertising 155-9 critique of 63-6 definition 60 and elasticity 98 and investment 204 and oligopoly 229 rules for 8 theories 59-66 time period 60-3

pure competition 82

quantity discounts 174 and stock costs 234-5

Raiffa, H. 44 Reekie, W. Duncan 98 n regression 102-4, 145 replacement cost 50 retail pricing 17 4-7 retailing 78, 174 returns to sc::le 126-8

and the cost curve 135-7 risk 22, 29-30

and investment 206, 217-20 and multiple products 181-2 premium 217 risk-aversion 29-30, 206 risk-structure 220

Rolls-Royce 163, 182 Royal Dutch Shell 179

saddle-point 88 St Petersburg paradox 30 sales-revenue maximisation 66-8

and advertising 159-61 Sandilands Report 52-4 satisficing 71 Scherer, F. M. 92, 165 n, 178,

228 n, 229 n, 236 shadow prices 197-200

Index

Silbertson, A. 74 Simon, H. A. 71 Simon, Julian 101 n, 223 Simplex method 188-93

and duality 198-200 skimming price policy 165 slack variables 189 Smith, C. A. 151 Stigler, G. 150 stocks 225-36

and oligopoly 166, 228-9 optimal stock 229-36

substitution effect 95 survivor technique 150

tax and investment 221 profit 78-9 and transfer pricing 173 value-added 78-9

Taylor, B., and Wills, G. 178 Theil, H. 110 n transfer pricing 171-3 trend curves 1 07-9

uncertainty 22-44 causes of 22 and diversification 182 and inventories 226-9 andinvestment 217-21

Unilever 77, 179, 182 utility

and decisions 28-35 function estimation 32-5 functions 29

value-added tax 78-9

Watson, D. S. 178 Weber, Jean D. 20 Weston, J. F. 202 Williamson, 0. E. 66, 204 Wiseman, J. 22 n, 44, 145 n

Yeomans, K. A. 104n