Microeconomics for the Critical Mind

This chapter introduces to the approach to value and distribution that historically preceded the currently dominant supply-and-demand approach: the classical approach of Adam Smith, David Ricardo and Karl Marx, which nowadays many economists consider worth resuming. This helps the reader to perceive the present complex situation of economic theory, characterized by the coexistence of competing approaches. The chapter explains the views on wages, profits, land rent and growth of these three authors; introduces the notion of long-period relative prices and its connection with the labour theory of value; explains how the difficulties of the latter theory can be surmounted, using only elementary mathematics. The chapter ends by explaining how the modern Keynesian approach to aggregate demand can be integrated with the classical approach. In the online Appendix to the chapter the reader finds the very interesting argument by Ricardo that technical progress can increase unemployment; and, for the reader new to economics, some elements of national accounting useful to understand the Keynesian approach.

This chapter introduces to a mathematically rigorous determination of long-period prices. This requires some notions of matrix theory that this chapter explains: decomposable matrices, eigenvalues and eigenvectors, the fundamental Perron–Frobenius theorem on eigenvalues of non-negative matrices. These tools are used to prove the determinability of long-period prices (for economies with no joint products and no scarce natural resources—see Chap. 10 for the generalization to these cases), the relationship between rate of profit and real wage (also through the notion of standard commodity), the dependence of production methods on income distribution. The Samuelson–Garegnani peculiar model and an ‘Austrian’ model by Paul Samuelson illustrate the possibility of re-switching of techniques that will be important in Chap. 7. The chapter also introduces to the basics–non-basics distinction, to the notion of subsystem, and to the Leontief open model; the Leontief inverse connects to the notion of subsystems and clarifies the meaning of labour embodied in a commodity. Finally the theory of long-period prices is extended to include fixed capital. The online Appendix adds some clarifications on the possibility of a standard commodity with non-basics; explains the Hawkins–Simon conditions historically used for the study of the Leontief model; illustrates the notion of vertically integrated technical coefficients.

Via very simple models, this chapter introduces to the basic structure of the marginal/neoclassical approach to competitive value and income distribution, explaining the direct and the indirect factor substitution mechanisms that allow the derivation of decreasing demand curves for the factors labour, land and capital (assumed in this chapter to consist of a single good). For the newcomer to economics, the notions of production function, isoquant, isocost, cost minimization, utility function, marginal utility, indifference curve, utility maximization are synthetically introduced, postponing more rigorous definitions and special cases to Chaps. 4 and 5. The First Fundamental Theorem of Welfare Economics is presented in intuitive terms for an exchange economy and for a two-factors production economy; to this end Pareto efficiency, the Edgeworth box and the Production Possibility Frontier are introduced. No more advanced mathematics is used than simple partial derivatives and the rule for the derivative of implicit functions. Robinson Crusoe is used to show that according to this approach the market solves efficiency issues in the same way as an optimally planned economy. The chapter ends by contrasting marginal/neoclassical and classical approach on labour exploitation, relative wages, Say’s Law. The root of the differences is found in the presence in the marginal approach of factor substitution mechanisms derived from a generalization of Ricardian intensive rent theory. The online Appendix to the chapter contains additions on the stationary state assumption and on the determination of intensive rent when advanced wages are separated from seed-corn.

This chapter is a standard chapter on mainstream consumer theory and demand theory, with the addition of an introduction to the general equilibrium of pure exchange which allows illustrating the importance of continuity of consumer demand functions for the existence of general equilibrium. It notices the different interpretation of consumption demand depending on whether one is determining a long-period or a short-period or an intertemporal equilibrium. It covers the standard notions of consumer theory, including indirect utility, expenditure function, elasticity of substitution, CES utility functions, Roy’s Identity, Shephard’s Lemma, Slutsky equation, substitution and income effects, saving decision, duality, Hicksian aggregability of goods, equivalent variation, compensating variation, consumer surplus, revealed preference. The Kuhn-Tucker theorem is introduced to study utility maximization. On labour supply the chapter argues that the standard upward-sloping shape is unrealistic, and proposes a more realistic shape with a discontinuity at the subsistence level. The Gorman consumer aggregability conditions are explained but the conditions for the existence of a general-equilibrium representatitve consumer are shown to be different from the Gorman conditions. The weak axiom of revealed preference is shown not to extend to market demand functions if there isn’t a representative consumer.

This chapter presents, in more rigorous form than in Chap. 3, standard producer theory and uses it to explain the notion of Marshallian short- and long-period partial equilibrium of a product market. It cautions about the dangers of netputs; it distinguishes three meanings of returns to scale; it illustrates activity-analysis isoquants; it studies cost minimization and profit maximization via the Kuhn–Tucker approach; it explains the profit function, the Weak Axiom of Profit Maximization, the Weak Axiom of Cost Minimization, Shephard’s Lemma for firms, Hotelling’s Lemma; it discusses inferior inputs and rival inputs; it illustrates the notion of quasi-rent; it explains the role of free entry for the notions of price taking and perfect competition. The Pareto efficiency of competitive partial equilibrium is proved. Then, after a criticism of the frequent assumption of a given number of firms, the equations of the non-capitalistic general equilibrium of production and exchange (without joint production) are presented, and it is shown that this equilibrium can be interpreted as an equilibrium of exchange: of indirect exchange of factor services. Demand is shown to influence relative product prices through its influence on income distribution. Some doubts are raised on whether preferences are as persistent and reversible as the approach would need them to be. The online Appendix to the chapter adds further observations on the influence of demand on product prices and develops formulae for the factor demand conditional elasticities used in applied research. The present chapter introduces to the neoclassical theory of competitive firms so as to arrive at the general equilibrium of production and exchange, still without capital goods. It will familiarize you with:

This chapter presents the main results on existence, uniqueness and stability, first of the general equilibrium of pure exchange and then of the non-capitalistic general equilibrium of exchange and production. For the exchange economy, attention is given to problems raised by survival; two proofs of existence of equilibrium are explained. On uniqueness, the chapter illustrates the Sonnenschein–Mantel–Debreu result and criticizes the usefulness of the notion of regular economies; Hicks’s conviction that income effects largely neutralize one another is questioned with a graphical example. On stability, the chapter presents the proof of tâtonnement stability under the Weak Axiom holding for market demand, using the notion of Lyapunov stability. For the production economy, the chapter notes that the gross substitutes assumption does not guarantee uniqueness, that the tâtonnement encounters a problem that renders a planner–auctioneer indispensable and that a new cause of possible instability arises, self-intensive consumption: Harry Johnson’s attempt to minimize its likelihood is reported. Mandler’s proof of stability under the Weak Axiom is reported, but an observation by Hildenbrand and Grodal renders the Weak Axiom even more unlikely to hold in a production economy. The online Appendix completes the criticism of regular economies by supplying an example.

This chapter explains how the founders of marginalist theory apart from Walras included capital goods into general equilibrium: by formulating long-period general equilibria in which the endowments of capital goods are variables, endogenously determined by the equilibrium, and treated as temporary embodiments of a single factor ‘capital’ capable of changing ‘form’ without changing in amount, whose endowment is given. This treatment of capital is needed to obtain a persistent equilibrium, and factor substitutability. But the determination of the given endowment of capital is logically circular. There are also demand-side deficiencies of this treatment of capital, highlighted by reswitching and reverse capital deepening. The ‘Austrian’ approach of Wicksell is shown to suffer from the same weaknesses. Hicks’s confusion between static and secular stationary equilibrium is dispelled. The meaning of traditional production functions with capital as one of the inputs is explained. Then the notion of Aggregate Production Function is illustrated, and its deficiencies highlighted. It is added that at the observed prices, wages may well correspond to the value marginal product of labour, but the causality is from wages to value marginal products, not vice-versa as the marginal approach argues. A final section argues that some perception of these problems favoured the shift in the 1930s to the currently dominant neo-Walrasian notions of general equilibrium (discussed in the next chapter). The online Appendix presents simplified Walrasian and Wicksellian models of general equilibrium to clarify their approaches.

This chapter presents the neo-Walrasian notions of intertemporal general equilibrium (without and with overlapping generations), and of temporary general equilibrium. It concentrates first on intertemporal equilibrium and explains futures markets, dated commodities, discounted prices, own rates of return. The indefensible assumption of complete futures markets can be avoided by assuming Radner sequential equilibria with Arrow securities and perfect foresight, but perfect foresight is logically indefensible, novelties cannot be predicted. The abandonment of the traditional method of long-period positions causes several problems, particularly serious are the impermanence problem, the price-change problem, the substitutability problem. The adjustment of investment to savings is simply assumed, in the tâtonnement too. The reference to intertemporal equilibria as the rigorous microfoundation of macro analyses is argued to be a smokescreen, the opposite of the truth; it is a previous faith in the neoclassical approach in its traditional versions that justifies the credit given to intertemporal equilibria as descriptive. Overlapping-generations intertemporal equilibria do not avoid these problems but reveal further interesting aspects: equilibria need not be in the core (the notion of core is explained), need not be Pareto efficient, and can be robustly indeterminate. Then the chapter illustrates the difficulties that explain why temporary equilibria have been abandoned. The online Appendix to the chapter includes. first, an example that clarifies the difference between the uniform convenience of all investments in an intertemporal equilibrium, and the long-period notion of uniform rate of return on all investments, and second, a brief explanation of the ‘neoclassical synthesis’ for the readers without a background in economics.

This chapter consists of two parts; first, a standard introduction to choice under uncertainty, and second, how uncertainty is introduced into general equilibrium theory. It starts with lotteries and utility over lotteries, it defines Von Neumann–Morgenstern expected utility and the axioms that justify its form; then it introduces the Arrow–Pratt measure of absolute risk aversion, CARA and CRRA utility functions, stochastic dominance, Jensen’s inequality and discusses how risk aversion explains insurance, risk pooling and portfolio selection among risky assets, including Tobin’s preference for liquidity. Then the chapter mentions state-dependent utility and subjective expected utility. A discussion of Allais’ and Ellsberg’s paradoxes is followed by an introduction to prospect theory. The notion of informational cascades allows an enlightening use of Bayes’ Rule. Then the chapter moves to how uncertainty is introduced into general equilibrium theory; after a section on traditional marginalist authors, the chapter describes the intertemporal general equilibrium with contingent commodities and introduces the Radner equilibrium with uncertainty. There follows a short introduction to incomplete markets and sunspot equilibria. The chapter ends with a summing up of conclusions on general equilibrium theory, which is found difficult to defend. The online Appendix explains the Anscombe–Aumann approach to the existence of subjective expected utility; then it reports Wilson’s example of non-existence of equilibrium with incomplete markets, and finally it reports an interesting page on insurance by Alfred Marshall that gives a taste of how traditional authors dealt with uncertainty.

This chapter asks whether a return to the theory of long-period prices can be a fruitful alternative to the problematic neo-Walrasian general equilibrium determination of prices. First, it discusses whether modern analyses undermine the traditional thesis of a gravitation towards a uniform rate of return, or of profit, on capital; the conclusion is that the traditional view remains convincing. Then the chapter enlarges the theory of long-period prices to include joint production and extensive and intensive land rent, using mostly a graphical analysis but also some results from linear programming; the meaning of negative labours embodied is clarified; some unusual forms of land rent appear; some cases emerge in which technical choice does not seem to bring to definite results. Then the chapter reports some discussion on the treatment of quantities as given in the ‘core’ (Garegnani’s meaning of the term) of classical theory, and on whether Sraffa’s analysis needs or not constant returns to scale. The conclusion is of moderate optimism, there are open problems but they do not appear to undermine the long-period method.

This chapter is an introduction to game theory, and to its application to situations of asymmetric information. It covers simultaneous and sequential games, dominant strategies, Nash equilibrium, backward induction, subgame perfection, repeated games, Bayesian games, sequential rationality, behavioural strategies, perfect Bayesian equilibrium, sequential equilibrium. The Centipede game is taken as an incentive to be critical of the usual definition of rationality; some doubts are also raised about the universal certainty that dominant strategies will always be played: some examples of Prisoners’ Dilemma suggest as plausible that players may choose ‘Cooperate’. The treatment of auctions is limited but rigorous, it is proved that a first-price sealed-bid (independent-private-values) auction and a second-price sealed-bid auction generate the same expected revenue for the seller, and on this basis the revenue equivalence theorem is sketched; for common-value auctions the winner’s curse is examined in detail. Then the chapter passes to asymmetric information, and discusses principal-agent, moral hazard, adverse selection, screening, signalling, and the intuitive criterion of Cho and Kreps. The dependence of all these analyses on the assumption that agents choose on the basis of VNM expected utility, which does not seem to correspond to how people actually choose, is noticed.

This chapter discusses real-world competition in product markets. It distinguishes flexible-prices markets from administered-prices markets; it argues that manufacturing firms mostly adopt full-cost pricing, which is associated with planned spare capacity; it discusses the determinants of spare capacity and concludes that capacity utilization is highly variable, which requires a reformulation of cost curves, and has important macroeconomic implications. The determination of desired capacity brings to discuss the determinants of the investment decisions of firms, and some widely accepted theories on this issue, in particular adjustment costs, are found unacceptable. Then the chapter passes to the theory of monopoly, which is straightforward although monopolies often do not exploit all their power in order not to incur sanctions by antitrust authorities (for space reasons the extensions of monopoly theory to discrimination and natural monopolies are in the online Appendix to the chapter). On oligopoly, all the standard oligopoly models are presented, including the Bertrand-Edgeworth model which produces no equilibrium; the game-theoretic interpretation of both the Cournot and the Bertrand model is found objectionable; monopolistic competition s compared with full-cost pricing; price matching is found a plausible hypothesis, with its consequence the kinked demand curve. Repeated interaction, cartels, and folk theorems are also discussed. The indeterminateness of oligopoly theory is greatly reduced by actual or potential free entry, which is argued to be extremely relevant because competition is more active than one might think even in markets with few firms and differentiated products. The online Appendix includes: a section on discrimination, patents, and natural monopolies; the proof that the Bertrand equilibrium is the same even admitting mixed strategies; a section on advertising and the Dorfman-Steiner model; and a presentation of the Cournot-Bertrand model by Kreps and Scheinkman, with a discussion of proportional versus efficient rationing.

This chapter is about welfare economics. After some considerations on the value judgements implicit in the notion of Pareto efficiency, the chapter explains why externalities and public goods are not efficiently treated by a market economy, and what can be done to correct the inefficiencies; the Coase theorem; the tragedy of the commons; and some problems with the Internet. Then it presents rigorous proofs of the First and Second Fundamental Theorems of Welfare Economics and notes the generally accepted limitations of the two theorems, which bring to critical considerations on the Pareto efficiency criterion itself. A non-neoclassical perspective adds further criticisms of the two Fundamental Theorems, above all the absence of full employment; the implications are important for the assessment of the welfare state. Cost–benefit analysis is argued to be potentially useful although potentially dangerous, with examples. Then the chapter explains the notion of social welfare function and its uses, followed by a proof of Arrow’s famous Impossibility Theorem; Arrow’s assumptions are found to be dispensable and aimed at showing the impossibility of an ethically neutral economic advisor, a perfectly acceptable conclusion. The chapter ends with a discussion of aspects of the economics of happiness that suggest that welfare economics ought to be centrally concerned with avoiding unemployment and reducing the working week. The online Appendix raises the difficult issue of the optimal amount of resources to be allocated to innovation.

This chapter is a review of the mathematical notions used in the book beyond elementary calculus; it is to be used as a quick refresher; it does not in the least aim at making it superfluous to attend dedicated maths courses or to study mathematical economics textbooks. Some mathematical notions used in the book, for example Kuhn–Tucker theorem, Envelope Theorem, eigenvalues and eigenvectors, Perron–Frobenius theorem on non-negative matrices, separating hyperplane theorem, are mentioned but not explained in this chapter because introduced in the text when first needed. The chapter covers: convex sets; convex and concave functions; matrices; connection between dot product and angle between vectors; hyperplanes; definite matrices; quadratic forms; open and closed sets; convergent sequences; sets of measure zero and genericity of a property; homogeneous functions and Euler’s theorem; gradient, Jacobian, Hessian; derivative of a function of several variables; directional derivative; total derivative; correspondences and upper hemicontinuity; expansion in Taylor series; second-order conditions for an optimum without and with constraints; linear programming and duality; complex numbers; a review of basic notions of probability and statistics, including Bayes’ Rule, properties of covariance, correlation coefficient, order statistics; Poisson process.