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Economic foundations for finance. From Main Street to Wall Street. (English) Zbl 1430.91004

Springer Texts in Business and Economics. Cham: Springer (ISBN 978-3-030-05425-0/hbk; 978-3-030-05427-4/ebook). xi, 178 p. (2019).
Finance, a relatively young science, is a combination of three fields: business administration, economics, and mathematics. Learning finance without its foundations might lead to a misunderstanding and misapplication of finance theory. The aim of this book is to cover the economic foundations of finance and to give an introduction to financial economics.
A major contribution of this book is that all market prices are considered from the perspective of the households as well as the firms. Both approaches need to lead to the market prices that balance supply and demand, otherwise the market equilibrium is not complete.
The book is organized as an Introduction, 7 Chapters and Conclusion. Also, three appendixes: ‘Mathematical tools’, ‘Sufficiency of the first order conditions’ and ‘Covariance of the stochastic differential equations and returns’, are given.
In the Introduction of the book some basic assumptions as rationality of decreasing marginal utility and decreasing marginal productivity, also and the market equilibrium are reminded. Three important functions of the financial markets – the intertemporal substitution of consumption, the enable risk sharing among many individual and the important information function are considered and graphically illustrated.
In Chapter 3 – the basic economical model, the definition of market equilibrium is presented. The interaction of firms and households is summarized in form of a circular flow diagram. The mathematical model of the market equilibrium is presented. Also, the basic feature of the market equilibrium is developed. Two basic observations – the absolute level of prices and wages does not matter in a marketMean Field Ga equilibrium and the second property is the Walras’s law, are developed and their mathematical models are given.
The important properties and assumptions of the production and utility functions are presented. The decision problems of the firm and the households are described. It is shown how the technological progress and population growth change the market equilibrium. The results of the implementations of the first welfare theorem and Walras’s law are described. The results under the assumption of a Cobb-Douglas product functions are presented. This chapter finishes with some exercises.
In Chapter 4 the basic economical models from Chapter 3 is extended to the model to capital. A market equilibrium in an economical model with a capital market is defined. At the different roles of households in a model with capital is looked. The households’s maximization problem and the profit maximization problem are mathematically described. Also, the cost minimization problem of firms is considered. The Walras’s law in the basic economical model is derived. Some fundamental properties of the interest rate are presented and discussed. The mathematical model of the central planner’s problem is developed. The decision problem of the household and the optimal investment decision of the firm are graphically illustrated and discussed. The concepts of the Cobb-Douglas product function and the logarithmic utility are presented. The effects of the population growth and the technological progress to the total utility function are shown.
In Chapter 5 the two-period model of previous chapter is extended to a model with multiple periods. The market equilibrium in a multiperiod setting is studied. Also, it is shown that the first Welfare Theorem holds. The effect of population growth and technological progress is examined. The mathematical model with time periods is developed. The form of the total utility function is given. Implementations of Modigliani and Miller theorem to the payout policy of mathematical model the firm are presented. Some graphically illustrations of the market equilibrium are presented. In two subsections of this chapter is examined how the market equilibrium changes with population growth and technological progress. The mathematical models and geometric illustrations are given. The distinguish between equity and dept is developed. It is explained how the population growth and technological progress affect stock prices and how stock returns compare to the returns on debt when there is no uncertainty. Also, the so-called Gordon growth model is developed. A simple valuation formula for the shares of growing is presented. In the end of this chapter the return on equity and the return on debt are compared.
In Chapter 6 the model to uncertainty in order the explain the crucial difference between equity and debt is extended. The concept of the uncertainty structure is presented under assumption for independent and identically distribution of the states. The case of two possible states is illustrated as a tree. Here, the infinite-horizon intertemporal planner’s optimization problem from Section 5.5 by adding uncertainty conditions is extended to the optimality condition to the planner’s problem. In the next section the market equilibrium is mathematically described. First the household’s decision problem is derived. The firm’s decision problem is also considered. The concept of the profit maximization problem of the firm is given. In Section 6.5 the return that households require for providing capital to the cost that firms are willing to pay in order to raise capital are compared. Some generalizations of the irrelevance propositions from Section 5.2 that go back to Miller and Midigliani theorem are presented. An estimate of the stochastic discount factor is obtained from option data. Two well-known asset pricing models – the more general consumption based capital asset pricing and the capital asset pricing model are derived.
Chapter 7 elaborates the results of Stiglitz within the discrete-time infinite-horizon model of Chapter 5 extended by exhaustible resources as an additional input factor for production. The Hotelling’s rule in the presence of population growth and technical progress is reconsidered. The mathematical model of the maximization problem of the central planner is developed. The notion of a market equilibrium with exhaustible resources is given. Under three input factors and resource-augmenting technological progress the Cobb-Douglas production is presented. The technological progress is considered as a growth driver. To analyze the model with a general rate of technological progress it is proceed as in Chapter 5 and the model is rewrite in labor-effective units. The components as economy grows, capital, output, consumption and the extracted exhaustible resource are explained. In the next step, in the case of a logarithmic unity function and a Cobb-Douglas production function how population growth and technical progress affect prices is investigated. This chapter finishes with exercises.
In Chapter 8 it is shown that the assumption of a complete market suffices that the entire economy can be modeled by a representative firm interacting with a representative household. It is shown that the first welfare theorem holds so that the market equilibrium allocations are Pareto-efficient in an economy with heterogeneous-agents. The notion of the complete financial market is given. Also, the notion of time-uncertainty structure is recalled and discussed. The so-called fundamental theorem of asset pricing is applied to a self-financing trading strategy. The notion of an intertemporal market equilibrium with multiple heterogeneous households and firms is defined. The first welfare theorem is presented and proved. It is shown how the multiple households in the economy can be aggregate into one representative households, which allows to determine equilibrium asset prices. The problem of an aggregation of firms is considered.
Chapter 9 of the book is a conclusion. The main accents here are the non-standard preferences to obtain time-varying risk aversion as a source of excess volatility, changes in the distribution of wealth, non-rational expectations, non-market interactions and sequential equilibria.
The book contains three appendixes. Because the book is intended for readers with relatively small interests to mathematics, in Appendix A some mathematical notations are reminded. The notions of function, continuous function, monotonically increasing and decreasing functions, concave and convex functions are reminded. Some notations related with ordinary and partial derivatives are presented. A notion of a homogeneous functions and the Euler’s theorem are given. Some notations from constrained optimization are reminded. Some elements of the probability as expectation, variance and covariance are explained. Some elements of the vector and matrix calculation are given. The systems of linear equations are explained.
In Appendix B the sufficiency of the first order conditions are presented.
In Appendix C the covariance of the stochastic differential equations is explained.

MSC:

91-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance
91G15 Financial markets
91B50 General equilibrium theory
91B62 Economic growth models
91B66 Multisectoral models in economics
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