Chapters 15 and 16
Study Guide by James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida
Oser Summary Main Page
Chapter 15: Mathematical Economics
Mathematical economics refers to a method of using graphs and mathematical symbols to supplement verbal explanations of definitions, postulates, and conclusions related to economic theory. Therefore, this chapter does not represent a separate school of economic thought, but a number of economic topics where math has been applied to enhance the analysis.
Econometrics
Econometrics is essentially a tool kit that combines theoretical, mathematical and statistical analysis to test economic theory, and to provide answers to a variety of questions related to economic phenomena. Input-output analysis and linear programming are examples of econometric techniques. The term econometrics was introduced by Norwegian economist Ragnar Frisch in 1926. The Econometric Society was founded in 1930 and publishes the journal Econometrica. Changing conditions such as growing government intervention in the economy, market analysis needed by large corporations, and unions stimulated econometric research. Explanations were needed for economic processes such as propensities to save, elasticities of demand, workers responses to wage changes, and farmers decisions based on market prices.
General Equilibrium
General equilibrium analysis considers the interrelationships between the various variables in the economy as a whole. The idea is that any change in the economy radiates outward with a gradually diminishing effect much like dropping a stone in a pond causes ever widening circles of ripples. General equilibrium theory provides an over-all framework of the basic price and output relationships for the economy as a whole. However, the theory does not provide a framework for determining actual prices, and it has not contributed to our understanding of economic growth and other changes over time.
Indifference Curves
Indifference curves were first used by Francis Ysidro Edgeworth (1845-1926) and Vilgredo Pareto (1848-1923) to avoid measuring utility quantitatively and exactly. An indifference curve joins all points that represent equal satisfaction. The case of two goods that are perfect substitutes is illustrated below with nickels and dimes.
Each indifference curve in the illustration above represents a different level of satisfaction 20 cents, 30 cents and 40 cents. Considering the curve that represents 30 cents, a person is equally well off regardless of which combination of nickels and dimes is indicated by a point on the curve, e.g., 6 nickels or 3 dimes, 4 nickels and 1 dime, or 2 nickels and 2 dimes.
Another case is where there is no substitutability between goods illustrated below with left shoes and right shoes. A person is better off as he moves to the next curve up and to the right, but equally well off at any point on one of the curves, e.g., 3 left shoes and 2 right shoes provides a person no more satisfaction than 2 left shoes and 2 right shoes.
A third example is illustrated below for two products that are partially, but not perfect substitutes for each other, potatoes and meat. Curves 1 and 2 are indifference curves showing a consumer's satisfaction with various combinations of potatoes and meat. Line 3 is a price line showing the amount of potatoes and meat that could be purchased with a certain amount of money, 20 pounds of potatoes or 4 pounds of meat, or some combination of potatoes and meat along line 3. Where line 3 is tangent to indifference curve 1 (point A) gives the greatest satisfaction with the combination of potatoes and meat that can be obtained with the amount of money represented by line 3. If the price of meat were cut in half, the consumer could buy 20 pounds of potatoes or 8 pounds of meat or some combination of potatoes and meat illustrated by the new price line 4. The consumer could move to the higher indifference curve 2 and obtain a higher level of satisfaction at point B.
Input-Output Analysis
Input-output analysis was developed by Wassily W. Leontief (1906-1999) and is similar to Quesnay's Economic Table discussed in Chapter 3. The original idea was to present general equilibrium theory in a simplified form to be used for empirical research. The analysis involves an input-output grid showing the relationship of each segment of the economy to every other segment. The rows in the input-output grid or table show the sales made by one economic sector to every other sector. The columns show what each sector purchased from every other sector. Assumptions of this type of model include: 1. the coefficients are assumed to be fixed, 2. production functions are assumed to be linear, and 3. prices are not variables given factor supplies, consumer demands, and prices set by those conditions. These assumptions are rather unrealistic, technological changes make the grid obsolete, and revisions to the forty thousand entries (the 1947 table) represent a tremendous task. The analysis is more suitable to a planned economy such as socialism, rather than a free enterprise economy such as capitalism. For some applications of input-output analysis to accounting, see my Chapter 14: Appendix 14-2: Input-Output Accounting in the related summaries below.
Linear Programming
Linear programming was developed during and after World War II and used by the United States Air Force. It is also used to solve many types of problems such as allocating scarce resources to maximize some predetermined objective. Oser provides two simple examples with graphic solutions. The first illustration involves finding the combination of two types of medicine to obtain the required quantity of the ingredients in each to stay healthy. Another example involves a cattle producer who wants to fatten his steers most economically with various possible combinations of hay and cottonseed cake, both containing the four required nutrients: protein, minerals, vitamins, and carbohydrates. For three similar illustrations, see my TOC problems and introduction to linear programming listed in the related summaries below.
Game Theory
Game theory applied to economic problems is based on John von Neumann's (1903-1957) and Oskar Morgenstern's (1902-1977) The Theory of Games and Economic Behavior published in 1944. The theory is applicable to situations analogous to games of strategy such as chess and poker, and it is complex and heavily mathematical. There are games of chance such as dice-shooting, and games with strategic uncertainty that include what the other player will do. Oser provides a simple example to illustrate the idea.
Chapter 16: Early American Economists
Franklin
Benjamin Franklin (1706-1790) was a scientist, inventor, philosopher, journalist, publisher, statesman, and diplomat. He founded many things including an academy of learning that later became the University of Pennsylvania. He invented an improved stove, a lightning rod, bifocals, and a glass hormonica. He advocated crop insurance and daylight savings time, and conducted emperiments and made observations on electricity, heat and light, earthquakes, chimneys, weather, climate, botany and medicine. He published a number of papers aganinst slavery, and in 1829 published The Nature and Necessity of a Paper-Currency using Sir William Petty's labor theory of value to attact mercantilism. According to Franklin, a country's riches should be valued by the quantity of labor its people are able to purchase, not by the quantity of silver and gold that they possess. Money is needed to carry on trade, but too much is of no use, and too little raises interest rates and cheapens land. Low interest rates will motivate investment in land, increase land values and invigorate trade that will help to remedy the excess of imports over exports and subsequent loss of specie.
In 1751 Franklin wrote Observations Conserning the Increase of Mankind, Peopling of Countries, Etc. claiming that population grows most rapidly when the means of sustenance are most plentiful. Population tends to double in America every twenty years where plenty of land is available and agriculture and handicrafts will continue to expand. The demand for British manufactured goods will continue to grow and America will not be able to produce manufactured goods more cheaply than the mother country because slave labor is more expensive than free labor.
In 1769 he glorified agriculture expressing the physiocratic doctrine that there are three ways for a nation to gain wealth: war which is robbery, commerce which is cheating, and agriculture which is the only honest way. In 1771 Franklin wrote that manufacturing only changed forms so that no wealth is created, but manufacturing does expand the market for agricultural products and keeps money within the country. Franklin viewed manufacturing as mainly a means to promote agriculture.
Paine
Thomas Paine (1737-1809) was more of a political pilosopher than economist, but he had a number of interesting views related to economics. In Rights of Man, Part II (1792) he advocated disarmament, independence of South America to open up trade, progressive taxation, old age pensions, free public education, and government work for the unemployed. He was an early advocate for a government sponsored social security system. In Agrarian Justice published in 1796 he provided an explanation for widespread poverty in the most advance nations. Man, according to Paine has a right to occupy the earth, but not to own any part of it. The fault of private land ownrship is with the system not with the present possessors, and it should be corrected over successive generations with a 10 percent tax on inheritances received by direct heirs, and a 100 percent tax if there are no direct heirs. The funds should be used to give fifteen pounds to every person reaching the age of twenty-one, ten pounds per year for life to those after age fifty, and ten pounds per year to those younger than fifty who are blind or lame or otherwise incapable of earning a livelihood.
Paine has received less attention than he deserves because of his attack on orthodox religious doctrines in The Age of Reason (1796). For example, in Chapter 1 of The Age of Reason Paine wrote that all national institutions of churches appear to be "no other than human inventions set up to terrify and enslave mankind, and monopolize power and profit."
Hamilton
Alexander Hamilton (1755-1804) was a pamphleteer, statesman, financier, and promoter of American nationalism and economic growth. He was on General Washington's staff during the Revolutionary War and a leading participant at the Constitutional Convention advocating an aristocratic centralized federal government. He was the first United States secretary of treasury in Washington's cabinet, and he used his influence to have Thomas Jefferson elected president in 1800, rather than Aaron Burr who later killed Hamilton in a duel.
Hamilton was a mercantilist (see Chapter 2) which is understandable since the American economic system was underdeveloped and the country could not compete effectively in manufacturing and trade with western Europe. He favored a strong industrial-commercial-financial system with business interests supported by a strong central government. In his Report on Manufactures submitted to the House of Representatives in 1791 he destroyed the physiocratic analysis (see Chapter 3). Hamilton argued that agricultural labor was less productive than highly skilled industrial labor, and that manufacturing was not sterile, but instead provided a surplus in the form of profit. He enumerated seven advantages of manufacturing: the division of labor, an extension of the use of machinery, added employment of people not ordinarily at work, promoted emigration from foreign countries, furnished a greater scope of talents and abilities, promoted the spirit of enterprise, and expanded the market for farm products. He viewed government interference and aid as indispensable, and recommended high protective tariffs and financial rewards and privileges to encourage new inventions and discoveries.
In his First Report on the Public Credit (1790) as secretary of treasury, Hamilton urged the federal government to guarantee full payment on all outstanding state and federal obligations at face value. A sound government debt would promote trade, manufacturing, and agriculture. Interest rates would be lowered, and land values would increase as money became more plentiful. In his Report on a National Bank (1790) he showed his understanding of banks creating credit though fractional reserve requirements by stating that money deposited in a bank will become the basis of a paper circulation since banks can circulate a greater sum than their actual capital in gold and silver. Paper could serve as money just as well as precious metals, and the wealth of a nation should be measured "by the quantity of the productions of its labor and industry." Hamilton was an enlightened mercantilist in that he blended the mercantilist ideas with more modern theory promoted by Adam Smith (See Chapter 5) and others.
Carey
Henry Charles Carey (1793-1879) inherited the leading publishing house in the United States from his father and produced an enormous publication output centered around four major themes: permanent protectionism, an attempt to revise Ricardian rent theory, his harmony-of-interest doctrine, and his opposition to Malthusian pessimism on population.
Carey became an ardent protectionist and attributed almost all the evils of the world to international trade. He wrote that foreign trade annihilates towns and villages, causes soil exhaustion, unemployment, war and plunder. It increases the wasteful transportation of goods, and compels more people to transport goods with production being neglected. The sailor and the wagon driver are constantly exposed to the grogshop and the brothel.
Carey disputed Ricardo's rent theory (see Chapter 6) saying that men go from poorer soil to better soil which causes rents to fall. Ricardo built his rent theory on static conditions assuming constant technology as the population increased. Carey developed the opposite idea that man's mastery over nature would increase average yield per acre, i.e., increasing returns to labor and capital rather than diminishing returns. Ricardo was correct for a static system, but Carey's principle of historically increasing returns has been correct for advanced countries.
Lawyers, traders, brokers, and shippers profit unduly through their activities, and impede the progress of society. Individuals and nations blinded by the idea of profit, pursue it to the exclusion of the common good, but in the long run everybody gains as society grows wealthier and more productive. The harmony of classes will lead to a harmony of nations with love and peace diffusing throughout the earth.
Malthus was incorrect because the Lord directed mankind to be fruitful and multiply, man's cooperation and mastery of nature will improve, plants and lower animals will provide the necessities for humanity, and as people become more intellectual, they will have fewer children, and the lower animals will decrease lowering the carbon dioxide in the atmosphere. The Divine Plan works harmoniously.
Walker
General Francis Amasa Walker (1840-1897) was a veteran of the Civil War, superintendent of the United States censuses of 1870 and 1880, a professor of political economy at Yale, and later president of Massachusetts Institute of Technology. He became the first president of the American Economic Association in 1885, and also served as president of the American Statistical Association.
Walker made two major contributions to economic thinking. He clearly distinguished between the roles of the capitalist and the entrepreneur, and attacked the wages-fund doctrine stating that labor is a residual claimant to the value of the output. The capitalist lends his wealth and receives interest as the reward for abstinence. Interest is the same for all capital except for differences in risk. The entrepreneur directs the efficient functioning of labor and capital, and receives profit as a reward for his industrial success. Profit is analogous to rent entering into the price of the product and causes no decrease in the wages of labor.
Walker denied the validity of the wages-fund doctrine saying that wages do not depend on the number of workers who share a fixed wages fund. Instead, wages represent a residual share of the product after rent, interest, and profit. This is the same as Jevons views on wages, but not Ricardo who said profits represented the residual share. Wages, according to Walker would increase as workers became more efficient and productive.
According to Walker, economic harmony would prevail under a system of perfect competition. However, where competition is imperfect, the population will sink lower and the rich will grow richer which requires limited state intervention to promote perfect competition, and a more equitable distribution of burdens and benefits throughout society.
George
Henry George (1839-1897) was at one time a gold prospector, a farm hand, a printer, a newspaper reporter, editor, and publisher. He published Progress and Poverty in 1879 after observing the speculative land craze in San Francisco in 1868, and the political corruption, monopolists, and profiteers associated with the construction of the transcontinental railroad. Although he could not find a publisher until he paid for the plates himself, two million copies of the book were printed over the next twenty-five years in many languages. George ran for mayor of New York City in 1886 on a labor party ticket, but lost to a Democrat who many believe stole the election from George. A young Theodore Roosevelt was the Republican candidate. George wrote the platform that favored taxation of land values, abolishing other taxes, municipal ownership of railroads and telegraph, and reforming the ballot system. Henry George ran for mayor again in 1897, but died on the Thursday before the election after speaking at four meetings.
The idea of taxing land values was based on Ricardian analysis (Chapter 6), although Ricardo was opposed to such a tax because he viewed it as unjust to tax only one class of people. George's proposal was more like the French physiocrats idea (Chapter 3) to only tax economic rent. But the physiocrats believed land was the only true source of wealth. George, on the other hand believed land rent was unearned income and should be taxed away completely. According to George, Produce = Rent + Wages + Interest. Therefore, Produce - Rent = Wages + Interest. Wages tend to be minimized because rents increase faster than society's productive power. Profits are also adversely affected by rising rents. George was opposed to socialism and socialistic solutions. For example, he viewed a graduated income tax as excessive government regulation which reduces the incentive to accumulate wealth. Instead, all economic rent derived from land should be taxed. Society creates rising land values, and the unearned income from land should belong to society. Present land owners should retain their titles to the improvements on the land such as building, and these should be tax free. No other taxes would be required since there would be a single tax on the economic rent of land.
_________________________________________
Go to the next Chapter. Chapter 17: The Institutionalist School: Thorstein Veblen (Summary).
Go to Chapter 1 and the links to all Chapters. (Summary).
Related summaries:
Sealth (Seattle), Chief. 1854. How Can You Buy or Sell the Earth? Chief Sealth's (Seattle's) reply to President Franklin Pierce. (Chief Seath's reply).
Martin, J. R. Not dated. A note on comparative economic systems and where our system should be headed. (Note).
Martin, J. R. Not dated. Chapter 14: Appendix 14-2: Input-Output Accounting - Illustration with Profit Centers and Transfer Pricing. Management Accounting: Concepts, Techniques & Controversial Issues. Management And Accounting Web. Chapter 14 Appendix
Martin, J. R. Not dated. TOC problems and introduction to linear programming. Management And Accounting Web. TOC Problems Intro To LP
Milanovic, B. 2019. Capitalism, Alone: The Future of the System That Rules the World. Harvard University Press. (Summary).
Piketty, T. 2014. Capital in the Twenty-First Century. Belknap Press. (Note and Some Reviews).
Porter, M. E. and M. R. Kramer. 2011. Creating shared value: How to reinvent capitalism and unleash a wave of innovation and growth. Harvard Business Review (January/February): 62-77. (Summary).
Thurow, L. C. 1996. The Future of Capitalism: How Today's Economic Forces Shape Tomorrow's World. William Morrow and Company. (Summary).
