# MICROECONOMICS II. Author: Gergely K hegyi. Supervised by Gergely K hegyi. February 2011

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1 MICROECONOMICS II. Sponsored by a Grant TÁMOP /2/A/KMR Course Material Developed by Department of Economics, Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department of Economics, Eötvös Loránd University Budapest Institute of Economics, Hungarian Academy of Sciences Balassi Kiadó, Budapest Author: Gergely K hegyi Supervised by Gergely K hegyi February

2 ELTE Faculty of Social Sciences, Department of Economics MICROECONOMICS II. week 1 Factor markets and income distribution, part 2 Gergely K hegyi Prepared by: Gergely K hegyi, using Jack Hirshleifer, Amihai Glazer és David Hirshleifer (2009) Mikroökonómia. Budapest: Osiris Kiadó, ELTECON-könyvek (henceforth: HGH), and Kertesi Gábor (ed.) (2004) Mikroökonómia el adásvázlatok. kertesi/kertesimikro/ (henceforth: KG). Endowment; buying and selling Where does income come from? So far we have considered I income as given in p 1 x 1 + p 2 x 2 = I budget constraint. Let's assume that we have ω 1, ω 2 amounts from the consumed goods, where (ω 1 0, ω 2 0). In this space of goods (ω 1, ω 2 ) is the vector of endowment. Self-suciency (autarchy): x 1 = ω 1, x 2 = ω 2, U(ω 1, ω 2 ). If market exchange of goods is possible (taking p 1, p 2 prices as given), total income from selling the goods is: I = p 1 ω 1 + p 2 ω 2 The new budget constraint (utility function is unchanged): p 1 x 1 + p 2 x 2 = p 1 ω 1 + p 2 ω 2 Lagrange-function: L = U(x 1, x 2 ) λ(p 1 x 1 + p 2 x 2 p 1 ω 1 p 2 ω 2 ) Demand: x i (p 1, p 2, ω 1, ω 2 ) Net demand: x N i = x i ω i Buying: x N i > 0, selling: x N i < 0 2

3 Endowment eect Slutsky theorem with Slutsky decomposition: Change in demand due to income change: Change in income due to price change: I p j x M i I = ω j (E.g.: (p 1ω 1+p 2ω 2) p 1 = ω 1 Endowment eect: Slutsky theorem: x M i I ω j E.g.: x M i p j = xs i p j xm I (x j ω j ) x M (p 1, p 2, p 1 x 1 + p 2 x 2) p 1 = 3

4 x S (p 1, p 2, x 1, x 2) xm p 1 I (x 1 ω 1 ) Optimal decision of the resource owner Work time and freetime Income: I Working hours: L Freetime (hours): R "Disposable" time (hours): R L + R = R Wage (price of a working hour and also the price of a freetime hour): h L = I R Total income: I = Ī + h LL, where Ī is the starting income (not from work). Budget constraint: h L R + I = h L R + Ī Utility function (with respect to free time and income): U(I, R) Both income and freetime are goods (as opposed to bads): U I Utility function (with respect to work hours and income): U(I, L) Income is a goods while work is a bad: U I Marginal rate of substitution: U > 0; L < 0 MRS R I R U MU R MU I Lagrange function: L = U(R, I) λ(h L R + I h L R Ī) First order condition: L R = MU R λh L = 0 L I = MU I λ = 0 h L R + I h L R Ī = 0 U > 0; R > 0 Optimum condition: MU R MU I = h L Optimum The E staring endowment consists of Ī income and R freetime. The (absolute value of the) slope of the budget constraint equals the hourly wage (rental fee) which one can gain by sacricing free time. The G point is the optimal decision of the resource-owner. 4

5 Income and price change 5

6 1. Statement. Changing the h L rental fee has an income and opposite sign substitution eect. With low income the substitution eect is larger: if someone works at all, with larger h L will make her work more. With higher income income eect can counteract substitution eect: increasing wages can act as an incentive to decrease work hours. Supply of labor The slope of the individual supply curve of labor is positive until the h L wage level, then it "bends back". Welfare and social security Eect of welfare Without any welfare the individual optimum is at G point on the U 0 utility function, where the employee would earn 7000 dollars, and would work = 250 days a year. If the welfare system guarantees a 6000 dollar minimum wage, (supplementing her wage if it is under this level) the real budget constraint will be MLK curve, with a break at L. 6

7 Labor force participation rates in the US Year man over 60 man over , , ,5 2010* 19,5 * forecast Source: Hirshleifer et al., 2009, 504. Equilibrium on the factor markets Labor market Labor market equilibrium Aggregate labor demand (D L ) and aggregate labor supply (S L ) curves. Equilibrium wage: h L Employment rate: L 7

8 Factors inuencing the labor market Demand side eects Technology. The level of technological development aects the marginal product functions of dierent resources and also the interaction between them. Demand for the nal product. The consumer preferences aect the demand for the nal product, and this indirectly aects the marginal product functions of the dierent resources used for the given nal product. Supply of complementary or substitute resources. The supply of complementary or substitute resources (depending on the strength of interaction) aect the marginal product of a given resource. Supply side eects Preferences.The preferences of the employees over work and leisure time, and over dierent jobs or occupations aects the shape of the resource-supply curves. Wealth. Preferences are aected by individual wealth. Richer people tend to keep most of their resources. So the greater one's wealth is, ceteris paribus, the less she is likely to oer for sale on the market. Demography. The size of the population, and also its age and sex composition also aects the labormarket supply; moreover it could also aect the supply of land and other resources. (Remember the example of black death in the previous chapter!) Social forces and laws. There are several jobs that woman could not have done (and cannot do still today). Child labor is still illegal in most countries. Laws can also constrain the use of land or other resources for dierent reasons (e.g. environmental protection). Potential reason for increasing gender wage gap Changes in wage dierences in the USA, (1963=100) Possible explanations: Year 90. percentile median 10. percentile Source: Hirshleifer et al., 2009, 516. International competition. Barriers of international trade have decreased over the last couple of decades. The expansion of trade and the growing international division of labor have increased the real wages internationally. Some groups, however, have suered. Uneducated low wage American labor have to compete with even lower waged Chinese, Indian, etc., uneducated labor force. On the other hand, highly educated European, Japanese, etc., labor also puts up a competition for the well educated highly paid Americans. It is not evident, therefore, that free trade, alone, would have increased wage dierences within the US. Technological change. The development of computers and other technology intensive jobs have increased the demand for high skills (analytical skills, adaptability, etc.). Low skilled labor, who can oer no more than physical strength, cannot prot from this (only as a consumer). On the other side the level of education of the US population have also increased. Thus the demand for as well as the supply of highly educated workforce have increased. So the net eect of technological change on wage dierences is not evident. 8

10 Factor market monopolies Trade union membership in the private and the public sector (million employees, ratio of trade union members) total empl. trade union memb. total empl. trade union memb. million million % million million % Private sector 71,2 11, ,6 8,7 8 Public sector 15,6 5, ,4 7,3 38 Source: Hirshleifer et al., 2009,520. Functional income distribution Conventional classication: Labor, Capital, Land LAND VERSUS CAPITAL. Land was traditionally dened as "the power of the natural and inexhaustible soil", while capital was "instrument used to produce". The "power of the soil" (fertility, location... etc.), however, is often the result of human activity. People have discovered the American continent, or have drained the great swamps in England. We might think that land and capital diers in their supply: while the quantity of the land is xed (supply curve is vertical), the production made capital has an upward sloping curve. The supply of land is not xed, however. On the one hand it can grow as a result of rising prices: gain land from the ocean. On the other hand it could become infertile, or erode. Even if the quantity of land would be physically xed, the quantity available for the market would denitely react to changing prices, because the owners can always decide to keep it for themselves. LABOR VERSUS CAPITAL. Labor and capital cannot be separated "functionally". In a modern society people do not oer their sole physical strength, but their skills and other characteristics as well, which is based on their education and experiences. The capital is thus not only the tool, but can also be the "human capital". So the skill of people to do work is just as a "produced capital" as any other tool or machine. Sources of income in Great Britain (top 10 percent of the population) Capital, Yield, Interest England and Wales United Kingdom Land 13 1 Investments Labor Total Source: Hirshleifer et al., 2009, 523. Value of the dierent sources of wealth in the 15 southern states, prices, million dollars Value of property and personal belongings 8644 Value of agricultural land 2550 Value of machines, equipment in use 104 Value of live-endowment 515 Value of freed slavery 3685 Total Source: Hirshleifer et al., 2009,

11 Real capital Capital value 1. Denition. Real capital (or capital goods): physical sources of production services: land, buildings, labor force, etc. 2. Denition. Capital value: the value of real capital Yield of assets: Cash-Flow: z A Capital value (price of assets): p A Expected change in capital value during the year: p A Rate of return (ROR): ROR A = z A + p A p A 2. Statement. All yields of assets are equal in equlibrium ROR A = ROR B =... = r 1. Consequence. Interest is not the yield of an asset (named capital). The relation between interest rate and capital is the following: in equilibrium, interest rate equal the yield of capital value of all assets, or factor of production. In other words, interest rate is the ratio of the net revenue (cash-ow) and the price of any given asset (corrected for the yearly devaluation or appreciation), in equilibrium. Economic rent Economic rent The revenue of a given asset. 11

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