Lecture notes: 101/105 (revised 9/27/00) Lecture 3: national Income: Production, Distribution and Allocation (chapter 3)

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1 Lecture notes: 101/105 (revised 9/27/00) Lecture 3: national Income: Production, Distribution and Allocation (chapter 3) 1) Intro Have given definitions of some key macroeconomic variables. Now start building theories about how these variables related to each other. Next couple weeks build up theories that we think hold in the long run, when prices are flexible and markets clear. Called Classical theory or Neoclassical. Idea of market is familiar, right? Two types of agents come together, suppliers and demanders. Supply and demand equal each other at an equilibrium price - this price clears the market suppliers want to supply the same amount that demanders want to demand. The macroeconomy involves three types of markets, where three types of commodities are traded: 1) Goods (and services) Market 2) Factors Market or Labor market, needed to produce goods and serices 3) Financial market - saving and borrowing Are also three types of agents in an economy, that interact with each other in these markets. 1) Households 2) Firms 3) Government Show you a road-map: we view the macroeconomy as a set of three markets, in which three types of agents interact with each other as supplier or demander. Goods market: firms supply goods and services, households demand them (for consumption) and government demand them (government expenditure), and other firms demand them (investment). Familiar from national income accounting. Labor market (factors of production) Firms need to hire labor to produce the goods. They buy labor from households. So labor is the commodity, firms are the demanders, and households are the suppliers. Financial market - households supply savings, which firms, government or other households borrow to finance their expenditures. Here we will develop a set of equations to characterize supply and demand in these markets, and how they interact to establish equilibrium. 1

2 work Labor Market hire saving Financial Market deficit borrowing Investment borrowing Households Government Firms consumption Gov. expend investment production Goods Market 2

3 2) Production Lets begin by looking at supply in the goods market. To produce a good, are two types of inputs: 1) Labor: hours of work, denote by L 2) capital: physical equipment or machinery, K Recipe by which combine certain amount of labor with certain amount of capital to produce a certain amount of output, describe by a function: Production function: Y = F ( K, L ), where F represents some equation involving K and L. F depends on the technology available - determines how combine K and L, and how much output get out. Most production functions are of a form, that have Constant returns to scale: an increase of equal percentage in all factors causes an increase in output of same percentage. Say multiply inputs by 10%, F(1.1K, 1.1L) = 1.1Y or do for and number z zy = F(zK,ZL) Is fairly reasonable assumption. Consider bakery economy. Have cookie dough mixing machine and workers producing cookies. If double size of bakery - build building next door, so that overall bakery now has double equipment and hire workers so double bakery s labor, will produce twice as much cookies. For now, will assume that factors are at fixed level, so level of output is fixed: write as: Y = F( K, L) We have here analyzed supply in the goods market. Will come back to demand in a minute. 3

4 3) Factors Market a) Lets look at the factors market. Supply and demand for L and K. Demand for factors comes from firms. Analyze decision of a typical firm. It must buy labor in the labor market, where price is wage, W. It must rent capital in the factors market, at rate R. It uses labor and capital to produce the good, which it must sell in the goods market, at price P. Assume is competitive, that is small relative to the market, so it does not affect the market price by its actions. It takes prices in markets as given - W,R, P It then chooses the optimal quantity of Labor and capital to buy to maximize its profit. How write profit: profit = revenue - labor costs - capital costs = PY -WL - RK = P F(K,L) - WL - RK Repeat: maximizes profit, which depends on factor quantities, which firm chooses, factor prices and output prices, which firm takes as given beyond its control. 4

5 Demand for labor depends on the marginal product of labor. Def marginal product of labor (MPL) = the extra amount of output the firm gets from one extra unit of labor. Can express an approximation: MPL = F(K,L+1) - F(K,L) Look at graph: Y 1 MPL F(K,L) L. More precise definition is change in output for a very small change in labor. Slope of curve at a particular point. More precise: Use L other than one. write MPL = (F(K, L+ L) - F(K,L)) / L. where becomes more precise as L becomes very small. In other words, it is the derivative of the production function wrt labor: MPL = f L (K,L) Text uses first definition, but we will use the more precise definition, using the derivative. Notice that production function becomes flatter as labor increases. This is diminishing marginal product, the MPL becomes smaller when increase one factor, holding the other constant. Example: bakery, if hire more workers, but not add extra machines or expand the building, the bakery becomes more crowded, and each additional baker produces less than the one hired before. 5

6 Reconsider the firm s decision of how many workers to hire. Want to maximize profit. How does hiring a new worker affect profit: 1) Produce more of good, which sells at price P, so raise revenue 2) But also have to pay worker, which raises cost: profit = revenue - cost = (P * MPL) - W If P*MPL exceeds wage, W, then an extra unit of labor increases profit. So will hire more labor until next unit would no longer be profitable, that is, until MPL falls to the point where extra revenue equals the wages. Therefore, firms demand for labor is determined by condition: or P x MPL = W MPL = W/P We call W/P the real wage. Real because it is measured in units of output rather than dollars. W = $/unit of work P = $/ unit of good W / P = ($/unit of work) / ($ / Unit of good) = units of good / one unit of work It is the amount of purchasing power, measured as a quantity of goods, that the firm pays fore each unit of labor. Repeat, to maximize profit, firm will hire up to the point where marginal product of labor equals the real wage. Consider bakery example: Suppose price of cookie is P=2$ per loaf, and worker earns W = $20. The real wage W/P= 10 loaves per hour. So firms will keep hiring workers until an additional worker increase output by only 10 loaves per hour (MPL=10). 6

7 Draw graph of MPL as a function of labor: Y 10 loaves MPL L1 L This graph can be read also as a demand curve for labor. For given labor L1, MPL is 10 loaves, produced per unit of labor. This also means that if the real wage were at this level, 10 loaves per unit of labor, then firm would find it profitable to hire labor equal to L1. Q: why is MPL down-sloping? Reflects curvature in production function. MPL falls as L rises. b) Marginal product of capital Can derive marginal product of capital in same way MPK is the extra output firm gets from hiring an extra unit of capital Can define as MPK = F(K + 1,L) - F(K,L) or more precisely, MPK = F K (K,L), Fk is the derivative of the production function with respect to capital the extra profit from renting an additional machine is the extra revenue from selling the output that machine makes minus the cost of renting that machine: profit = revenue - cost = (P * MPK) - R To maximize profit, the firm continues to rent more capital until the MPK falls to equal the real rental price: MPK = R/P Example Black Death According to our theory, when quantity of labor falls, marginal product rises, and so real wage should rise. This happened during Black deat in 1300s. Larg fraction of European population died. Fewer people per unit of land or capital, so real wage went up, doubled by some data. So those lucky enough to survive prospered. However, rent price of land fell in half. 7

8 c) Division of National Income: Found that if firms competitive, then factors of production will be paid their marginal contribution to the production process. The real wage paid to each worker is MPL, so total real wage bill is MPL x L. The real rental price paid to each owner of capital equals MPK, so total real return to capital owners is MPK x K. Income that remains after firms have paid the factors of production is the economic profit of the owners of the firm: Def: Economic profit = Y - (MPL x L) - (MPK x K) However, if production function has the property of constant returns to scale, economic profit must be zero. Nothing left over after factor are paid. Euler s theorem says if constant returns to scale, then Y = (MPL x L) + (MPK x K) This then suggests that economic profit is zero. Lesson is that under these assumptions, (constant returns to scale, profit maximization, and competition) total output is divided between the payments to capital and the payments to labor, depending on their marginal productivities. d) Example: Cobb-Douglas production function Y = AK α L 1-α A is a constant, representing technology Show has constant returns to scale: multiply factors by Z F(ZK,ZY) = A (ZK) α (ZL) 1-α = A Z α K α Z 1-α L 1-α = A Z α Z 1-α K α L 1-α = Z x A K α L 1-α = Z x F(K,L) Compute marginal products: MPL = (1-α) x A K α L -α MPK = α x A K α-1 L 1-α compute MPL x L + MPK x K = (1-α) x A K α L -α x L + α x A K α-1 L 1-α x K = (1-α) x A K α L 1-α + α x A K α L1 -α = A K α L 1-α = Y 8