《宏观经济学》课程教学资源（英文版）Lecture2-3 -National Income- Where It Comes From and Where It Goes

Worth: Mankiw Economics 5e CHAPTER 3 National Income: Where It Comes From and Where It Goes 45 The Production Function The available production technology determines how much output is produced from given amounts of capital and labor. Economists express the available tech- nology using a production function. Letting Y denote the amount of output we write the production function as Y=FK, L) This equation states that output is a function of the amount of capital and the amount of labor The production function reflects the available technology for turning capital and labor into output. If someone invents a better way to produce a good, the re- sult is more output from the same amounts of capital and labor. Thus, technolog ical change alters the production function Many production functions have a property called constant returns to scale. a production function has constant returns to scale if an increase of an equal percentage in all factors of production causes an increase in output of the same percentage. If the production function has constant returns to scale, then percent. Mathematically, a production function has constant returns to scaler o e get 10 percent more output when we increase both capital and labor by zY= F(2K, 2L) for any positive number z. This equation says that if we multiply both the amount of capital and the amount of labor by some number z, output is also multiplied by z In the next section we see that the assumption of constant returns to scale has an important implication for how the income from production is distributed. As an example of a production function, consider production at a bakery. The kitchen and its equipment are the bakery's capital, the workers hired to make the bread are its labor, and the loaves of bread are its output. The bakery's production function shows that the number of loaves produced depends on the amount of equipment and the number of workers. If the production function has constant returns to scale, then doubling the amount of equipment and the number of workers doubles the amount of bread produced The Supply of Goods and Services We can now see that the factors of production and the production function to- gether determine the quantity of goods and services supplied, which in turn equals the economy's output. To express this mathematically, we write Y=F(K, L) In this chapter, because we assume that the supplies of capital and labor and the technology are fixed, output is also fixed (at a level denoted here as Y). When we User JOENA: Job EFF01419: 6264_ch03: Pg 45: 24981 #/eps at 1009 I ed,Feb13,20028:554M

User JOEWA:Job EFF01419:6264_ch03:Pg 45:24981#/eps at 100% *24981* Wed, Feb 13, 2002 8:55 AM The Production Function The available production technology determines how much output is produced from given amounts of capital and labor. Economists express the available tech￾nology using a production function. Letting Y denote the amount of output, we write the production function as Y = F(K, L). This equation states that output is a function of the amount of capital and the amount of labor. The production function reflects the available technology for turning capital and labor into output. If someone invents a better way to produce a good, the re￾sult is more output from the same amounts of capital and labor.Thus, technolog￾ical change alters the production function. Many production functions have a property called constant returns to scale. A production function has constant returns to scale if an increase of an equal percentage in all factors of production causes an increase in output of the same percentage. If the production function has constant returns to scale, then we get 10 percent more output when we increase both capital and labor by 10 percent. Mathematically, a production function has constant returns to scale if zY = F(zK, zL) for any positive number z.This equation says that if we multiply both the amount of capital and the amount of labor by some number z, output is also multiplied by z. In the next section we see that the assumption of constant returns to scale has an important implication for how the income from production is distributed. As an example of a production function, consider production at a bakery.The kitchen and its equipment are the bakery’s capital, the workers hired to make the bread are its labor, and the loaves of bread are its output.The bakery’s production function shows that the number of loaves produced depends on the amount of equipment and the number of workers. If the production function has constant returns to scale, then doubling the amount of equipment and the number of workers doubles the amount of bread produced. The Supply of Goods and Services We can now see that the factors of production and the production function to￾gether determine the quantity of goods and services supplied, which in turn equals the economy’s output.To express this mathematically, we write Y = F(K _ , L _ ) = Y _ . In this chapter, because we assume that the supplies of capital and labor and the technology are fixed, output is also fixed (at a level denoted here as Y –).When we CHAPTER 3 National Income: Where It Comes From and Where It Goes | 45

Worth: Mankiw Economics 5e 46 PART 11 Classical Theory: The Economy in the Long Ru discuss economic growth in Chapters 7 and 8, we will examine how increases in capital and labor and improvements in the production technology lead to growth in the economys or 3-2 How Is National Income distributed to the Factors of production? As we discussed in Chapter 2, the total output of an economy equals its total in- come. Because the factors of production and the production function together determine the total output of goods and services, they also determine national income. The circular flow diagram in Figure 3-1 shows that this national in- come flows from firms to households through the markets for the factors of In this section we continue developing our model of the economy by dis- cussing how these factor markets work. Economists have long studied factor markets to understand the distribution of income.(For example, Karl Marx, the noted nineteenth-century economist, spent much time trying to explain the in- comes of capital and labor. The political philosophy of communism was in part based on Marx's now-discredited theory. Here we examine the modern theory of how national income is divided among the factors of production. This theory, called the neoclassical theory of distribution, is accepted by most economists today. Factor Prices The distribution of national income is determined by factor prices. Factor prices are the amounts paid to the factors of production-the wage workers earn and the rent the owners of capital collect. As Figure 3-2 illustrates, the price each factor of production receives for its services is in turn determined by the supply and demand for that factor. Because we have assumed that the economy's factors of production are fixed, the factor supply curve in Figure 3-2 is vertical. The intersection of the downward-sloping factor demand curve and the vertical supply curve determines the equilibrium factor price To understand factor prices and the distribution of income, we must examine the demand for the factors of production. Because factor demand arises from the housands of firms that use capital and labor, we now look at the decisions faced by a typical firm about how much of these factors to employ. The Decisions Facing the Competitive Firm The simplest assumption to make about a typical firm is that it is competitive A competitive firm is small relative to the markets in which it trades, so it has little influence on market prices. For example, our firm produces a good and sells it at the market price. Because many firms produce this good, our firm can sell as User JOENA: Job EFF01419: 6264_ch03: Pg 46: 24982#/eps at 1009 II ed,Feb13,20028:554M

User JOEWA:Job EFF01419:6264_ch03:Pg 46:24982#/eps at 100% *24982* Wed, Feb 13, 2002 8:55 AM discuss economic growth in Chapters 7 and 8, we will examine how increases in capital and labor and improvements in the production technology lead to growth in the economy’s output. 3-2 How Is National Income Distributed to the Factors of Production? As we discussed in Chapter 2, the total output of an economy equals its total in￾come. Because the factors of production and the production function together determine the total output of goods and services, they also determine national income. The circular flow diagram in Figure 3-1 shows that this national in￾come flows from firms to households through the markets for the factors of production. In this section we continue developing our model of the economy by dis￾cussing how these factor markets work. Economists have long studied factor markets to understand the distribution of income. (For example, Karl Marx, the noted nineteenth-century economist, spent much time trying to explain the in￾comes of capital and labor.The political philosophy of communism was in part based on Marx’s now-discredited theory.) Here we examine the modern theory of how national income is divided among the factors of production.This theory, called the neoclassical theory of distribution, is accepted by most economists today. Factor Prices The distribution of national income is determined by factor prices. Factor prices are the amounts paid to the factors of production—the wage workers earn and the rent the owners of capital collect. As Figure 3-2 illustrates, the price each factor of production receives for its services is in turn determined by the supply and demand for that factor. Because we have assumed that the economy’s factors of production are fixed, the factor supply curve in Figure 3-2 is vertical. The intersection of the downward-sloping factor demand curve and the vertical supply curve determines the equilibrium factor price. To understand factor prices and the distribution of income, we must examine the demand for the factors of production. Because factor demand arises from the thousands of firms that use capital and labor, we now look at the decisions faced by a typical firm about how much of these factors to employ. The Decisions Facing the Competitive Firm The simplest assumption to make about a typical firm is that it is competitive. A competitive firm is small relative to the markets in which it trades, so it has little influence on market prices. For example, our firm produces a good and sells it at the market price. Because many firms produce this good, our firm can sell as 46 | PART II Classical Theory: The Economy in the Long Run

Worth: Mankiw Ecol CHAPTER 3 National Income: Where It Comes From and Where It Goes 47 Factor price How a Factor of production is to any factor of production supply mand for that factors services Because we have assumed that supply is fixed, the supply curve is vertical. The demand curve downward sloping. The factor price Quantity of factor much as it wants without causing the price of the good to fall, or it can stop sell ing altogether without causing the price of the good to rise. Similarly, our firm cannot influence the wages of the workers it employs because many other local firms also employ workers. The firm has no reason to pay more than the market wage, and if it tried to pay less, its workers would take jobs elsewhere. Therefore, the competitive firm takes the prices of its output and its inputs as giver To make its product, the firm needs two factors of production, capital and labor. As we did for the aggregate economy, we represent the firms production technology by the production function =F(K, L) where Y is the number of units produced (the firms output), K the number of machines used(the amount of capital), and L the number of hours worked by the firms employees(the amount of labor). The firm produces more output if it has more machines or if its employees work more hours The firm sells its output at a price P, hires workers at a wage w, and rents cap ital at a rate R. Notice that when we speak of firms renting capital, we are assum- ing that households own the economy's stock of capital. In this analysis, households rent out their capital, just as they sell their labor. The firm obtains both factors of production from the households that own them. I The goal of the firm is to maximize profit. Profit is revenue minus costs--it is what the owners of the firm keep after paying for the costs of production. Rev- enue equals Px Y, the selling price of the good P multiplied by the amount of I This is a simplification In the real world, the ownership of capital is indirect because firms own apital and households own the firms. That is, real firms have two functions: owning capital and producing output. To help us understand how the factors of production are compensated, however, we assume that firms only produce output and that households own capital directly. User JOENA: Job EFF01419: 6264_ch03: Pg 47: 24983#/eps at 1009 Il wed,Feb13,20028:564M

User JOEWA:Job EFF01419:6264_ch03:Pg 47:24983#/eps at 100% *24983* Wed, Feb 13, 2002 8:56 AM much as it wants without causing the price of the good to fall, or it can stop sell￾ing altogether without causing the price of the good to rise. Similarly, our firm cannot influence the wages of the workers it employs because many other local firms also employ workers.The firm has no reason to pay more than the market wage, and if it tried to pay less, its workers would take jobs elsewhere.Therefore, the competitive firm takes the prices of its output and its inputs as given. To make its product, the firm needs two factors of production, capital and labor. As we did for the aggregate economy, we represent the firm’s production technology by the production function Y = F(K, L), where Y is the number of units produced (the firm’s output), K the number of machines used (the amount of capital), and L the number of hours worked by the firm’s employees (the amount of labor).The firm produces more output if it has more machines or if its employees work more hours. The firm sells its output at a price P, hires workers at a wage W, and rents cap￾ital at a rate R. Notice that when we speak of firms renting capital, we are assum￾ing that households own the economy’s stock of capital. In this analysis, households rent out their capital, just as they sell their labor. The firm obtains both factors of production from the households that own them.1 The goal of the firm is to maximize profit. Profit is revenue minus costs—it is what the owners of the firm keep after paying for the costs of production. Rev￾enue equals P × Y, the selling price of the good P multiplied by the amount of CHAPTER 3 National Income: Where It Comes From and Where It Goes | 47 figure 3-2 Equilibrium factor price Factor supply Factor demand Quantity of factor Factor price How a Factor of Production Is Compensated The price paid to any factor of production depends on the supply and de￾mand for that factor’s services. Because we have assumed that supply is fixed, the supply curve is vertical. The demand curve is downward sloping. The inter￾section of supply and demand determines the equilibrium factor price. 1This is a simplification. In the real world, the ownership of capital is indirect because firms own capital and households own the firms.That is, real firms have two functions: owning capital and producing output.To help us understand how the factors of production are compensated, however, we assume that firms only produce output and that households own capital directly

Worth: Mankiw Economics 5e 48 PART 11 Classical Theory: The Economy in the Long Ru che good the firm produces Y Costs include both labor costs and capital costs. Labor costs equal WX L, the wage W times the amount of labor L Capital costs equal r x K, the rental price of capital R times the amount of capital K. We can Profit= Revenue- Labor Costs-Capital Costs WL RK To see how profit depends on the factors of production, we use the production function Y= F(K, L)to substitute for Y to obtain Profit= PF(K, L)-WL-RK This equation shows that profit depends on the product price P, the factor prices W and R, and the factor quantities L and K. The competitive firm takes the product price and the factor prices as given and chooses the amounts of labor and capital that maximize profit The Firm's Demand for Factors We now know that our firm will hire labor and rent capital in the quantities that maximize profit. But what are those profit-maximizing quantities? To answer this question, we first consider the quantity of labor and then the quantity of capital The Marginal Product of Labor The more labor the firm employs, the more output it produces. The marginal product of labor(MPL) is the extra amount of output the firm gets from one extra unit of labor, holding the amount of capital fixed. We can express this using the production function MPL= F(K, L+1)-F(K, L) m first term on the right-hand side is the amount of output produced with K of capital and L+ 1 units of labor; the second term is the amount of output oduced with K units of capital and L units of labor. This equation states that the marginal product of labor is the difference between the amount of output produced with L+ 1 units of labor and the amount produced with only L units of labor Most production functions have the property of diminishing marginal product: holding the amount of capital fixed, the marginal product of labor de creases as the amount of labor increases. Consider again the production of bread at a bakery. As a bakery hires more labor, it produces more bread. The MPL is the amount of extra bread produced when an extra unit of labor is hired. As more labor is added to a fixed amount of capital, however, the MPL falls. Fewer addi- tional loaves are produced because workers are less productive when the kitchen is more crowded. In other words, holding the size of the kitchen fixed, each ad ditional worker adds fewer loaves of bread to the bakery's output Figure 3-3 graphs the production function. It illustrates what happens to the amount of output when we hold the amount of capital constant and vary the User JoENA: Job EFFo1419: 6264_ch03: Pg 48: 24984#/eps at 1004 mI wed,Feb13,20028:564M

User JOEWA:Job EFF01419:6264_ch03:Pg 48:24984#/eps at 100% *24984* Wed, Feb 13, 2002 8:56 AM the good the firm produces Y. Costs include both labor costs and capital costs. Labor costs equal W × L, the wage W times the amount of labor L. Capital costs equal R × K, the rental price of capital R times the amount of capital K.We can write Profit = Revenue − Labor Costs − Capital Costs = PY − WL − RK. To see how profit depends on the factors of production, we use the production function Y = F(K, L) to substitute for Y to obtain Profit = PF(K, L) − WL − RK. This equation shows that profit depends on the product price P, the factor prices W and R, and the factor quantities L and K. The competitive firm takes the product price and the factor prices as given and chooses the amounts of labor and capital that maximize profit. The Firm’s Demand for Factors We now know that our firm will hire labor and rent capital in the quantities that maximize profit. But what are those profit-maximizing quantities? To answer this question, we first consider the quantity of labor and then the quantity of capital. The Marginal Product of Labor The more labor the firm employs, the more output it produces. The marginal product of labor (MPL) is the extra amount of output the firm gets from one extra unit of labor, holding the amount of capital fixed.We can express this using the production function: MPL = F(K, L + 1) − F(K, L). The first term on the right-hand side is the amount of output produced with K units of capital and L + 1 units of labor; the second term is the amount of output produced with K units of capital and L units of labor.This equation states that the marginal product of labor is the difference between the amount of output produced with L + 1 units of labor and the amount produced with only L units of labor. Most production functions have the property of diminishing marginal product: holding the amount of capital fixed, the marginal product of labor de￾creases as the amount of labor increases. Consider again the production of bread at a bakery. As a bakery hires more labor, it produces more bread.The MPL is the amount of extra bread produced when an extra unit of labor is hired. As more labor is added to a fixed amount of capital, however, the MPL falls. Fewer addi￾tional loaves are produced because workers are less productive when the kitchen is more crowded. In other words, holding the size of the kitchen fixed, each ad￾ditional worker adds fewer loaves of bread to the bakery’s output. Figure 3-3 graphs the production function. It illustrates what happens to the amount of output when we hold the amount of capital constant and vary the 48 | PART II Classical Theory: The Economy in the Long Run

Worth: Mankiw Economics 5e CHAPTER 3 National Income: Where It Comes From and Where It Goes 49 figure 3-3 RK, L) 2. As more MPL 1. The slope of MPL function equals The Production Function This curve shows how output depends on labor input, holding the amount of capital constant. The marginal product of labor MPL is the change in output when the labor input is increased by 1 unit. As the amount of labor increases, the production function becomes flatter, indicating diminishing marginal product. amount of labor. This figure shows that the marginal product of labor is the slope of the production function. As the amount of labor increases, the production function becomes fatter, indicating diminishing marginal product From the Marginal Product of Labor to Labor Demand When the compe titive, profit-maximizing firm is deciding whether to hire an additional unit of labor, it considers how that decision would affect profits. It therefore compares the extra revenue from the increased production that results from the added labor to the extra cost of higher spending on wages. The increase in revenue from an addi- onal unit of labor depends on two variables: the marginal product of labor and the price of the output. Because an extra unit of labor produces MPL units of output and each unit of output sells for P dollars, the extra revenue is P X MPL. The extra cost of hiring one more unit of labor is the wage w. Thus, the change in profit from hiring an additional unit of labor is △ Profit=△ Revenue-△Cost =(P×MPL)-W The symbol A(called delta) denotes the change in a variable User JOENA: Job EFF01419: 6264_ch03: Pg 49: 24985#/eps at 1009 II wed,Feb13,20028:564M

User JOEWA:Job EFF01419:6264_ch03:Pg 49:24985#/eps at 100% *24985* Wed, Feb 13, 2002 8:56 AM amount of labor.This figure shows that the marginal product of labor is the slope of the production function. As the amount of labor increases, the production function becomes flatter, indicating diminishing marginal product. From the Marginal Product of Labor to Labor Demand When the compe￾titive, profit-maximizing firm is deciding whether to hire an additional unit of labor,it considers how that decision would affect profits.It therefore compares the extra revenue from the increased production that results from the added labor to the extra cost of higher spending on wages.The increase in revenue from an addi￾tional unit of labor depends on two variables: the marginal product of labor and the price of the output. Because an extra unit of labor produces MPL units of output and each unit of output sells for P dollars, the extra revenue is P × MPL. The extra cost of hiring one more unit of labor is the wage W.Thus, the change in profit from hiring an additional unit of labor is D Profit = DRevenue − DCost = (P × MPL) − W. The symbol D (called delta) denotes the change in a variable. CHAPTER 3 National Income: Where It Comes From and Where It Goes | 49 figure 3-3 F(K, L) Output, Y Labor, L MPL 1 MPL 1 MPL 1 1. The slope of production function equals marginal product of labor. 2. As more labor is added, the marginal product of labor declines. The Production Function This curve shows how output depends on labor input, holding the amount of capital constant. The marginal product of labor MPL is the change in output when the labor input is increased by 1 unit. As the amount of labor increases, the production function becomes flatter, indicating diminishing marginal product