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,Feb13,20028:554MUser 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