ECONOMIC SECOND EDITION in MODULES S Paul Krugman Robin Wells with Margaret Ray and David Anderson MODULE 18 54 The Production Function Krugman Wells The importance of the firm s production function the relationship between quantity of inputs and quantity of output Why production is often subject to diminishing returns to inputs 3 of 13 The Production Function A production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces A fixed input is an input whose quantity is fixed for a period of time and cannot be varied A variable input is an input whose quantity the firm can vary at any time 4 of 13 Inputs and Output The long run is the time period in which all inputs can be varied The short run is the time period in which at least one input is fixed The total product curve shows how the quantity of output depends on the quantity of the variable input for a given quantity of the fixed input 5 of 13 Production Function and Total Product Curve for George and Martha s Farm Quantity of wheat bushels 100 80 Adding a 7th worker leads to an increase in output of only 7 bushels Adding a 2nd worker leads to an increase in output of only 17 bushels 60 40 20 0 1 2 3 4 5 Quantity Quantity of labor L of wheat Q workers bushels 0 0 Total product TP 1 19 2 36 3 51 4 64 5 75 6 84 7 91 8 96 6 7 MP of labor bushels per worker 19 17 15 13 11 9 7 5 8 Quantity of labor workers Although the total product curve in the figure slopes upward along its entire length the slope isn t constant as you move up the curve to the right it flattens out due to changing marginal product of labor 6 of 13 Marginal Product of Labor The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input 7 of 13 Diminishing Returns to an Input There are diminishing returns to an input when an increase in the quantity of that input holding the levels of all other inputs fixed leads to a decline in the marginal product of that input The following marginal product of labor curve illustrates this concept clearly 8 of 13 Marginal Product of Labor Curve Marginal product of labor bushels per worker There are diminishing returns to labor 19 17 15 13 11 9 7 5 Marginal product of labor MPL 0 1 2 3 4 5 6 7 8 Quantity of labor workers The first worker employed generates an increase in output of 19 bushels the second worker generates an increase of 17 bushels and so on 9 of 13 Total Product Marginal Product and the Fixed Input a Total Product Curves Quantity of wheat bushels 160 140 120 100 80 60 40 20 0 TP 20 TP 10 1 2 3 4 5 6 7 8 Quantity of labor workers With more land each worker can produce more wheat So an increase in the fixed input shifts the total product curve up from TP10 to TP20 10 of 13 Total Product Marginal Product and the Fixed Input b Marginal Product Curves Marginal product of labor bushels per worker 30 25 20 15 10 5 0 1 2 3 4 5 6 7 MPL20 MPL 10 8 Quantity of labor workers This shift also implies that the marginal product of each worker is higher when the farm is larger As a result an increase in acreage also shifts the marginal product of labor curve up from MPL10 to MPL20 11 of 13 Was Malthus Right In 1798 Thomas Malthus authored the book An Essay of the Principle of Population which introduced the concept of diminishing returns to an input Malthus argued that as a country s population grew but its land area remained fixed it would become increasingly difficult to grow enough food Over the long term Malthus s predictions have turned out to be wrong due to technological progress 12 of 13 1 The cost of using a resource for a particular activity is the opportunity cost of that resource 2 Some opportunity costs are explicit costs they involve a direct payment of cash 3 Other opportunity costs however are implicit costs they involve no outlay of money but represent the inflows of cash that are forgone 4 Companies use capital and their owners time So companies should base decisions on economic profit which takes into account implicit costs such as the opportunity cost of the owners time and the implicit cost of capital 5 A normal profit is the amount needed to keep resources employed in the business to keep the business in business 13 of 13