1. 1 Module 13 The Short Run Production Function

2. 2   Define a production function, define the three concepts of production–total product, marginal product, and average product, know how to calculate these production variables and be able to graph the product curves.   Define the law of diminishing marginal returns and understand its significance.   Understand the relationship between marginal product and average product. ObjectivesObjectives

3.  A production function is the relationship between the quantities of various inputs used and the maximum quantity that can be produced per period of time.  For example, the production function for producing bread can be expressed as: Q = f (labor, capital, flour, sugar...) Objective 1: Define a production function,.… 3

4.  In this module, we will use a simple two-input production function which can be expressed as: Q = f (L, K) where Q = total product or output, L = labor and K = capital  Recall that in the short run, at least one factor is fixed. So a short run production function must reflect this. For example,  In this module, we will use a simple two-input production function which can be expressed as: Q = f (L, K) where Q = total product or output, L = labor and K = capital  Recall that in the short run, at least one factor is fixed. So a short run production function must reflect this. For example, 4

5. Objective 1:…the three concepts of total product 1. Total product of labor (TPL) This is simply the total output produced by labor, holding capital fixed. Total product is also called output. 2. Average product (APL) = Q/L The average product of labor or average output is the commonly used measure of productivity. 3. Marginal product (MPL) = ∆Q/∆L It is defined as the additional output produced when the firm hires one more unit of labor input, holding capital fixed. 5

6. Numerical Example: The Acme Box Company produces wooden boxes using two inputs, L and K. Capital (K) is fixed at K 0. The total product schedule is given in the Table below. Labor Total Product of Labor 18 223 342 457 567 674 779 882 983 1082 1181 6

7. Numerical Example: Calculating average product (1)(2)(3) = (2)÷(1) Labor(L) Total Product of Labor (TPL) Average Product of Labor (APL) 188÷1 = 8 22323÷2 = 11.50 34243÷3 = 14 45757÷4 = 14.25 56713.4 67412.33 77911.29 88210.25 9839.22 10828.20 11817.36 7

8. (1)(2)(3) = (2)÷(1)(4) =∆(1)/∆(2) Labor(L) Total Product of Labor (TPL) Average Product of Labor (APL) Marginal Product of Labor (MPL) 188÷1 = 8(8−0)÷1 = 8 22323÷2 = 11.50(23−8)÷1 = 15 34243÷3 = 14(42-23) ÷1 = 19 45757÷4 = 14.25(57-42) ÷1 = 15 56713.410 67412.337 77911.295 88210.253 9839.221 10828.20−1 11817.36−1 8 Numerical Example: Calculating marginal product

9. The Acme Box Company Increasing Marginal Returns Diminishing Marginal Returns Negative Marginal Returns (1)(2)(3) = (2)÷(1)(4) =∆(1)/∆(2) Labor(L) Total Product of Labor (TPL) Average Product of Labor (APL) Marginal Product of Labor (MPL) 188÷1 = 8(8−0)÷1 = 8 22323÷2 = 11.50(23−8)÷1 = 15 34243÷3 = 14(42-23) ÷1 = 19 45757÷4 = 14.25(57-42) ÷1 = 15 56713.410 67412.337 77911.295 88210.253 9839.221 10828.20−1 11817.36−1 9

10.  Columns (1) and (2) of the Table represent the total product schedule. Graphing this data gives the total product curve. The total product curve is also called the graph of the short run production function. 10 (1)(2)Labor(L) Total Product of Labor (TPL) 18 223 342 457 567 674 779 882 983 1082 1181

11.  Based on the marginal product column in the Table, we can identify three distinct regions of Acme’s production function: increasing marginal returns followed by diminishing marginal returns and finally negative marginal returns.  The region of economic interest is the segment that displays diminishing marginal returns. 11 (1)(4)Labor(L) Marginal Product of Labor (TPL) 18 215 319 415 510 67 75 83 91 − 1 11− 1

12. Objective 2  The law of diminishing marginal returns states that in the presence of a fixed factor, after some point, equal increments in a variable input will increase output by a progressively smaller amount.  The law of diminishing marginal returns applies only in the short run where there is a fixed input. Define the law of diminishing marginal returns and understand its significance. Define the law of diminishing marginal returns and understand its significance. 12

13. Objective 3   Suppose 20 students take an Economics exam and the average score is 80%.Then one more student, Rose, takes the exam and her score is 87%.   If Rose scored 87% and if I re-calculate the class average (based on 21 students), what happens to the average score? It will be > 80%.   If Rose scored 74%, what happens to the class average now? It will be less than 80%. Understand the relationship between marginal product and average product 13

14.   If Rose scored 80%, what happens to the class average? It will remain at 80%.   The general marginal-average relationship is:   When the marginal value is below the average value, it pulls the average value down.   When the marginal value is above the average value, it pulls the average value up.   When the marginal value equals the average value, the average value is constant. 14 Objective 3: The marginal-average relationship

15. Between 1 and 4 units of labor, marginal product lies above average product, and average product is increasing. 15 15

16. Objective 3: The marginal-average relationship Between the 5th and the 11th unit of labor, marginal product lies below the average product and average product is falling. 16

17. Objective 3: The relationship between marginal product and average product. Diminishing marginal returns set in after the 3rd unit of labor where marginal product reaches a maximum. 17

18. Objective 3: …marginal product curve From the 4th to the 9th unit of labor marginal product is positive but it is diminishing.