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Chapter 5 The Production Process and Costs Production function shows the relation between the maximum amount of output and inputs. Example: 2 inputs Labor (L) and Capital (K) Inputs called also factors. Production Function: Q=f(L,K) If L and K assume discrete values, then the production function is discrete. If L and K assume continuous values, then the production function is continuous. Short-run versus Long-run In the short run, some inputs are fixed. Example: plant size (capital) is fixed in the short- run; labor is variable in the short run. In the long-run, all inputs are variable. Measures of Productivity Total product (TP) is the maximum amount of output for a given amount of inputs. For example, when K=1 and L=2, then Q=4. Say L=2 workers and K=1 tractor can produce Q=4 holes. Q=4 holes is the maximum output. You can always produce less than 4 holes if, say, the workers slack. When K is fixed, the Total Product function of Labor (TP L ) will show how Q changes as L changes while holding K fixed. It is also known as the short-run production function. Mathematically, TP L = Q = f(L/K), i.e. the amount of output as a function of L for a fixed K. An example of a short-run production function (picture below): K (plant size) is fixed at some level. As we vary L, the output (total product) changes according the function below. If L=L A , Q=Q A (say, L A =100 workers, Q A =200 units of output). If L=L B , Q=Q B (say, L B =140, Q B =220). If L=L C , Q=Q C (say, L C =300, Q C =230). We will talk more about the shape of the production function later. 1 Q C Q C B Average Product Average Product of Labor = AP L = Q/L (units per worker) Average Product of Capital = AP K =Q/K (units per capital) Marginal Product The Marginal Product of Labor, MP L , shows the change in output associated with a one unit change in labor, holding all other factors (inputs) constant . MP L = L Q when L is discrete MP L = dL dQ when L is continuous MP L is units per worker. For example, MP L =5 for the 1 st worker, MP L =7 for the second worker, etc. Example: Calculating MP L (K is fixed at some level) L Q MP L 1 15 15 2 31 16 3 48 17 4 59 11 5 68 9 6 72 4 7 73 1 8 72 -1 9 70 -2 10 67 -3 A L TP L O Q B Q A L A L B L C 2 The Marginal Product of Capital, MP K , shows the change in output associated with a one unit change in capital, holding all other factors (inputs) constant . MP K = K Q when K is discrete MP K = dK dQ when K is continuous The relationship between AP and MP As long as MP is above AP, AP is increasing. If MP is below AP, AP will decrease. Intuition GPA Analogy Example. GPA is your average grade. Individual grade is like a marginal grade. If the grade from a new course is greater than your existing GPA, your GPA will go up. If the new grade is lower than your existing GPA, your GPA will go down. ... View Full Document
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