Chapter 8 - Costs curves. This chapter presents the following content: Introduction, long run cost functions, short run cost functions, the relationship between long run and short run cost functions. | 1 Costs Curves Chapter 8 Copyright (c)2014 John Wiley & Sons, Inc. 1 2 Chapter Eight Overview Introduction Long Run Cost Functions Shifts Long run average and marginal cost functions Economies of scale Deadweight loss – "A Perfectly Competitive Market Without Intervention Maximizes Total Surplus" Short Run Cost Functions The Relationship Between Long Run and Short Run Cost Functions Chapter Eight Copyright (c)2014 John Wiley & Sons, Inc. 3 Chapter Eight Long Run Cost Functions Definition: The long run total cost function relates minimized total cost to output, Q, and to the factor prices (w and r). TC(Q,w,r) = wL*(Q,w,r) + rK*(Q,w,r) Where: L* and K* are the long run input demand functions Copyright (c)2014 John Wiley & Sons, Inc. 4 Chapter Eight Long Run Cost Functions As Quantity of output increases from 1 million to 2 million, with input prices(w, r) constant, cost minimizing input combination moves from TC1 to TC2 which gives the TC(Q) curve. Copyright (c)2014 John Wiley & Sons, . | 1 Costs Curves Chapter 8 Copyright (c)2014 John Wiley & Sons, Inc. 1 2 Chapter Eight Overview Introduction Long Run Cost Functions Shifts Long run average and marginal cost functions Economies of scale Deadweight loss – "A Perfectly Competitive Market Without Intervention Maximizes Total Surplus" Short Run Cost Functions The Relationship Between Long Run and Short Run Cost Functions Chapter Eight Copyright (c)2014 John Wiley & Sons, Inc. 3 Chapter Eight Long Run Cost Functions Definition: The long run total cost function relates minimized total cost to output, Q, and to the factor prices (w and r). TC(Q,w,r) = wL*(Q,w,r) + rK*(Q,w,r) Where: L* and K* are the long run input demand functions Copyright (c)2014 John Wiley & Sons, Inc. 4 Chapter Eight Long Run Cost Functions As Quantity of output increases from 1 million to 2 million, with input prices(w, r) constant, cost minimizing input combination moves from TC1 to TC2 which gives the TC(Q) curve. Copyright (c)2014 John Wiley & Sons, Inc. 5 Chapter Eight What is the long run total cost function for production function Q = 50L1/2K1/2? L*(Q,w,r) = (Q/50)(r/w)1/2 K*(Q,w,r) = (Q/50)(w/r)1/2 TC(Q,w,r) = w[(Q/50)(r/w)1/2]+r[(Q/50)(w/r)1/2] = (Q/50)(wr)1/2 + (Q/50)(wr)1/2 = (Q/25)(wr)1/2 What is the graph of the total cost curve when w = 25 and r = 100? TC(Q) = 2Q Long Run Cost Functions Examples Copyright (c)2014 John Wiley & Sons, Inc. 6 Q (units per year) TC ($ per year) TC(Q) = 2Q $4M. Chapter Eight A Total Cost Curve Copyright (c)2014 John Wiley & Sons, Inc. 7 1 M. $2M. Chapter Eight TC ($ per year) Q (units per year) TC(Q) = 2Q A Total Cost Curve Copyright (c)2014 John Wiley & Sons, Inc. 8 1 M. 2 M. $2M. $4M. Chapter Eight A Total Cost Curve TC ($ per year) Q (units per year) TC(Q) = 2Q Copyright (c)2014 John Wiley & Sons, Inc. 9 Chapter Eight Long Run Total Cost Curve Tracking Movement Definition: The long run total cost curve shows minimized total cost as output varies, holding input prices constant. Graphically, .
