Walter Nicholson Christopher Snyder Amherst College Christopher Snyder Dartmouth College PowerPoint Slide Presentation | Philip Heap, James Madison University ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

CHAPTER 7 Costs ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chapter Preview Last chapter we saw how a firm’s output changes as it uses more inputs. In this chapter we will focus on two issues: How the firm chooses the inputs it uses to produce a given output at the lowest possible cost. How the firm’s production costs change as it changes the number and mix of its inputs. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Basic Cost Concepts Opportunity cost: The cost of a good measured by the alternative uses that are foregone by producing the good. Accounting cost: The actual cost paid for inputs. Economic cost: The amount required to keep an input in its present use or the amount that input would be worth in its next best alternative use. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Basic Cost Concepts Labor costs: Wage payments are an explicit costs Wage rate is the amount a worker would earn in her next best alternative employment. Capital costs: An accountant uses the historical cost of capital and some depreciation rule. An economist treats the cost of capital as a sunk cost, which is an expenditure that once made can’t be recovered. The implicit cost of capital is equal to its rental rate. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Basic Cost Concepts Entrepreneurial costs: Owners of the firm are entitled to the difference between revenue and costs: accounting profit Entrepreneurial cost is the salary an owner of the firm could earn at his or her next best alternative employment. Economic profit: Accounting profit minus the entrepreneurial cost. Revenue minus total costs, which include both explicit and implicit costs. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Economic Profits and Cost Minimization Assumptions: Two inputs: labor (L) and capital (K). Inputs are hired in a perfectly competitive market. Total costs: TC = wL + vK Economic profit = π = Total Revenues – Total Costs π = Pq – wL – vK π = Pf(K,L) – wL – vK Note that a firm’s economic profit depend only on the amount of labor and capital it hires. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Minimizing Input Choice How does a firm produce a given output at the lowest possible cost? We’ll look a this three ways: RTS = w/v Graphically this is the point where the isoquant is tangent to the total cost line. MPL/w = MPK/v Parallel between the consumer’s utility maximizing choice and firm’s cost minimizing choice. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Minimizing Input Choice: RTS = w/v Assume the firm makes q units of output with 10 K and 10 L. The RTS = 2, w = $1 and v = $1 What’s wrong? Total costs = $20 = 10 x $1 + 10 x $1 But RTS = 2 ≠ w/v = 1 Since the RTS = 2, the firm could replace two units of capital with one worker This would allow the firm to reduce costs by $1. Therefore, as long as RTS ≠ w/v the firm can substitute one input for the other and reduce its costs. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Minimizing Input Choice: Graphical Approach Capital per week At this point the RTS > w/v. So the firm should use more labor, and less capital. It continues to do this until RTS = w/v. K* q TC1 TC2 TC3 L* Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Minimizing Input Choice: MPL/w = MPK/v Last chapter we showed that: RTS = MPL/MPK We also know to minimize costs: RTS = w/v Therefore: MPL/MPK = w/v MPL/w = MPK/v To minimize costs the firm should hire inputs so that the output per dollar spent on the last unit of labor is equal to the output per dollar spent on the last unit of capital. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Minimizing Input Choice: MPL/w = MPK/v Suppose that at its current input mix, the MPL/w > MPK/v. Should the firm hire more labor or more capital? Since MPL/w > MPK/v, the firm could spend $1 more (less) on labor (capital), and increase total output. As the firm hires more labor (less capital) the MPL (MPK) falls (rises). Therefore, MPL/w falls, and MPK/v rises. . . . MPL/w > MPK/v. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

The Firm’s Expansion Path Expansion path. The set of cost-minimizing input combinations a firm will use to produce different levels of output. Capital per week q3 K1 q2 q1 L1 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Curves What is the relationship between output and total costs? Depends on the nature of production: constant, decreasing, increasing returns to scale. Returns to scale and the relationship between input and output. Now look at the relationship between output and costs. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Curves: Constant Returns to Scale Total Cost TC As output expands, costs expand proportionally. Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Curves: Decreasing Returns to Scale Total Cost TC Costs expand more rapidly than output. Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Curves: Increasing Returns to Scale Total Cost TC Costs expand less rapidly than output. Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cost Curves: Optimal Scale Total Cost TC Over lower levels of output there are increasing returns As output expands decreasing returns kicks in Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Average and Marginal Costs Average Cost is total cost divided by output. Marginal Cost is the additional cost of producing one more unit of output. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Average and Marginal Cost Curves: Constant Returns AC, MC As output expands, MC and AC remain the same. AC, MC Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Average and Marginal Cost Curves: Decreasing Returns AC, MC MC AC As output expands, both MC and AC increase. Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Average and Marginal Cost Curves: Increasing Returns AC, MC As output expands, both MC and AC decrease AC MC Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Average and Marginal Cost Curves: Optimal Scale AC, MC MC AC q* Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

The Short Run and the Long Run Short run – the period of time in which a firm must consider some inputs to be fixed. Long run – the period of time in which a firm may consider all of its inputs to be variable. Fixed Costs – costs associated with inputs that are fixed in the short run. Variable Costs – costs associated with inputs that can be varied in the short run. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Input Inflexibility and Cost Minimization Will a firm always be able to use the cost minimizing combination of inputs in the short run? No. Capital is fixed in the short run so the firm may have to use non-optimal amounts of labor to produce some given output. What about the long run? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Input Inflexibility and Cost Minimization Suppose the amount of capital is fixed at K1, and the firm produces q0 units. Capital per week To produce q0 the firm would use L0 and face costs STC0. STC0 To produce q1 the firm would use L1 and face costs STC1. STC1 K1 q1 q0 L0 L1 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Input Inflexibility and Cost Minimization To produce q2 the firm would use L2 and face costs STC2. Capital per week For which output level is the firm minimizing costs? STC0 q1: only for this output is the RTS equal to the ratio of input prices. STC1 STC2 K1 q2 q1 q0 L0 L1 L2 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Shifts in Cost Curves Three changes will affect the shape and position of a firm’s cost curves. Changes in input prices such as wages. An increase (decrease) in input prices will cause the cost curves to shift up (down). Will depend on the firm’s ability to substitute inputs. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Shifts in Cost Curves Changes in input prices. Technological innovation. Cost curves will shift down. Technological change may be “biased”. Economies of scope. Relates to multiproduct firms. Expansion of one product may improve the ability to produce another product. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Example Back at Hamburger Heaven TC = $5K + $5L q = 40 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Example 40 hamburgers per hour Total Cost = $40 Capital Labor per hour ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Example Total Cost Total Cost 80 60 40 20 20 40 60 80 Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Example AC and MC Average and marginal cost $1 20 40 60 80 Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Example Suppose we now fix the number of grills to 4 SAC falls MC rises SAC rises ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Example AC and MC Average and marginal cost SMC (4 grills) SAC (4 grills) $1 AC and MC 20 40 60 80 Quantity per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Summary To minimize the cost of producing a given level of output, the firm should choose a point on its isoquant so that the RTS = input price ratio. To minimize the cost of producing a given level of output, the firm should choose its inputs so MP/Input Price is the same for all inputs. The expansion path shows the minimum cost way of producing any level of output. From firm’s total cost curve can be derived from the expansion path. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Summary Average and marginal costs can be constructed from the total cost curve. The shape of these curves depend on the nature of the production process. In the short run at least one input is fixed and short run costs are not generally the lowest cost the firm could achieve. Short run costs increase rapidly due to diminishing marginal productivities. Cost curves will shift due to a change in input prices, technological change, and economies of scope. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.