Next Week Complete Homework 8 on Homework advantage by Sunday, October 1 at 11:55 pm. Read Chapter 9, Perfect Competition and the Supply Curve

Chapter 8 Behind the Supply Curve: Inputs and Costs September 28, 2006

Motivation: Why study the relationship between inputs and costs? (In answering this question, assume the perspective of a producer or firm.) Our ultimate goal is to understand how a profit- maximizing firm chooses the quantity of output it will supply at different prices (supply curve), and how it decides whether to enter or exit the market (industry) for that good. This understanding depends understanding the cost relationships between input and output.

Motivation, cont. Profit maximization and the output decision The rule for determining whether a firm is profitable depends on a comparison of the market price (P) of the good to the firm’s break even price. A firm’s break even price is its minimum average total cost (ATC): –If P > ATC, the firm earns a profit –If P = ATC, the firm breaks even –If P < ATC, the firms incurs a loss The proof of the pudding (the rule) is reserved for Chapter 9. From Chapter 8 we can get answers to the questions on the next slide.

Today’s focus How can a firm identify its minimum average total cost ATC? Why does it matter if the firm makes its production decisions in the long run rather than the short run, and vice versa? –Short run: a time period in which at least one input is fixed –Long run: a time period in which all inputs are variable (their quantity can be adjusted).

Preview of conclusions: identifying minimum ATC 1.Most firms have U-shaped average total cost (ATC) curves because average total cost consists of two parts: –Average fixed cost which falls as output rises (the spreading effect) –Average variable cost which rises with output (diminishing returns effect). 2.When ATC is U-shaped, the bottom of the U is the level of output at which average total cost in minimized. 3.Moreover, the marginal cost (MC) curve crosses the ATC curve from below at the point of minimum- cost output.

Primary conclusions: Costs in the long run 1.A firm’s costs may be different in the long run than in the short run because in the long run, a firm may choose its level of fixed input and hence its fixed cost. In contrast, fixed cost is taken as a given in the short run. 2.A firm chooses its fixed cost in the long-run on the basis of the level of output it expects to produce.

identifying minimum ATC Step 1: Know the production function Production function: the relationship between the quantity of inputs a firm uses and the quantity of output it produces. Step 2: Use the price of inputs to translate the relationship between input and output into the relationship between output and costs.

identifying minimum ATC Step 3: Identify FC, VC fixed cost (FC): a cost that does not depend on the quantity of output produced. It is the cost of the fixed input. variable cost (VC): a cost that depends on the quantity of output produced. It is the cost of the variable input. Step 4: Calculate total costs (TC) total cost: the sum of the fixed cost and the variable cost of producing a specific quantity of output: TC = FC + VC

Discrete Example of fixed and variable costs of production for a toy manufacturing company QVC*FCTC 00$30 1$ * Labor needed to produce Q x price of labor

Notes about toy manufacturing The variable input is labor. As more toys are produced, variable costs rise as more labor is hired. The marginal product of labor falls with each additional unit of labor. Because labor is paid an hourly wage, we measure FC per hour. Note that total cost always rises as more toys are produced.

identifying minimum ATC Step 5: Calculate AFC, AVC, ATC average total cost: total cost divided by quantity of output produced. ATC = TC/Q average fixed cost: the fixed cost per unit of output. AFC = FC/Q average variable cost: the variable cost per unit of output. AVC = VC/Q

Example of fixed and variable costs of production for a toy manufacturing company Q (1000s) VCFC (per hour) TC (VC+FC) AVC (VC/Q) AFC (FC/Q) ATC (TC/Q) 00$ $

Questions about the costs of toy manufacturing At what rate of production (Q) is ATC at a minimum? Why is it important for a company to know what its average total cost per item is? Why does average fixed cost always fall?

Answers At what rate of production (Q) is ATC at a minimum? –Between 3000 and 4000 toys Why is it important for a company to know what its ATC per item is? –Because firms calculate their profit per unit from their ATC in relation to market ATC. Why does average fixed cost always fall? –Mathematically, because you are dividing a fixed dollar amount by an increasing quantity. In terms of economic intuition, you are spreading the fixed cost over more more toys produced.

identifying minimum ATC Corresponding Graph 1.Most firms have U-shaped average total cost (ATC) curves because average total cost consists of two parts: –Average fixed cost (AFC) which falls as output rises (the spreading effect) –Average variable cost (AVC) which rises with output (diminishing returns effect). 2.When ATC is U-shaped, the bottom of the U is the level of output at which average total cost in minimized.

identifying minimum ATC Adding MC to the picture Definition of Marginal cost (MC): the change in total cost generated by a change in the quantity of output-- i.e., the slope of the total cost curve as output increases by one unit: the “rise” (∆TC) divided by the “run” (∆Q). MC = ∆TC/∆Q

identifying minimum ATC Adding MC to the picture Q (1000s) TC (VC + FC) MC (∆TC/∆Q) 0$30 $

identifying minimum ATC Adding MC to the picture QATCMC 0-- $10 1$ Over what range of toy production does the spreading effect dominate? 2.Over what range of production does the diminishing returns effect dominate? 3.Now what is the minimum-cost output level? 4.What is the relationship between ATC and MC at this level?

identifying minimum ATC Adding MC to the picture QATCMC 0-- $10 1$ Over what range of toy production does the spreading effect dominate? 1000 to Over what range of production does the diminishing returns effect dominate? 4000 to Now what is the minimum-cost output level? 3000 to What is the relationship between ATC and MC at this level? ATC = MC

identifying minimum ATC QATCMC 0-- $10 1$

identifying minimum ATC 3.Moreover, the marginal cost (MC) curve crosses the ATC curve from below at the point of minimum-cost output. –If MC is less than ATC, ACT is falling. Increasing Q will reduce ATC. –If MC is greater than ATC, ATC is rising. Decreasing Q will lower ATC.

FC versus VC Example Problem Consider the following costs that an airline company faces: –Administrative salaries –Cost of jets –Food –jet fuel –Landing fees –Marketing costs –Salaries of pilots and crew –Web site maintenance Which of these costs are variable costs? Which costs stay the same even if they fly the plane (fixed costs)?

FC versus VC: Example Problem Consider the following costs that an airline company faces: –Administrative salaries –Cost of jets –Food –jet fuel –Landing fees –Marketing costs –Salaries of pilots and crew –Web site maintenance Which of these costs are variable costs? Which costs stay the same even if they fly the plane (fixed costs)?

ATC versus MC Consider the following costs that an airline company faces: –Administrative salaries –Cost of jets –Food –jet fuel –Landing fees –Marketing costs –Salaries of pilots and crew –Web site maintenance Now consider the airline’s decision to fly the next flight. Which costs are relevant to that decision? The sum of these costs is the MC of the next flight. ATC or MC? How would you calculate the average total costs (the cost per passenger mile)?

ATC versus MC Consider the following costs that an airline company faces: –Administrative salaries –Cost of jets –Food –jet fuel –Landing fees –Marketing costs –Salaries of pilots and crew –Web site maintenance Now consider the airline’s decision to fly the next flight. Which costs are relevant to that decision? ATC or MC –MC are the relevant costs because they are the only costs incurred by authorizing the flight. How would you calculate the average total costs (the cost per passenger mile)? –Divide the total costs of flying a fixed number of miles by that fixed number.

Why does it matter if the firm makes its production decisions in the long run rather than the short run? A firm’s costs may be different in the long run than in the short run because in the long run, a firm may choose its level of fixed input and hence its fixed cost. In contrast, fixed cost is taken as a given in the short run.

costs in the long run A firm chooses its fixed cost in the long-run on the basis of the level of output it expects to produce. There is a tradeoff between higher fixed cost and lower variable cost for any given level of output, and vice versa.

costs in the long run For each output level, there is some choice of fixed cost that minimizes a firm’s average total cost for that output level. The locus of these points is the firm’s long-run average cost curve (LRATC).

costs in the long run The firm will always try to produce at some point on the LRATC. If demand conditions move it off the LRATC curve, it moves along its short-run average total cost curve until it can adjust its fixed input to the new output level. The adjustment will return it to its LRATC curve.

Costs in the long run 5.The shape of a firm’s LRATC curve is determined by the presence of scale effects in production. There are: –economies of scale when LRATC decreases as output increases –Constant returns to scale when if LRATC do not change as output increases –diseconomies of scale when LRATC increases as output increases. The presence of scale effects depends on technology.