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chapter 11 Behind the Supply Curve: Inputs and Costs Chapter Objectives • Discuss the firm’s production function to define the relationship between the quantity of inputs and the quantity of output. • Explain why production is often subject to diminishing returns to inputs such as labor and capital. • Define the various types of costs the firm faces. • Illustrate the marginal and average total cost curves. • Explain why a firm’s cost may differ in the short run versus the long run. • Explain the concept of increasing returns to scale. Chapter Outline Opening Example: The example describes why European farmers are more productive than U.S. farmers in producing wheat: European government policies provide incentives for using more inputs, and with more inputs comes increased productivity. I. The Production Function A. Definition: A production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces. B. Inputs and outputs 1. Definition: A fixed input is an input whose quantity is fixed for a period and cannot be varied. Examples include, the number of acres of land a farmer cultivates, the number of copiers a school has. 2. Definition: A variable input is an input whose quantity the firm can vary at any time. Examples include the number of workers (amount of labor) a firm hires 3. Definition: The long run is the period in which all inputs can be varied. 4. Definition: The short run is the period in which at least one input is fixed. 5. Definition: The total product curve shows how the quantity of output depends on the quantity of the variable input, for a given amount of the fixed input. 6. The slope of the total product curve is not constant. The slope of the total product curve is equal to the marginal product of the variable input. 141 142 CHAPTER 11 BEHIND THE SUPPLY CURVE: INPUTS AND COSTS a. Definition: The marginal product of an input is the additional quan- tity of output that is produced by using one more unit of that input. Change in quantity of output b. Marginal product of labor = Changge in quantity of labor = Change in quantity of output generated by one additional unit of labor, or MPL = ∆Q/∆L 7. Definition: There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input. a. Diminishing returns only holds if the quantity of all other inputs is fixed. A change in the fixed input will shift the total product curve and the marginal product curve. C. From the production function to cost curves 1. Definition: A fixed cost is a cost that does not depend on the quantity of output produced. It is the cost of the fixed input. 2. Definition: A variable cost is a cost that depends on the quantity of out- put produced. It is the cost of the variable input. 3. Definition: The total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output. 4. Total cost = Fixed cost + Variable cost, or TC = FC + VC 5. Definition: The total cost curve shows how total cost depends on the quantity of output. a. The total cost curve becomes steeper as more output is produced due to diminishing returns. This is illustrated in text Figure 11-4, shown next. Total Cost Curve Cost Total cost, TC $2,000 I 1,800 H 1,600 G 1,400 F 1,200 E 1,000 D 800 C 600 B 400 A 200 0 19 36 51 64 75 84 91 96 Quantity of wheat (bushels) CHAPTER 11 BEHIND THE SUPPLY CURVE: INPUTS AND COSTS 143 II. Two Key Concepts: Marginal Cost and Average Cost A. Marginal cost Change in total cost 1. Marginal cost = Change in quantity of outtput = Change in total cost generated by one additional unit of labor or MC = ∆TC/∆Q 2. Marginal cost rises because there are diminishing returns to inputs when a variable input is increased as quantities of the other inputs are fixed. B. Average total cost 1. Definition: Average total cost, often referred to simply as average cost, is total cost divided by quantity of output produced. Total cost TC ATC = = Quantity of output Q 2. Average total cost is important because it tells the producer how much the average or typical unit of output costs to produce. Marginal cost tells the producer how much the last unit of output costs to produce. 3. Definition: A U-shaped average total cost curve falls at low levels of output, then rises at higher levels. 4. Definition: Average fixed cost is the fixed cost per unit of output. Fixed cost FC AFC = = Quantity of output Q 5. Definition: Average variable cost is the variable cost per unit of output. Variable cost VC AVC == Quantity of output Q 6. Average fixed cost falls as more output is produced. Another way to think of this is that as more output is produced, the fixed cost is spread over more units of output. This is illustrated in text Figure 11-8, shown next. Marginal Cost and Average Cost Curves Cost of case $250 MC 200 150 ATC AVC 100 M 50 AFC 0 1 2 3 4 5 6 78910 Quantity of salsa Minimum-cost output 144 CHAPTER 11 BEHIND THE SUPPLY CURVE: INPUTS AND COSTS 7. Average total cost is the sum of average fixed cost and average variable cost. It has a U shape because these components move in opposite direc- tions as output rises. a. When the U-shaped average total cost curve slopes downward, the “spreading effect” dominates: Fixed cost is spread over more units of output. b. When the U-shaped average total cost curve slopes upward, the “diminishing returns effect” dominates: An additional unit of output requires more variable inputs. C. Minimum average total cost 1. Definition: The minimum-cost output is the quantity of output at which average total cost is lowest—the bottom of the U-shaped average total cost curve. 2. Falling marginal cost pulls the average total cost downward, and rising marginal cost pulls the average total cost upward. This is illustrated in text Figure 11-9, shown next. The Relationship Between the Average Total Cost and the Marginal Cost Curves Costs of unit If marginal cost is MC above average total ATC cost, average total MCH cost is increasing. B2 A1 M B1 A2 MCL If marginal cost is below average total cost, average total cost is decreasing. Quantity 3. Three general principles that are always true: a. At minimum-cost output, average total cost is equal to marginal cost. b. At output less than the minimum-cost output, marginal cost is less than average total cost and average total cost is falling. c. At output greater than the minimum-cost output, marginal cost is greater than average total cost and average total cost is rising. D. Does the marginal cost curve always slope upward? 1. Marginal cost curves often slope down as a firm increases its production from zero up to some low level due to gains from specialization. They slope upward only at higher levels of production, when all gains from specialization have been realized. 2. If there are early gains from specialization, the marginal cost curve will have a “swoosh” shape, and the average variable cost curve will be U-shaped. CHAPTER 11 BEHIND THE SUPPLY CURVE: INPUTS AND COSTS 145 III. Short-Run versus Long-Run Costs A. Definition: The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to min- imize total cost for each level of output. This is illustrated in text Figure 11-12, shown next. Short-Run and Long-Run Average Total Cost Curves Cost of case Constant returns Increasing returns to scale to scale Decreasing returns to scale ATC3 ATC6 ATC9 LRATC B Y A X C 0 35476 8 9 Quantity of salsa (cases) 1. In the long run, when a producer has had time to choose the fixed cost appropriate for its desired level of output, that producer will be on the long-run average total cost curve. 2. If the output level is altered, the firm will no longer be on its long-run average total cost curve and will instead be moving along its current short-run average total cost curve. 3. Once the firm has adjusted its fixed cost, it will operate on a new short- run average total cost curve and on the long-run average total cost curve. B. Returns to scale 1. Definition: There are increasing returns to scale, also known as econo- mies of scale, when long-run average total cost declines as output increas- es. 2. Definition: There are decreasing returns to scale, also known as diseconomies of scale, when long-run average total cost increases as out- put increases. 3. Definition: There are constant returns to scale when long-run average total cost is constant as output increases. 4. Scale effects depend on the technology of production..
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