Production and Costs Bibliography: Mankiw and Taylor, Ch. 6.
The Importance of Cost in Managerial Decisions Containing costs is a key issue in managerial decisionmaking Firms seek to reduce the number of people on the payroll while still performing the same services Firms seek to reduce the cost of capital through a variety of financial operations Firms consolidate operations in order to share resources mergers usually involve staff cuts Firms outsource components of their businesses and seek to hire temporary staff instead of committing to permanent, full time staff
Costs of Production/Supply Relevant costs: all costs that are affected by a management decision Example: restaurant Inputs (e.g. ingredients used to cook food in a restaurant) Equipment (e.g. kitchen appliances, tables, cutlery) Workers (e.g. cooks, waiters) Energy (e.g. electricity, gas...) Rent (e.g. building) Other services (e.g. accounting, cleaning...)
Sunk Costs and Incremental Costs Sunk cost: a cost that was incurred in the past and is not affected by current managerial decisions e.g. the cost of past investment in infrastructure resources (such as special purpose factory buildings, rail tracks or fixed line telephony Sunk costs are fixed (i.e. independent from the amount of output produced) and have to be incurred even if the firm shuts down (i.e. stops producing) the firm can only free itself from sunk costs if it closes down and sells the infrastructure Incremental cost: a cost that is affected by current managerial decisions it is measured by the change in cost resulting from a change in a particular activity (e.g., construction of a new building, entry into the market with a new product, development of new software )
Fixed Costs and Variable Costs Fixed cost is a cost that does not vary with the level of business activity (i.e. amount of output produced) a sunk cost is a type of fixed cost Variable cost is a cost that does vary with the level of business activity (i.e. amount of output) Fixed and variable costs depend on a time reference a cost that is fixed in the short run may be variable in the long run
Time Periods: Fixed and Variable Costs in the Short and Long Run Fixed and variable costs depend on a time reference a cost that is fixed in the short run may be variable in the long run: The production capacity, or Scale of operations, of a factory is the maximum amount of output a factory is capable of producing over a fixed period of time Scale of operations usually cannot be changed in the short run since it takes time for capacity investments to become operational Hence, capacity/scale investment costs are fixed in the short run, since they do not change with the amount of output produced In the long run, all costs are variable, since the firm can change its scale of operations and sell infrastructure
Opportunity Costs and Out-of- Pocket Costs Opportunity cost is the amount foregone when choosing one activity over the next best alternative what you give up to get a something Out-of-pocket cost is the monetary cost associated with the choice of one activity over another For example, the out-of-pocket cost of leaving one s job to attend school on a full-time basis is the tuition, books, etc.; the opportunity cost is the loss of income (wages) from the job
Opportunity Costs of Investment This is the income (e.g. interest) not earned on financial capital: When you invest money on a firm or financial asset you are foregoing the returns for alternative uses of your savings Example: you invest 1,000 in shares of business and obtain a yearly return of 10% ( 100); the best alternative use for the 1,000 would be to buy Treasury bills that would have paid you a 5% return ( 50) this is your opportunity cost for the use of the 1,000 Your accounting profit corresponds to the financial return of 100; Your economic profit corresponds to the financial return minus the opportunity cost: 100 50 = 50
Implicit Costs vs. Explicit Costs A firm s explicit costs include all production costs that require an outlay of money by the firm these are the costs that matter for accountants Implicit costs do not require an outlay of money by the firm; what matters is the earnings foregone by investing in the firm (opportunity costs) these costs matter for economists For accountants, the firm s production costs include only explicit costs For economists, the firm s total production costs include the explicit costs plus all the opportunity costs from choosing to invest (i.e. be) in the market
Costs: Economists vs. Accountants
Exercises To an economist, total costs include: A) explicit, but not implicit costs. B) implicit, but not explicit costs. C) explicit and implicit costs. D) neither explicit nor implicit costs. Costs of production that change with the rate of output are: A) sunk costs. B) opportunity costs. C) fixed costs. D) variable costs.
Exercises Economic profit equals accounting profit minus A) explicit costs. B) implicit costs. C) fixed costs. D) variable costs. Which of the following is most likely a fixed cost? A) expenditures for raw materials. B) wages for unskilled labor. C) fuel cost. D) property taxes. Changes in short-run total costs result from changes in only: A) variable costs. B) fixed costs. C) zero. D) total fixed costs.
Production, Resources, and the Law of Diminishing Returns The law of diminishing returns states that in all productive processes, adding more of one factor of production while holding all others constant, will at some point yield lower returns per-unit The law of diminishing returns does not imply that adding more of a factor will decrease total production This occurs for two main reasons: Factors of production are not perfectly substitutable (or interchangeable) Resources are finite, meaning that the per-unit cost of adding ever-increasing amounts of a factor (e.g. labor) would will become higher and higher
The Production Function The Production Function determines the relationship between the quantity produced by a firm (output) and the amount of inputs (factors) used in production The Marginal Product of a production factor is the additional level of output achieved by adding one more unit of that input to the production process Diminishing Marginal Product is the property whereby the marginal product of an input declines as the quantity of the input increases (an outcome of the law of diminishing returns) Example: As more and more workers are hired at a firm, each additional worker contributes less and less to production because the firm has a limited amount of equipment
Production Function and Total Cost: A Pizza Factory/Restaurant
Quantity of Output (pizzas per hour) 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 Pizza Factory/Restaurant Production Function Production function Output increases get smoother as the quantity of input rises because of diminishing marginal product 0 1 2 3 4 5 Number of Workers Hired
The Cost Function The Cost Function determines the relationship between the quantity produced by a firm (output) and the total cost of production The relationship between the quantity a firm can produce and its costs determines pricing decisions
Fixed and Variable Costs Total Cost (TC): the cost of all inputs involved in the production of output Q; it is expected to increase as Q increases: C = C (Q) = TVC + TFC Total fixed cost (TFC) includes all costs that do not change with output Total variable cost (TVC): the cost associated with variable inputs, found by multiplying the number of units of output by the unit price of inputs: TVC = TVC (Q)
Average and Marginal Costs Total average cost (AC) is the total cost per unit produced: AC = TC / Q; AFC = TFC / Q; AVC = TVC / Q Marginal cost (MC) is the rate of change in total variable cost: MC = dc(q) / dq = dtvc(q) / dq The law of diminishing returns implies that MC will eventually increase, since the productivity of inputs decreases with their use
The Various Measures of Cost: A Coffee Shop
Coffee Shop s Total Cost Curve Total Cost $15.00 14.00 13.00 12.00 11.00 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 Total Cost curve 0 1 2 3 4 5 6 7 8 9 10 The total-cost curve gets steeper as the quantity of output increases because of diminishing marginal product Quantity of Output (cups of coffee per hour)
Exercises The Average fixed cost: A) does not change as total output increases or decreases. B) varies directly with total output. C) falls continuously as total output expands. D) rises as the output is expanded. The Average fixed cost is A) AC minus AVC. C) AVC minus MC. B) TC divided by Q. D) TC minus TVC. When a firm increased its output by one unit, its AFC decreased. This is an indication that: A) the law of diminishing returns has taken effect. B) MC < AFC. C) the firm is spreading out its total fixed cost. D) AVC < AFC.
Relationship Between Average Costs and Marginal Costs: MC < AC If MC < AC, producing an additional unit of output costs less than the unit cost of the units already produced hence producing that additional unit will lower the total average cost e.g. if the firm is producing 10 units at an average cost of 2 per unit ( 20 total cost) and the marginal cost of producing one more unit is equal to 1, then the new average cost will be: AC = ( 20 + 1) / 11 = 1,91 which is lower than 2
Relationship Between Average Costs and Marginal Costs: MC > AC If MC > AC, producing an additional unit of output costs more than the unit cost of the units already produced hence producing that additional unit will increase the total average cost e.g. if the firm is producing 10 units at an average cost of 2 per unit ( 20 total cost) and the marginal cost of producing one more unit is equal to 3, then the new average cost will be: AC = ( 20 + 3) / 11 = 2,09 which is higher than 2
Relationship between Average Costs and Marginal Costs When AC = MC, producing an additional unit does not change the total average cost If AC decreases when MC < AC and increases when MC > AC, then the minimum average cost is reached when MC = AC MC ATC
The Various Measures of Cost: A Coffee Shop (Again)
Costs $3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 Average and Marginal Cost Curves for the Coffee Shop MC 0 1 2 3 4 5 6 7 8 9 10 ATC AVC AFC Quantity of Output (cups of coffee per hour) This figure shows the average total cost (ATC), average fixed cost (AFC), average variable cost (AVC), and marginal cost (MC). The cost curves show three features that are common to many firms: (1) Marginal cost rises with the quantity of output; (2) The average total cost curve is U-shaped (3) The marginal-cost curve crosses the average-totalcost curve at its minimum point.
Typical Shapes of Cost Curves Marginal cost eventually rises with the quantity of output. The average total cost curve is U-shaped. The marginal cost curve crosses the average total cost curve at its lowest point.
Marginal and Variable Cost Curves for a Typical Firm Costs $3.00 2.50 2.00 1.50 1.00 0.50 MC ATC 0 2 4 6 8 10 12 14 Quantity of Output Many firms experience increasing returns (i.e. decreasing average costs, marginal costs lower than average costs) before diminishing returns set in (i.e. increasing average costs and marginal costs greater than average costs)
Some Typical Total Cost Function Specifications The previous analysis assumes a linear specification for the total cost function (relating total cost and output): TC = a + b.q (were MC = AVC = b) Alternative specifications of the total cost function include: Quadratic relationship: as output increases, total cost increases at an increasing rate: TC = a + b.q + c.q 2 Cubic relationship: as output increases, total cost first increases at a decreasing rate, then increases at an increasing rate: TC = a + b.q + c.q 2 + d.q 3
Short and Long Run Costs Assumptions: the firm employs two inputs, labor and capital the firm produces a single product the firm operates in a short-run production period where labor is variable, capital is fixed the firm employs a fixed level of technology and the law of diminishing returns applies the firm operates at every level of output in the most efficient way (i.e. minimizes costs) the firm operates in perfectly competitive input markets and must pay for its inputs at a given market rate (it is a price taker )
Short Run Cost Functions Total fixed cost (TFC) is the total cost of using the fixed input, capital (K) Total variable cost (TVC) is the total cost of using the variable input, labor (L) Total cost (TC) is the total cost of using all the firm s inputs: TC = TFC + TVC Average fixed cost (AFC) is the average per-unit cost of using the fixed input K: AFC = TFC/Q
Short Run Cost Functions Average variable cost (AVC) is the average per-unit cost of using the variable input L: AVC = TVC/Q Average total cost (AC) is the average per-unit cost of all the firm s inputs: AC = AFC + AVC = TC/Q Marginal cost (MC) is the change in a firm s total cost (or total variable cost) resulting from a unit change in output: MC = dtc / dq = dtvc / dq
Effects of Changes in Short Run Costs: Fixed Costs A reduction in the firm s fixed cost would cause the average cost line to shift downward Consider that the fixed cost is 200, while the variable costs are 2 per unit produced; then: TC = 200 + 2.Q Suppose the fixed cost decreases to 140; the new cost curve will have the same slope but a lower intercept with the Y-axis: TC = 140 + 2.Q The average total cost will be lower by: (200-140)/Q = 60/Q
Effects of Changes in Costs: Variable Costs A reduction in the firm s variable cost would cause all three cost lines (AC, AVC, MC) to shift downward Consider the same cost curve: TC = 200 + 2.Q; then: AVC = 2.Q/Q = 2 and MC = dtc / dq = 2 Suppose the variable cost coefficient decreases to 1,2 per unit produced; then, the new cost curve will have the same intercept with the Y-axis but a smaller slope: TC = 200 + 1,2.Q AC, AVC and MC all decrease by (2-1,2) = 0,8
Exercises The relationship between MC and AC can best be described as: A) when AC increases, MC starts to increase. B) when MC increases, AC starts to increase. D) when MC exceeds AC, AC increases. When a firm increased its output by one unit, its AC rose from $45 to $50. This implies that its MC is: A) $5. B) between $45 and $50. B) C) greater than $50. D) Cannot be determined from the data. When a firm's MC curve shifts to the right, it implies that A) new firms are entering the market. B) labor productivity is decreasing. C) labor productivity is increasing. D) the firm's total fixed costs are decreasing.
Exercises If a firm's rent increases, how will it affect the firm s cost structure? A) AVC will increase. C) TFC will increase. B) MC will increase. D) All of the above will increase. When a firm increased its output by one unit, its AC decreased, thus: A) MC < AC. B) MC = AC. C) MC < AFC. D) the law of diminishing returns has not yet taken effect. Which of the following relationships implies that a given firm's short-run cost function is linear? A) MC = AC C) AC = AFC + AVC B) MC = AVC D) MC > AC
Long-run Costs In the long run, all inputs to a firm s production function may be changed: Because there are no fixed inputs, there are no fixed costs: LRTC = C(Q) Increases in long run output are increases (i.e. investments) in the capacity (scale) of production The firm s long run marginal cost is associated to returns to scale (i.e. the capital invested in production capacity) A firm experiences constant returns to scale when longrun average total cost stays the same as the quantity of output changes
Average Total Cost Average Total Cost in the Short and Long Runs SRAC in short run with small factory SRAC in short run with medium factory SRAC in short run with large factory LRAC 10,000 0 1,000 Quantity of Cars per Day The LRAC is a curve that encircles (envelopes) the SRACs for each scale at the points where each SRAC achieves efficiency.
Long Run Average Cost Function In long run, the firm can choose any level of capacity (or scale of production) Once it commits to a level of capacity, at least one of the inputs (usually capital) must be fixed Efficiency then becomes a short run problem in which the firm chooses the optimal level of those inputs that may change in short run (i.e. labor) For each scale (capacity) of production there will be a short run average cost curve (SRAC) The long run average cost curve (LRAC) is an envelope of SRAC curves, and outlines the lowest per-unit costs the firm will incur over a range of output.
Increasing Returns to Scale (Capital) When a firm experiences increasing returns to scale, a proportional increase in all inputs increases output by a greater proportion As the scale of operations increases by some percentage, long run total cost of increases by some lesser percentage Hence, long run average total cost falls as the scale (capacity) of production increases Under these circumstances, a firm is said to experience increasing returns to scale (i.e. economies of scale) In the short run, when the scale of production is fixed, any reductions in short run average costs resulting from increases in output result from better use of available capacity of production, and not from scale economies
Decreasing Returns to Scale (Capital) Economies of scale occur where a firm s long run average cost (LRAC) declines as output/scale increases Diseconomies of scale apply to the opposite situation: a proportional increase in all inputs increases output by a smaller proportion as the scale of operations increases by some percentage, long run total cost of production increases by a greater percentage Hence, long run average total cost (LRAC) increases as the scale (capacity) of production increases
Economies of Scale Average Total Cost ATC in short run with small factory ATC in short run with medium factory ATC in short run with large factory ATC in long run 10,000 Economies of scale Constant returns to scale Diseconomies of scale 0 1,000 Quantity of Cars per Day
U-shaped Long Run Average Cost In general, the LRAC curve is u-shaped, meaning that there is an initial section with increasing returns to scale, followed by a section with decreasing returns. The minimum efficient scale (MES) is the minimum capacity for which the the LRAC is minimized (in this case, Q=40)
Reasons for the Existence of Economies of Scale Specialization of labor and capital Prices of inputs may fall with volume discounts in firm s purchasing Use of capital equipment with better price-performance ratios Larger firms may be able to raise funds in capital markets at a lower cost Intellectual property costs (e.g. patents) may be spread over a larger output Larger firms may be able to spread out promotional costs
Reasons for the Existence of Diseconomies of Scale Scale of production is not optimal for the total market demand (too small) Transportation costs tend to rise as production grows, due to handling expenses, insurance, security, and inventory costs Cost of capital increases as the firm borrows more in order to increase capacity
Economies of Scope Economies of scope occur when firm s unit cost is reduced by producing two or more products jointly rather than separately Scope Economies are similar to scale economies but apply to a range of products: The joint production, sale and/or distribution cost of two or more products is less than the cost of pursuing them separately Examples: ( Q, 0) + CT( 0, Q ) CT( Q Q ) CT > 1 2 1, Toiletries: soap, shampoos, conditioners, bath gel Distribution: supermarkets vs. specialized stores Marketing economies, R&D, warehouse costs, suppliers discounts 2
Learning/Experience Economies Learning economies: the more experience a firm accumulates in producing a particular product, the lower its costs per unit The unit or average cost of production decreases with the accumulated output Learning curve: line showing the relationship between labor cost and additional units of output: A downward slope indicates additional cost per unit declines as the level of output increases because workers improve with practice The production process also improves as engineers and other development personnel gain more experience
Learning Curve ( ) = αq β C Q C Q 100 67 56 47 40.............................................................................. 1 5 10 20 40 Q Where: C(Q) is the unit cost of accumulated production α is the cost of the first unit β>0 is the parameter that measures the intensity of the economies of experience
Exercises Which of the following statements best represents a difference between short run and long run cost? A) Less than one year is considered the short run; more, long run. B) There are no fixed costs in the long run. C) In the short run labor is variable and capital is fixed. D) All of the above are true. Economies of scale are indicated by: A) declining long-run AVC. C) declining long-run AC. B) declining long-run AFC. D) declining long-run TC. As a firm attempts to increase production, its long-run average costs eventually rise because of: A) the law of diminishing returns. C) fixed capital. B) diseconomies of scale. D) insufficient demand.
Exercises Economies of scale are created by greater efficiency of capital and by: A) longer chains of command in management. C) smaller plant sizes. B) better wages for labor. D) increased specialization of labor. Which level indicates the point of maximum economic efficiency? A) lowest point on AC curve. C) lowest point on MC curve B) lowest point on AVC curve D) None of the above Which of the following actions has the best potential for experiencing economies of scope? A) producing a product that has appeal to a wider segment of the market B) producing computers and software C) producing spaghetti and soft drinks D) producing cars and trucks
Exercises Which of the following is the best example of economies of scope? A) Coca-Cola expands its global operations to sub-saharan Africa. B) Alcohol for car fuel is produced from corn. C) Amazon.com decides to rent out its website to independent companies. D) A company gets bigger discounts for bulk purchases. The learning curve indicates that: A) economies of scale are taking effect. B) repetition of various production tasks cause unit costs to decrease. C) workers must learn new skills in order to improve. D) it takes time to learn a new skill.
Additional Exercises How would each of the following affect the firm's marginal, average, and average variable cost curves? a. An increase in wages. b. A decrease in the energy costs c. The government fines the firm a fixed amount due to excess pollution. d. The rent that the firm pays on the building that it leases decreases. Carefully explain if the following statements are true or false. a. If average cost is increasing, marginal cost must be increasing. b. If there are diminishing returns, the marginal cost curve must have a positive slope. For each of the following cost functions, compute MC, AC, and AVC a. TC = 200 + 10.Q b. TC = 180 + Q + 0,2.Q 2 Explain whether there are diminishing or increasing returns.