10--Costs & Prod

10--Costs & Prod - Lecture 10 Lecture 10 Production...

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Unformatted text preview: Lecture 10 Lecture 10 Production and Costs A simple production function is: Q = f (K,L), where K is capital, L is labor Here we assume K is “fixed” at K* This creates “short run” in contrast to “long run” Long run: all factors are variable Short run: some factors (K) are fixed, locked in place With fixed K*, we vary L and observe changes in output, Q Some definitions Some definitions Total product: total output in a given time Average product: total product (Q), divided by the amount of an input (L) used to produce it: – It is a ratio, such as Q/L Marginal product: the change in output (Q) as the amount of an input (L) changes: – It is a derivative, such as dQ/dL Diminishing marginal product: the decline in marginal product that takes place as use of an input rises (a fact of nature) A simple business: A simple business: pizza production per hour in pizza shop (L) (Q) (dQ/dL = MPL) Laborers Pizzas Change in pizzas APL (Q/L) 0 0 ­ ­ 1 8 8 8 2 22 14 11 3 29 7 9.67 4 31 2 8.75 5 29 ­2 5.8 6 20 ­9 3.33 Note how labor productivity rises then falls in fixed production scale. How many pizzas do you produce? How many pizzas do you produce? (assume sale price is $3 each) (L) (Q) (dQ/dL = MPL) Laborers Pizzas Change in pizzas APL (Q/L) TR = PxQ 0 0 ­ ­ 1 8 8 8 $24 2 22 14 11 $66 3 29 7 9.67 $87 4 31 2 8.75 $93 5 29 ­2 5.8 $87 6 20 ­9 3.33 $60 Where TR (total revenue) equals price times quantity sold. New Components of Costs Components of Costs In the short run, some inputs (“capital” or K) are fixed—here, the size of the pizza shop is fixed. Total cost has two components: – Fixed or unavoidable (“sunk”) costs – Variable or avoidable (“incremental”) costs Accounting “costs” are only relevant when they can be avoided, i.e., when they are economic costs – Fixed costs cannot be avoided; thus, fixed costs are accounting notions only – Fixed costs do not affect production decisions in the short run Costs Costs Total costs = Fixed costs + Variable costs – C = F + V F is a constant, independent of output and unavoidable in the short run V depends on inputs, and thus outputs: – V = (L * w) + (I * p) – Where w is the wage rate paid per unit of L – Where I are ingredients and p their price Remember Remember “A sunk cost is an unrecoverable past expenditure. Such costs should seldom be taken into account when determining what to do in the future because, other than possible tax effects, they are irrelevant to what can be recovered.” Charles Koch, CEO Koch Industries, p.33, “The Science of Success” How many pizzas do you produce? How many pizzas do you produce? Suppose ingredients cost per pizza $1. (L) (Q) Laborers Pizzas TR = PxQ – Cost of pizza supplies 0 0 ­ 1 8 $24 ­ $8 = $16 2 22 $66 ­ $22 = $44 3 29 $87 ­ $29 = $58 4 31 $93 ­ $31 = $62 5 29 $87 ­ $29 = $58 6 20 $60 ­ $20 = $40 Pizza ingredients (tomato, etc.) are what kind of costs? What about labor? How many pizzas do you produce? How many pizzas do you produce? Suppose Labor is $6 per hour. (L) (Q) Laborers Pizzas TR = PxQ – Cost – Labor = Net 0 0 ­ 1 8 $24 ­ $8 = $16 ­ $6 = $10 2 22 $66 ­ $22 = $44 ­ $12 = $32 3 29 $87 ­ $29 = $58 ­ $18 = $40 4 31 $93 ­ $31 = $62 ­ $24 = $38 5 29 $87 ­ $29 = $58 ­ $30 = $28 6 20 $60 ­ $20 = $40 ­ $36 = $4 But what about fixed costs (building, taxes, ovens)? Does that affect our decision? How many pizzas do you produce? How many pizzas do you produce? Suppose Labor is $20 per hour. (L) (Q) Laborers Pizzas TR = PxQ – Cost – Labor = Net 0 0 ­ 1 8 $24 ­ $8 = $16 ­ $20 = $­4 2 22 $66 ­ $22 = $44 ­ $40 = $4 3 29 $87 ­ $29 = $58 ­ $60 = $­2 4 31 $93 ­ $31 = $62 ­ $80 = $­18 5 29 $87 ­ $29 = $58 ­ $100 = $­42 6 20 $60 ­ $20 = $40 ­ $120 = $­80 But what about fixed costs (building, etc.)? Some Notes on Costs Some Notes on Costs The law of supply: The higher the selling price of a good, the greater the amount that will be provided by producers. Marginal costs determine the rate of output. Total cost per unit production determines only if the firm can produce at a profit. Marginal costs are usually higher when there are higher speeds of production and for quick changes in output (increasing costs of higher rates of production). This is technical reality, not economic theory. Visualize it this way in the short run Visualize it this way in the short run The supply curve is the Marginal Cost (MC) curve: the change in Total Cost P from a unit change in output (Q). Managers consider their changes in cost compared to their change in MR revenue (P). MC D Q Typical Multiple Measures of Cost Typical Multiple Measures of Cost Total Total Average Avg. Avg. Fixed Variable Total Marginal Fixed Var. Total Output Cost Cost Cost Cost Cost Cost Cost 0 60 0 60 ­ ­ ­ ­ 1 60 30 90 30 60 30 90 2 60 49 109 19 30 24.5 54.5 3 60 65 125 16 20 21.7 41.7 4 60 80 140 15 15 20 35 5 60 100 160 20 12 20 32 6 60 124 184 24 10 20.7 30.7 7 60 150 210 26 8.6 21.4 30 8 60 180 240 30 7.5 22.5 30 9 60 215 275 35 6.7 23.9 30.6 10 60 255 315 40 6 25.5 31.5 Measures of Production Costs (Short Run) Production and Costs: Production and Costs: The Long Run The long run Formally – A period of time (or set of contracts) sufficient to permit all inputs to be variable; all costs are avoidable – There is no distinction between “types” of costs (fixed or variable); all costs are variable in the long run – C = (K*r) + (L*w) + (I*p) – Objective: choose a set of inputs (K,L,I) that minimizes total costs at each rate of output – Although the algebra is tedious, the basic geometry is quite simple Cost in the Long Run Cost in the Long Run MC goes through minimum of ATC. Now ALL costs are variable. Is Q where we should produce? MC ATC Average and Marginal Costs Output Economics of scale Economics of scale The behavior of average costs as output varies For Q < Q m, AC is falling: “Increasing returns to scale” For Q > Q m, AC is rising: “Decreasing returns to scale” At Q = Q m, AC is constant: “Constant returns to scale” Average and Marginal Costs MC ATC 0 Q m Output (Q) Scale Economy Example Scale Economy Example Study of hospitals in the U.S. found that per unit cost of providing hospital services was minimized at 250 beds. Hospitals with only 50 beds have costs 20­30% higher per bed service. That is, AC drops and drops until Q is about 250 beds. Then is stable but begins to rise again eventually. Note the relationship here… Note the relationship here… If our output sells at price P* we will keep producing units (Q) If so long as we cover the cost of producing added units. Difference between MC and ATC is profit for those units. Difference Price/ Costs MC ATC P* AC* Profits per unit 0 Q* Output (Q) An Example: Making Olive Oil (short run) An Example: Making Olive Oil (short run) Marcello owns (or rents) the olive trees; he hires migrant workers at $4 per hour to pick olives and press oil. Labor Input (hours) Olive Oil Output (gallons) 100 200 300 400 500 600 700 800 900 1000 1100 30 100 200 350 800 1200 1400 1575 1700 1800 1850 Production and Cost of Olive Oil Production and Cost of Olive Oil Calculate total labor cost at various levels of output. Calculate average cost per gallon. Calculate marginal cost per gallon — since data are not gallon by gallon, calculate it based on the jumps from one level to the next. Then, draw the cost curves: total on one diagram, average and marginal on another. Cost Measures [Output in gallons. Cost Measures Input in hours of labor.] Input Output 100 200 300 400 500 600 700 800 900 1000 1100 30 100 200 350 800 1200 1400 1575 1700 1800 1850 $ TC 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 __ AC $13.33 8.00 6.00 4.57 2.50 2.00 2.00 2.03 2.12 2.22 2.37 MC $13.33 5.71 4.00 2.67 0.89 1.00 2.00 2.28 3.20 4.00 8.00 Draw the cost curves (approximately) Cost curves Cost curves Total, Average and Marginal Costs. Is point of lowest average cost where we should produce? $ Total Cost $/gallon MC $2 Lowest Average Cost AC Lowest Average Cost Output Output Questions Questions Suppose the market price of olive oil is $2.30 per gallon. How much oil does Marcello produce to maximize profits? Does he make a profit? Answer Remember the Golden Rule Answer MR = MC Produce where MR ($2.30) equals MC. The golden rule! MR = MC That would be 1575 gallons, where MC is $2.28 per gallon. If he increased production to 1700 gallons by hiring another 100 hours of labor, his MC would rise to $3.20 for the additional gallons. 1575 gallons at $2.30 equals $3622 revenue minus cost of $3200 for a profit of $422. But—is that really his profit? Fixed Cost Question Fixed Cost Question In the 1920s there were some British ships that burned coal for power. Not as efficient as new oil burning ships. Their owners made enough money carrying cargo to pay variable costs—labor, fuel, etc.—but not enough revenue to cover all repayment costs (interest and principal) on the ships. Was it foolish to continue to use the ships? What should the banks do about the loans? What kind of cost? What kind of cost? Ford used palladium as an input in catalytic converters for pollution control. In 1992, price was $80 an ounce. In 2000, price was $750 per ounce. Management decided to stockpile the metal. What do you think the elasticity of supply would be for palladium? What would be the impact of Ford’s high demand? Change Is Costly Change Is Costly Price went past $1,000 an ounce by 2001. Ford had over 2 million ounces. Engineers determined how to cut use of palladium in half and devised substitutes for it. Demand for palladium fell—price went to $300 an ounce. Ford lost over $1 billion on its stockpile. ...
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